Question

factor each trinomial. if the trinomial cannot be factored write prime. show ALL work!1.) x^2-6x-272.) x^2+14x-32

Answer 1

factor each trinomial. if the trinomial cannot be factored write prime. show ALL work!



1.) x^2-6x-27



2.) x^2+14x-32

Part 1

x^2-6x-27

Complete the square

x^2-6x=27

(x^2-6x+9)=27+9

rewrite as perfect squares

(x-3)^2=36

square root both sides

x-3=(+/-)6

x=3(+/-)6

x=9 and x=-3

therefore

x^2-6x-27=(x-9)(x+3)

Part 2

x^2+14x-32

Find the roots applying the formula of quadratic equation

a=1

b=14

c=-32

substitute

`x=\frac{-14\pm\sqrt[]{14^2-4(1)(-32)}}{2}`
`x=\frac{-14\pm\sqrt[]{324}}{2}`
`x=(-14\pm18)/(2)`

the values of x are

x=2 and x=-16

therefore

x^2+14x-32=(x-2)(x+16)