Question

Factor completely x^2 + 12x - 45

Answer 1

Hey there!

You can factor this by splitting the middle term. 

First, you'll multiply the coefficient of the first term (x²) by the constant (–45). Since the first coefficient is just 1, this number will just be –45. 

Next, find the two factors of –45 that add up to your middle term. Here's some factors of –45:

–45*1 = –45
–1*45 = –45
–15*3 = –45 
–3*15 = –45
–9*5 = –45
–5*9 = –45

All you need to do is see which one adds up to +12:

–45 + 1 = –44
–1 + 45 = +44
–15 + 3 = –12 
–3 + 15 = +12
–9 + 5 = –4
–5 + 9 = +4

You'll use –3x and 15x instead of 12x in your equation. Your equation should be x² – 3x + 15x – 45. 

Then, split this polynomial into two binomials, (x² – 3x) and (15x – 45). Factor out any GCFs you see. Both of the binomials in parentheses after this step should be the same. 

(x² – 3x)(15x – 45)
x(x – 3)*15(x – 3)

Lastly, just rearrange your equation. One binomial will be just your GCFs, the other will be the binomial in the parenthesis (there will only be one). 

(x + 15)(x – 3)

This is your final factorization. Hope this helped you out! :-)