# Product of a linear factor and cubic factor

#### jazz2112

##### New member

I am not sure how to do part b) was wondering if someone could help out and set me on the right track

#### MarkFL

##### Super Moderator
Staff member
What did you find for part (a)? What does this imply?

#### MarkFL

##### Super Moderator
Staff member

Since $$\displaystyle P(-1)=0$$ , we know by the factor theorem then that $$P(x)$$ must have as a factor $$x+1$$. We can use synthetic division to complete part (b):

$$\displaystyle \begin{array}{c|rr}& 2 & -5 & 0 & 6 & -1 \\ -1 & & -2 & 7 & -7 & 1 \\ \hline & 2 & -7 & 7 & -1 & 0 \end{array}$$

And so, we conclude:

$$\displaystyle P(x)=(x+1)\left(2x^3-7x^2+7x-1\right)$$

#### jazz2112

##### New member
Thankyou so much!!