Question

need help factoring these 4 proBlems
1) s^2-6s-9
2)-x^5+20x^4-100x^3
3)7x^2-63
4) 3b^2-75

Answer 1

These are all special forms, or reducible to special forms. By special forms, I mean (a+b)^2, (a-b)^2 or a^2-b^2.

Answer 2

On the third and fourth ones, factor out the common factor first, then they will be in the form of difference of squares.

Answer 3

for third one is it 7(x^2-9)

Answer 4

Actually, I don't think (1) factors at all. I think you might have made a sign error on the constant term. If it is +9, then it will be a perfect square.

Answer 5

thats what i thought... i didnt mess up so it i think its just you cant do it

Answer 6

The third one will factor further:\[7x^2-63=7(x^2-9)=7(x+3)(x-3)\]

Answer 7

The fourth one is similar in pattern to the third.

Answer 8

oh so i need to factor twice... okay i get that

Answer 9

what about 2nd one though? i dont get it

Answer 10

It is a perfect square. Recall \[(a+b)^2=a^2+2ab+b^2\]

Answer 11

\[-x^5+20x^4-100x^3=-x^3(x^2-20x+100)=-x^3(x-10)^2\]

Answer 12

oh thaat maeks sense

Answer 13

Factor out the common terms, and look for known patterns before trying to fiddle too much with your regular factoring strategy. Sometimes, it will save you a bunch of trouble.