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Home > Algebra calculators
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Educational Level
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Secondary school, High school and College |
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Program Purpose
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Provide step by step solutions of your problems using online calculators (online solvers)
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Problem Source
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Your textbook, etc |
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1. Addition, subtraction, multiplication, division of two polynomials
1.1 Addition of two polynomials eg.`(x^3-4x^2+4x-8) + (x-2)`
1.2 Subtraction of two polynomials eg.`(x^3-4x^2+4x-8) - (x-2)`
1.3 Multiplication of two polynomials eg.`(x^3-4x^2+4x-8) xx (x-2)`
1.4 Long division of two polynomials eg.`(x^3-4x^2+4x-8) -: (x-2)`
1.5 Synthetic division of two polynomials eg.`(x^3-4x^2+4x-8) -: (x-2)`
1.6 Remainder theorem eg.`(x^3-4x^2+4x-8) -: (x-2)`
2. Factoring Polynomials
2.1 Factor out GCF (Taking common) eg.`x^2+2x`
2.2 Difference of squares eg.`x^2-9`
2.3 Sum and Difference of cubes eg.`x^3-27, x^3+27`
2.4 Whole square of a binomial eg.`4x^2+12xy+9y^2`
2.5 Reverse FOIL method (Splitting the middle term) eg.`x^2+10x+24`
2.6 Perfect square trinomial eg.`4x^2+y^2+1+4xy+4x+2y`
2.7 Factorization with the help of factor theorem eg.`x^3-3x^2-6x+8`
2.8 Cyclic Expressions eg.`a^2(b-c)+b^2(c-a)+c^2(a-b)`
2.9 Factorization of fourth power polynomial eg.`x^4+x^2+1`
3. Expand and simplify polynomial
3.1 FOIL Method eg.`(2x-1)(4x+5)`
3.2 Expand Difference of Squares eg.`(x-6)(x+6)`
3.3 Expand Perfect Squares of binomial eg.`(x-3)^2`
3.4 Expand Cubes eg.`(x-3)^3`
3.5 Expand Trinomials eg.`(a+b)(a^2-ab+b^2)`
3.6 Expand Perfect Squares of trinomial eg.`(2x+3y+4z)^2`
3.7 Binomial expansion eg.`(2x+3y)^5`
4. Complete square, Is perfect square, Find missing term
1. Completing the square for quadratic equation
eg. `9x^2+6x+1= 9( x+1/3 )^2`
2. Determining if the polynomial is a perfect square
eg. (1) `x^2-4xy+4y^2`, (2) `3x^2+5x+2`
3. Find the missing term in a perfect square trinomial
eg. (1) `9x^2` - __ + 16, (2) __ + `12x^2` + 9, (3) `49x^2` + 56 xy + __
5.1 HCF(GCD)-LCM of Polynomials
eg. Find GCD, LCM of `(2x^2-4x), (3x^4-12x^2), (2x^5-2x^4-4x^3)`
5.2 Find other polynomial when one polynomial its GCD and LCM are given
6. Rational Expression of Polynomials
1. Reduce rational expressions
eg. `(4x^2-25)/(8x^3-125)`
2. Adding, subtracting, multiplying, dividing of rational expressions polynomials
eg. `(x-3)/(x+1)-(x-6)/(x)`
7. Simplifying Algebraic Expressions
eg. (1) `(4x+1)/(3x-2)=3/2`, (2) `(2x-1)/(3x+1)+(4x-1)/(6x)=0`
8.1 Quadratic Equation
1.1 Solving quadratic equations by factoring,
eg. (1) `25x^2-30x+9=0`, (2) `x^2+10x-56=0`
1.2 Solving quadratic equations using the quadratic formula,
eg. (1) `25x^2-30x+9=0`, (2) `x^2+10x-56=0`
1.3 Discriminant
eg. (1) `25x^2-30x+9=0`, (2) `x^2+10x-56=0`
1.4 Discriminant & Nature of Roots
eg. (1) `25x^2-30x+9=0`, (2) `x^2+10x-56=0`
2. Find the quadratic equation whose roots are `alpha` and `beta`
eg. (1) `alpha=3, beta=-4`, (2) `alpha=1+3sqrt(2), beta=1-3sqrt(2)`
3. Roots for non-zero denominator
eg. (1) `(5x-18)/(x+2)=(2x-6)/(x-1)`, (2) `(x)/(x+1)+(x+1)/(x)=5/2`,
(3) `4((4x+1)/(4x-1))^(2)+(4x+1)/(4x-1)=3`, (4) `(4x+1)/(4x-1)+(4x-1)/(4x+1)=3`
4. Roots of non-quadratic equation
