How do you factor completely x^2 - 8x + 16x28x+16?

1 Answer
Feb 29, 2016

This is a perfect square trinomial, because the first and last terms are perfect squares (sqrt(x^2) = x and sqrt(16) = 4)(x2=xand16=4)

Explanation:

Method 1:

(x - 4)(x - 4)(x4)(x4)

(x - 4)^2(x4)2

You can also double check by making sure term b (the middle term) satisfies the equation b = 2acb=2ac only once you have factored, or when you have taken the square root of the first and last term. We check: 8 = 2(x)(4)8=2(x)(4). So, we have factored the trinomial properly. Also, you can check by doing FOIL (first, outside, inside and last), multiplying out.

Method 2:

Factor as a regular trinomial of the form ax^2 + bx + c, a = 1ax2+bx+c,a=1. This method, although longer, is good to get used to because you will have to learn at one point to factor trinomials such as x^2 + 8x + 15x2+8x+15, and it is the most safe and foolproof method.

To factor a trinomial of the form ax^2 + bx + c, a = 1#, you must find two numbers that multiply to c and that add to b.

We must find two numbers that multiply to +16 and add to -8. These two numbers are -4 and -4.

So, (x - 4)(x - 4). Since the parentheses repeats itself twice, we can rewrite the expression as (x - 4)^2(x4)2

Practice exercises:

  1. Factor the following trinomials using method 1

a) x^2 + 10x + 25x2+10x+25

b) 16x^2 - 56x + 4916x256x+49

2 . Factor the following trinomials using method 2

a) x^2 - 22x + 121x222x+121

b) x^2 + 5x + 6x2+5x+6

c) x^2 - 8x - 33x28x33

d) x^2 - 14x + 45x214x+45

3 . Find the value of mm that makes the following trinomials perfect square trinomials

a) 4x^2 + mx + 644x2+mx+64

b) 25x^2 - 40x + m25x240x+m

Good luck!