Question

Given a polynomial and one of its factors, find the remaining factors.

Answer 1

\[2x^{3} + 15x^{2} - 14x - 48\]
factor: \[(x-2)\]

Answer 2

Well, you could use polynomial division or synthetic division to find the remaining factors, or you can just factor the cubic.

Answer 3

You are given x - 2 as one of the factors, therefore, you can just split the polynomial in accordance with the given factor:

2x^3 + 15x^2 - 14x - 48

= 2x^3 - 4x^2 + 19x^2 - 38x + 24x - 48
= 2x^2(x - 2) + 19x(x - 2) + 24(x - 2)
= (x - 2)(2x^2 + 19x + 24)

Factor 2x^2 + 19x + 24 to find the remaining factors

Answer 4

@Hero how would it work doing synthetic?
@JoyLin

Answer 5

Just out of curiosity, did you understand the method that I presented?

Answer 6

no...

Answer 7

Basically you split the polynomial from left to right. Start with 2x^3 + 15x^2

When you factor your first two terms you want x - 2 to be a factor, so split the 15x^2 to

2x^3 - 4x^2 + 19x^2

Answer 8

where did the x-2 go?

Answer 9

Obviously now 2x^3 - 4x^2 factors to 2x^2(x - 2)

So now the next pair of terms to deal with is

19x^2 - 14x

Again, you want to be able factor something out so that x - 2 is a factor, so split the -14x to 19x^2 - 38x + 24x

Answer 10

It takes a bit of working in order to get it. But you can become good at it.

Answer 11

I really dont understand this method can you walk me through synthetic?

Answer 12

Watch a youtube video on it.

Answer 13

I have watched multiple videos but my numbers arent coming out i cant get it to factor

Answer 14

Did you watch Patrick JMT?

Answer 15

no i get how to do it but for some reason im not getting the right numbers

Answer 16

is this right?