eg. (1) `6(x^2+1/x^2)-25(x-1/x)+12=0`, (2) `(x^2+1/x^2)-8(x+1/x)+14=0`
5. If `alpha` and `beta` are roots of equation `2x^2-3x-6=0`, then find `alpha^2+beta^2`
6. If `alpha` and `beta` are roots of equation `2x^2-3x-6=0`, then find equation whose roots are `alpha^2` and `beta^2`
7. Find value of `k` for which `2x^2+kx+2=0` has real roots
9. Solve linear equation in two variables by (eg. Solve `7y+2x-11=0` and `3x-y-5=0` using Substitution method)
1. Substitution method
2. Elimination method
3. Cross multiplication method
4. Addition-Subtraction method
5. Inverse matrix method
6. Cramer's Rule method
7. Graphical method
10. Solve linear equation of any number of variables (simultaneous equations) using
1. Inverse Matrix method
2. Cramer's Rule method
3. Gauss-Jordan Elimination method
4. Gauss Elimination Back Substitution method
5. Gauss Seidel method
6. Gauss Jacobi method
7. Elimination method
8. LU decomposition method / Crout's method
9. Cholesky decomposition method
10. SOR (Successive over-relaxation) method
11. Relaxation method
11.1 Find the value of h,k
1. Find the value of h,k for which the system of equations has a Unique solution
2. Find the value of h,k for which the system of equations has Infinite solution
3. Find the value of h,k for which the system of equations has No solution
4. Find the value of h,k for which the system of equations is consistent
5. Find the value of h,k for which the system of equations is inconsistent
11.2 Determine whether the system of linear equations
1. Determine whether the system of linear equations has a Unique solution
2. Determine whether the system of linear equations has Infinite solution
3. Determine whether the system of linear equations has No solution
4. Determine whether the system of linear equations is consistent
5. Determine whether the system of linear equations is inconsistent
12. Variation Equations
1. Find value of variation using given value
(1) x `prop` y and x=6 when y=3. Find y=? when x=18,
(2) x `prop` `y/z`. x=8 when y=4 and z=3. Find x=? when y=6 and z=4.
2. Prove results for given variation
(1) If x `prop` y then prove that `x^3+y^3 prop x^2y-xy^2`,
(2) If 3x-5y `prop` 5x+6y then prove that x `prop` y.
13. If `x+1/x=2` then find `x-1/x, x^2-1/x^2, x^3+1/x^3`
1. If `x-1/x=6` then find (1) `x^2+1/x^2` (2) `x+1/x` (3) `x^2-1/x^2`
2. If `x+y=5` and `xy=6` then find `x^2+y^2`
3. If `x^2+y^2+z^2=29` and `xy+yz+zx=-14` then find `x+y+z`
4. If `x+y+z=1,xy+yz+zx=-1` and `xyz=-1` then find `x^3+y^3+z^3`
14. Interval notation and set builder notation
eg. (1) `3 <= x <=7`, x is odd. (2) `|x^3-2| <= 25`, x in Z. (3) `x in[2,8)`
15. Set Theory
eg. `A={x<=5; x in N}, B={2<=x<=8; x in N}, C={x^3-3x^2-4x=0},` Find
1. Union
eg. `A uu (B uu C)=(A uu B) uu C`
2. Intersection
eg. `A nn (B uu C)=(A nn B) uu (A nn C)`
3. Complement
eg. `(A uu B)'=A' nn B'`
4. Power set (Proper Subset)
eg. `P(A)`
5. Difference
eg. (1)`A-B`, (2) `A-(B uu C)=(A-B) nn (A-C)`
6. Symmetric difference
eg. (1)`A Delta B`, (2) `B Delta C`, (3) `A Delta C`
7. Cross Product
eg. `A xx B`
8. Prove that any two expression is equal or not
eg. `A-(B uu C)=(A-B) nn (A-C)`
9. Cardinality of a set
eg. `n(A)`
10. is Belongs to a set
eg. `2inB` ?
11. is Subset of a set
eg. `AsubB` ?
12. is two set Equal or not
eg. `A=B` ?
16. Functions
1. Find Range of `f:A->B`
eg. 1. `f(x)=5x+2` where `A={1<=x<5}`, 2. `f(x)=sqrt(x)` where `A={1,4,16,36}`
2. Composite functions and Evaluating functions
eg. 1. `f(x)=2x+1`, `g(x)=x+5`. Find `fog(x)`, also evaluate at `x=2`
2. `fog(x)=(x+2)/(3x), f(x)=x-2`. Find g(2).
