Can somebody please help me write each product as a polynomial in standard form.?

Question

3.(x-4)(5x^2+3x+7)
4. (x+2)(x-8)(x-1)
5. (2x-5)(x+1)^2
6.(3x-1)^3

Answer 1

3.) 5x^3-17x^2-5x-28

4.) x^3-7x^2-10x+16

5.) 2x^3+15x^2+12x+5

6.) 27x^3-27x^2+9x-1

yeah just as the others said, just distribute each of the terms and combine the resulting like terms

Answer 2

All you have to do is distribute each term from the first over the second.

In the first example, we have (5x^2*x)+(3x)(x)+(7)(x)-(4)(5x^2)-(4)(3x)-(4)(7)

See how that works?

So simplified it becomes 5x^3+3x^2+7x-20x^2-12x-28

Or 5x^3-17x^2-5x-28

Now for the second, simply foil the first two terms as the first step and for the second step, treat it like I did the first problem.

For the third one expand (x+1)^2 which is like (x+1)(x+1), FOIL that and then treat it like the first one.

The last problem is like (3x-1)(3x-1)(3x-1), take the first two, FOIL, and then do the last term like I did in the first problem.

I know you can do it!

Answer 3

5x^3+3x^2+7x-20x^2-28-12x

5x^3-17x^2-5x-28

x^2+2x-8x-16
x^2-6x-16)(x-1)
x^3-x^2-6x^2+6x-16x+16

x^3-7x^2-10x+16

(2x+5)(x+1)^2
(2x+5)(x^2+2x+1)
2x^3+5x^2+2x+10x^2+10x+5

2x^3+15x^2+12x+5

(3x-1)^3
(3x-1)^2(3x-1)

9x^2-6x+1(3x-1)
27x^3-9x^2-18x^2+6x+3x-1

27x^3-27x^2+9x-1