FACTORING TRINOMIALS

Many polynomials in the form of x^2 + bx + c can be written as the product of 2 binomials in the form of (x+t)(x+s)

To factor the trinomial, we need to find:

-> 2 numbers that ADD to give us b

-> 2 numbers that MULTIPLY to give us c

This can be called the product-sum method.

x^2 - 7x -18 -9 x 2 = -18

=(x-9) (x+2) -9 + 2 = -7

In some cases, you may need to common factor first.

2x^2 + 14x + 24

=2(x^2 + 7x + 12) 4 x 3 = 12

=2(x+4) (x+3) 4 + 3 = 7

8x (y-7) + 3 (y-7)

= (y-7) (8x+3)

This is when the binomials are the common factor.

When there is no common factor - we can group terms together that have a common factor.

d^2 + 5d + 3d + 15

= (d^2 + 5d) + (3d + 15) <- group like terms together

= d (d+5) + 3(d+5) <- the brackets should be the same

= (d+3)(d+5) <- factor the binomial

A complex trinomial is when there is a coffeicent great than 1, in front of the x^2 term.

2 methods to factor complex trinomials are:

-> Decomposition

-> Trial and Error

Decomposition

-Step 1: Multiply the 1st and the last number to find the 5x^2 - 14x + 8 product. 5 x 8 = 40

-Step 2: Use the product/sum method with the product

above.

-10 x -4 = 40

-10 x -4 = -14

-Step 3: Rewrite the middle terms with the 2 factors. = 5x^2 - 10x - 4x + 8

-Step 4: Factor by grouping = (5x^2 - 10x) - (4x + 8)

= 5x (x -2) -4 (x -2)

-Step 5: Binomial common factoring = (x - 2) (5x - 4)

Trial and Error

credits to patrickJMT

QUADRATICS