3. `gof(x)=1/x^2, f(x)=2+x^2`. Find g(x).
3. Find value
eg. 1. `f(x)=x(x+1)(2x+1)`. Find `f(x)-f(x-1)`, 2. `f(x)=x^2-2^x`. Find `f(2)-f(0)`
4. Verifying if two functions are inverses of each other
eg. 1. `f(x)=x+3,g(x)=x-3`, 2. `f(x)=4x-3,g(x)=(x+3)/4`, 3. `f(x)=x/(x-1),g(x)=(2x)/(2x-1)`
17. Functions
1. Domain of a function
2. Range of a function
3. Inverse of a function
4. Properties of a function
5. Parabola Vertex form
6. Parabola Focus
7. axis symmetry of a parabola
8. Parabola Directrix
9. Intercept of a function
10. Parity of a function
11. Asymptotes of a function
18. Descartes' rule of signs
eg. `x^5-x^4+3x^3+9x^2-x+5`
19. Ratio and Proportion
1. If `a:b:c=2:3:5` then find value of `(a^2+b^2+c^2)/(ab+bc+ca)`
2. If `a:b=2:3,b:c=4:5` then find `a:b:c`
3. If `a/b=c/d=e/f` then prove that `(2a+3c-4e)/(2b+3d-4f)=(5a-4c+3e)/(5b-4d+3f)`
4. If `x/(y+z)=y/(z+x)=z/(x+y)` then prove the value of each ratio is `1/2` or `-1`
5. Geometric Mean
6. Ratios(duplicate, triplicate) and proportional(mean, third, fourth)
6.1 Duplicate Ratio
6.2 Triplicate Ratio
6.3 Sub-Duplicate ratio
6.4 Sub-Triplicate Ratio
6.5 Compounded Ratio
6.6 Mean proportional
6.7 Third proportional
6.8 Fourth proportional
6.9 Compare ratios
20. Partial Fraction decomposition
eg. `(5x-4)/(x^2-x-2)`
21.1 Logarithmic equations eg. `log(20)+log(30)-1/2log(36)`
21.2 Log | Logarithm
21.3 ln - Natural log
21.4 Antilog | Antilogarithm
21.5 Anti Natural log
22. Simple Interest
23. Compound Interest
24. Percentage
25. Arithmetic Progression
26. Geometric Progression
27. Present value, Future value
27.1 Future value using Simple Interest
27.2 Future value using Compound Interest
27.3 Future value of Annuity
27.4 Future value of Annuity Due
27.5 Present value using Simple Interest
27.6 Present value using Compound Interest
27.7 Present value of Annuity
27.8 Present value of Annuity Due
27.9 Contineous Compounding
28.1 Future value factor
28.2 Present value factor
28.3 Discount factor
28.4 Future value factor table
28.5 Present value factor table
28.6 Discount factor table
29.1 Effective interest rate
29.2 Nominal interest rate
30. Amortization
31. Net Present Value (NPV)
32. Polynomial
1. Polynomial in ascending order
2. Polynomial in descending order
3. Degree of a polynomial
4. Leading term of a polynomial
5. Leading coefficient of a polynomial
6. Determine expression is a polynomial or not
7. Zeros of a polynomial
8. Rational Zeros Theorem to find all possible rational roots of a polynomial
33.1 Sine Calculator
33.2 Cosine Calculator
33.3 Tangent Calculator
33.4 Cosecant Calculator
33.5 Secant Calculator
33.6 Cotangent Calculator
34.1 Inverse Sine Calculator
34.2 Inverse Cosine Calculator
34.3 Inverse Tangent Calculator
34.4 Inverse Cosecant Calculator
34.5 Inverse Secant Calculator
34.6 Inverse Cotangent Calculator
35.1 Hyperbolic Sine Calculator
35.2 Hyperbolic Cosine Calculator
35.3 Hyperbolic Tangent Calculator
35.4 Hyperbolic Cosecant Calculator
35.5 Hyperbolic Secant Calculator
35.6 Hyperbolic Cotangent Calculator
36.1 Inverse Hyperbolic Sine Calculator
36.2 Inverse Hyperbolic Cosine Calculator
36.3 Inverse Hyperbolic Tangent Calculator
36.4 Inverse Hyperbolic Cosecant Calculator
36.5 Inverse Hyperbolic Secant Calculator
36.6 Inverse Hyperbolic Cotangent Calculator
37. Law of Sines Calculator
38. Law of Cosines Calculator
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