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Educational Level

Secondary school, High school and College 
Program Purpose

Provide step by step solutions of your problems using online calculators (online solvers)

Problem Source

Your textbook, etc 
1. Addition, subtraction, multiplication, division of two polynomials
1.1 Addition of two polynomials eg.`(X^34X^2+4X8) + (X2)`
1.2 Subtraction of two polynomials eg.`(X^34X^2+4X8)  (X2)`
1.3 Multiplication of two polynomials eg.`(X^34X^2+4X8) xx (X2)`
1.4 Long division of two polynomials eg.`(X^34X^2+4X8) : (X2)`
1.5 Synthetic division of two polynomials eg.`(X^34X^2+4X8) : (X2)`
2. Factoring Polynomials
eg. (1) `25x^236`, (2) `4x^2+12xy+9y^2`, (3) `x^33x^26x+8`, (4) `a^2(bc)+b^2(ca)+c^2(ab)`
3. Expand and simplify polynomial
eg. (1) `(X+2)(X+3)`, (2) `(2X+3Y)^2`, (3) `(2X+3Y+4Z)^2`, (4) `102^2`, (5) `102 xx 106` (Expand using the identity)
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^24xy+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. HCF(GCD)LCM of Polynomials
eg. Find GCD, LCM of `(2X^24X), (3X^412X^2), (2X^52X^44X^3)`
6. Rational Expression of Polynomials
1. Reduced terms of rational expressions
eg. `(4X^225)/(8X^3125)`
2. Adding, subtracting, multiplying, dividing of rational expressions polynomials
eg. `(X3)/(X+1)(X6)/(X)`
7. Simplifying Algebraic Expressions
eg. (1) `(4x+1)/(3x2)=3/2`, (2) `(2x1)/(3x+1)+(4x1)/(6x)=0`
8. Quadratic Equation
1.1 Solving quadratic equations by factoring,
eg. (1) `25x^230x+9=0`, (2) `x^2+10x56=0`
1.2 Solving quadratic equations using the quadratic formula,
eg. (1) `25x^230x+9=0`, (2) `x^2+10x56=0`
1.3 Discriminant & Nature of Roots
eg. (1) `25x^230x+9=0`, (2) `x^2+10x56=0`
2. Find the quadratic equation whose roots are alpha and beta
eg. (1) `alpha=3, beta=4`, (2) `alpha=1+3sqrt(2), beta=13sqrt(2)`
3. Roots for nonzero denominator
eg. (1) `(5x18)/(x+2)=(2x6)/(x1)`, (2) `(x)/(x+1)+(x+1)/(x)=5/2`,
(3) `4((4x+1)/(4x1))^(2)+(4x+1)/(4x1)=3`, (4) `(4x+1)/(4x1)+(4x1)/(4x+1)=3`
4. Roots of nonquadratic equation
eg. (1) `6(x^2+1/x^2)25(x1/x)+12=0`, (2) `(x^2+1/x^2)8(x+1/x)+14=0`
9. Solve linear equation in two variables by (eg. Solve `7y+2x11=0` and `3xy5=0` using Substitution method)
1. Substitution method
2. Elimination method
3. Cross multiplication method
4. AdditionSubtraction 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. GaussJordan 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
11. 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^2yxy^2`,
(2) If 3x5y `prop` 5x+6y then prove that x `prop` y.
12. If `X+1/X=2` then find `X1/X, X^21/X^2, X^3+1/X^3`
1. If `x1/x=6` then find
(1) `x^2+1/x^2` (2) `x+1/x` (3) `x^21/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`
13. Interval notation and set builder notation
eg. (1) `3 <= x <=7`, x is odd. (2) `x^32 <= 25`, x in Z. (3) `x in[2,8)`
14. Set Theory
eg. `A={x<=5; x in N}, B={2<=x<=8; x in N}, C={x^33x^24x=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)`AB`, (2) `A(B uu C)=(AB) nn (AC)`
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)=(AB) nn (AC)`
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` ?
15. 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. `f(x)=2x+1`, `g(x)=x+5`. Find `fog(x)`, `gof(x)`, `fog(2)`, `f(3)`, `g(4)`
3. Find value
eg. 1. `f(x)=x(x+1)(2x+1)`. Find `f(x)f(x1)`, 2. `f(x)=x^22^x`. Find `f(2)f(0)`
16. Descartes' rule of signs
eg. `x^5x^4+3x^3+9x^2x+5`
17. 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+3c4e)/(2b+3d4f)=(5a4c+3e)/(5b4d+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 SubDuplicate ratio
6.4 SubTriplicate Ratio
6.5 Compounded Ratio
6.6 Mean proportional
6.7 Third proportional
6.8 Fourth proportional
6.9 Compare ratios
18. Partial Fraction
eg. `(5x4)/(x^2x2)`





