I forgot how to factor these can anyone help?

Question

x^3+5x^2-5x-25

and

6+2x-3x^3-x^4

and

8x^5-^x2+12x^3-9

thank you so much for your help!!!

Answer 1

For all of these 3 sets of expressions, factoring by grouping is the best method to use:

x^3+5x^2-5x-25

= x^3 + 5x^2 - 5x - 25

= (x^3 + 5x^2) - (5x + 25)

= x^2(x + 5) - 5(x + 5)

= (x + 5)(x^2 - 5)

and

6+2x-3x^3-x^4

= 6 + 2x - 3x^3 - x^4

= (6 + 2x) - (3x^3 + x^4)

= 2(3 + x) - x^3(3 + x)

= (3 + x)(2 - x^3)

and

8x^5-6^x2+12x^3-9

= (8x^5 - 6^x2) + (12x^3 - 9)

= 2x^2(4x^3 - 3) + 3(4x^3 - 3)

= (4x^3 - 3)(2x^2 + 3)

Answer 2

x(x^2-5)+5(x^2-5)

(x+5)(x^2-5)

-x^4-3x^3+2x+6

-x(x^3-2)-3(x^3-2)

(-x-3)(x^3-2)

must have missed something for that last one.

make it a good day

Answer 3

For these sets of problems, you have to group the numbers together and take out common factors to factor them.

1.  x^3 + 5x^2 - 5x - 25

(x^3 + 5x^2) - (5x + 25)

x^2(x + 5) - 5(x + 5)

(x^2 - 5) (x + 5)

(x - 5^1/2) (x + 5^1/2) (x + 5)

2.  6 + 2x - 3x^3 - x^4

(6 + 2x) - (3x^3 + x^4)

3(3 + x) - x^3(3 + x)

(3 - x^3)(3 + x)

8x^5 - ^x2 + 12x^3 - 9

Not sure about this one, it seems like you wrote it wrong. But you should have gotten the hang of it by the last two problems, you just have to watch out for the negative signs!

Answer 4

x^3+5x^2--5x--25 = x^2(x+5) --5(x+5) = (x+5)(x^2--5)

6+2x--3x^3--x^4= 2(3+x) --x^3(3+x) = (3+x)(2--x^3)

8x^5--6x2+12x^3--9 = 2x^2(4x^3--3) + 3(4x^3--3) = (4x^3--3)(2x^2+3)