Factoring!!! HELP?

Question

Factor completely:
x7y2 – 4x5y2 – 21x3y2 (ALL THE NUMBERS EXCEPT FOR 4 AND 21 ARE EXPONENTS..sorry the computer would not let me type superscript)


Factor completely:
x3 – 2x2 – 4x – 8
(all numbers except for 2 and 4 and 8 are exponents... the first 2 is a coefficent, the second is the superscript)

Factor completely:
2x2 – 18y2

(2 and 18 are the only things not exponents)

THANKS IN ADVANCE!! I DONT GET THIS FACTORING THING!

Answer 1

x^7y^2-4x^5y^2-21x^3y^2
=x^3y^2(x^4-4x^2-21)
=x^3y^2(x^4-7x^2+3x^2-21)
=x^3y^2{x^2(x^2-7)+3(x^2-7)}
=x^3y^2(x^2-7)(x^2+3)
2.There is some discrepancy of sign in this factorisation.
3.2x^2-18y^2
=2(x^2-9y^2)
=2{(x)^2-(3y)^2}
=2(x+3y)(x-3y)

Answer 2

x^7 y^2 - 4x^5 y^2 - 21x^3 y^2

This is a harder-than-average factoring problem. First, factor out the biggest monomial.

x^3 y^2 (x^4 - 4x^2 y^2 - 21y^2)

Now, decompose x^4 into x^2 and x^2 and 21y^2 into -7y and +3y. Notice by doing this, the outer product and inner product add up to -4x^2 y^2, so this is the correct factorization.

x^3 y^2 (x^2 - 7y) (x^2 + 3y)

Answer 3

I got x^4y^2(x^2 + 3)(x - 7) for the first. Didn't check it, though, so you may wanna....


I couldn't do anything to the second.

2(x + 3y)(x - 3y) should be #3.

Answer 4

x^7y² -4x^5y² -21x³y²

x³y²(x⁴-4x² - 21)

x³y²(x⁴- 7x² + 3x² - 21

x³y²[x²(x² - 7) + 3(x² - 7)]

x³y²(x² + 3)(x² - 7)

- - - - - - - - - - - - - - - -

x³ -2x² - 4x - 8

x²(x - 2) - 4(x - 2)

(x² - 4)(x - 2)

- - - - - - - - - -s-