Product of a linear factor and cubic factor

[jazz2112]

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

 

[MarkFL]

What did you find for part (a)? What does this imply?

 

[MarkFL]

To follow up:

Since [MATH]P(-1)=0[/MATH] , 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):

[MATH]\begin{array}{c|rr}& 2 & -5 & 0 & 6 & -1 \\ -1 & & -2 & 7 & -7 & 1 \\ \hline & 2 & -7 & 7 & -1 & 0 \end{array}[/MATH]
And so, we conclude:

[MATH]P(x)=(x+1)\left(2x^3-7x^2+7x-1\right)[/MATH]

 

[jazz2112]

Thankyou so much!!