polynomial operations
Find the sum of: -2x2 + 5x+ 10 and -7x-3
-2x2 - 2x +7
Evaluate: i9⋅i10⋅i19⋅i24
-1
Solve for all values of x in simplest form: |8x|=64
x=8, x=-8
Function
A relation where every input (x) has exactly one output (y).
Solve the inequality: 13+5x≤38
x≤5
multiply: -4(x2 + 5x)
-4x2 - 20x
Simplify the expression to a+bi form: (5 + 4i) - (12 - 6i)
-7+10i
Solve for all values of x in simplest form: |-2x+11|=31
x=−10,x=21
Parent Function
The most basic function in a family (e.g., f(x)=x2 is the parent of all quadratic functions).
Solve the inequality: -6+7x>1
x>1
Express as a trinomial: x+10)(3x+10)
3x2 + 40x + 100
Simplify the expression to a + bi form: (8+8i)(-3+9i)
-96+48i
solve the following inequality algebraically: |x-8|≤5
3≤x≤13
Compound Inequality
Two or more inequalities joined by "and" (intersection) or "or" (union).
Solve the inequality: 4+5x>19+6
x > 4.2 or 21/5
Expand the expression to a polynomial in standard form: (2x+1)(x2 −x−7)
2x3 -x2 -15x-7
Write (3+2i)3 in simplest a+bi form
-9+46i
solve the following inequality algebraically:|x+2<13+11
-26<x<22
Extraneous Solution
A solution derived from solving an equation (especially radical or absolute value) that does not satisfy the original equation.
Solve the following inequality for c. Write your answer in simplest form:−7c−(2c+2)>−4c−2+6c
c<0
Find the quotient of 6z3 + 6z2 +14z divided by 2z
3z2 + 3z + 7
Write (8+3i+9)2 in simplest a+bi form
55+48i
Solve the following inequality algebraically: |x-9-4|≤ 6+26
-19≤x≤45
System of Equations
A set of two or more equations with the same variables; solving a system means finding the intersection point(s).
Solve the following inequality for b. Write your answer in simplest form:−7b+3(−9b+5)≥10b+6+10
b≤−1/44