Answer to Question #170046 in Algebra for Benedictus

Question

𝐠+2is afactor of the polynomial 𝐵3 − 2𝐲 + 𝐵− 18.When this polynomialis divided by 𝐠+ 1the remainder is 18.a. Find the values of 𝐠and 𝐮b. With thesevalues find the remaining factorsof the polynomial.c. Hence,solve the equation 𝐵3 −2𝐲 +𝐵 = 18.d. Sketch the graph of the polynomialusing the values of 𝐠and𝑹ou have found.

Answer 1

The given Polynomial is $B^3-2y+B-18.$

As g+2 is a factor of polynomial

Then (-2) is a factor od polynomial

$\Rightarrow (-2)^3-2y+(-2)-18=0\\\Rightarrow 2y=-8-2-18\\\Rightarrow y=-14$

Put this value in Polyomial

we get polynomail as $B^3+28+B-18$

i.e. $B^3+B+10=0$