Question

Factor 4x^4-52x^2+144 by grouping please show work >.< (open study wont let me comment so plz be descriptive)

Answer 1

\[\Large 4x^4-52x^2+144\]First factor out a 4, since all terms have a GCF of 4 \[\Large 4(x^4-13x^2+36)\]
You need two numbers that multiply to 36 and add up to -13... -9 and -4, so break up -13x^2 into -9x^2 and -4x^2
\[\Large 4(x^4-9x^2-4x^2+36)\]

Answer 2

Now you can factor by grouping.

Group the first two terms and last two terms in brackets, also factor the negative out of the last two \[\Large 4[(x^4-9x^2)-(4x^2-36)]\]

Answer 3

Then pull the common factor x^2 out of the first pair of brackets, and common factor 4 out of the second pair

\[\Large 4[x^2(x^2-9)-4(x^2-9)]\]
Then pull out the common factor (x^2-9) \[\Large 4[(x^2-9)(x^2-4)]\]