Question

Completely factor the polynomial
5x^3+40x^2+5x+40

Answer 1

First factor out the common factor which is 5

Answer 2

so would it be x^2+8x+x+8

Answer 3

5(x^3+8x+x+8)

Answer 4

when factoring 3x^9+6x^8-9x^7+6x^6 would you just divide it by 3?

Answer 5

8x^2.

Answer 6

Not done with the first one yet.

Answer 7

The factors of 8 are possible rational roots so use synthetic division to find if there are any rational roots.

Answer 8

oh okay 8x^2....?

Answer 9

rational roots?

Answer 10

You are supposed to factor. If you know the roots, you know the factors.

Answer 11

okay so for 5(x^3+8x^2+8) would be (2x+4)(2x+4)

Answer 12

That or it could be 4

Answer 13

You are trying to factor x^3+8x^2+x+8

Answer 14

If there are any rational zeros, they are factors of 8. What are the factors of 8?

Answer 15

are the they ones we add or multiple to get 8?

Answer 16

because if we are multiplying it would be 2*4
adding would be 4+4 or 6+2

Answer 17

Factors of 8 are positive 1 and negative 1, positive 2 and negative 2, positive 4 and negative 4, positive 8 and negative 8

Answer 18

Now use synthetic division to find out if any of those possibilities are actual roots.

Answer 19

Does any of this sound familiar?

Answer 20

some but never heard the term of
synthetic division?

Answer 21

What are you studying and what method did your teacher show you for factoring cubics?

Answer 22

Oh...I bet you're supposed to factor by grouping.

Answer 23

algebra 1, he hasn't shown us anything it's all been online. He isn't really much help.

Answer 24

Group the first two terms and factor out 5x^2. Group the last two terms and factor out 5

Answer 25

factoring out 5x^2 = 4x(x-1)