Factoring trinomials
Factor into two binomials: x2+8x+12
(x+6)(x+2)
What are factors
Factors are mathematical quantities that are multiplied together
Factor: 4 + x2
This polynomial is prime (can't be factored)
Factor: 14n2+10n
2n(7n+5)
Factor completely: x2+2x+4x+8
(x+2)(x+4)
Factor into two binomials: m2-11m+18
(m-9)(m-2)
What is a polynomial
A polynomial is an expression with terms that contain coefficients and variables raised to integer powers
Factor: 81x3y2 - 9x2y2 - 18xy
9xy(9x2y - xy -2)
Factor: 18x3-6x
6x(3x2-1)
Factor completely: xy-5x+9y-45
(x+9)(y-5)
Factor into two binomials: x2+5x-24
(x+8)(x-3)
What is the greatest common factor (GCF) of a polynomial
The greatest common factor is the largest polynomial that is a factor of each term in the polynomial
Factor completely: a2-16a+64
(a-8)(a-8)
Factor: 7x(x+y)-(x+y)
(x+y)(7x-1)
Factor completely: 3x3-2x2-6x+4
(x2-2)(3x-2)
Factor into two binomials: y2-6y-7
(y-7)(y+1)
What is a term
A term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs,
x2+7x-30
(x+10)(x-3)
Factor: 6x2(5x-1)+(5x-1)
(5x-1)(6x2+1)
Factor completely: cx-dx+dy-cy
(c-d)(x-y)
Factor into two binomials: x2-x-56
(x-8)(x+7)
What is a trinomial
A trinomial is a polynomial consisting of three terms
Factor completely: 3x2y-6xy-45y
3y(x-5)(x+3)
Factor: (x+4)(x+5)+(x-1)(x+5)
(x+5)(2x+3)
Factor completely: xnyn-xn+2yn-2
(xn+2)(yn-1)