Anybody up for a Factoring challenge ( show your work now)?

Question

Make sure to superscript all exponents. If you believe that a polynomial is not factorable, label it as prime. Show all stages of factoring separately (i.e., show the result of factoring out a GCF before taking the resulting polynomial and factoring it again).

1. Factor completely:
x5y3 – 3x4y2 – 28x3y



2. Factor completely:
x3 – 2x2 + 6x – 12



3. Factor completely:
x2 + 17x + 16



4. Factor completely:
3x2 – 75y2



5. Factor completely:
8x2 + 6x – 5



6. Factor completely:
4x2 + 44x + 96

Answer 1

1. x^5y^3 - 3x^4y^2 - 28x^3y
= x^3y (x^2y^2 - 3xy - 28)
= x^3y (xy - 7) (xy + 4).

2. x^3 - 2x^2 + 6x - 12
= x^2(x - 2) + 6(x - 2)
= (x^2 + 6) (x-2).

3. x^2 + 17x + 16
= (x + 16) (x + 1)

4. 3x^2 - 75y^2
= 3(x^2 - 25y^2)
= 3 (x - 5y) (x + 5y)

5. 8x^2 + 6x - 5
= (4x + 5) (2x - 1)

6. 4x^2 + 44x + 96
= 4(x^2 + 11x + 24)
= 4(x + 8) (x + 3)

Answer 2

1. x^3y(x^2y^2-3xy-28)
x^3y(xy-7)(xy+4)

2. x^2(x-2)+6(x-2)
(x^2+6)(x-2)

3. (x+1)(x+16)

4. 3(x^2-25y^2)
3(x+5y)(x-5y)

5. (2x-1)(4x+5)....easiest way to do this one is ac method: what two numbers can be multiplied to get the same as 8 and -5 but added together will give you a sum of 6: 10 and -4 multiplied get -40 but added together give you 6 so then substitute them in as follows:
8x^2-4x+10x-5
Factor out 4x from the first two terms: 4x(2x-1)
then factor out 5 from last two terms: 5(2x-1)
put them together: (4x+5)(2x-1)

6. First factor out 4 from entire equation: 4(x^2+11x+24)
4(x+3)(x+8)

Hope this helps!!

Answer 3

Wow you're lazy. One or two questions fine but 6?

Answer 4

Haha, forget that. Have fun doing that... I hope it's not due tomorrow morning...