Let . The following information is given: • is a zero of . • is a zero of . • is a…

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

F(x)=x^{5}+mx^{4}+nx^{3}+px^{2}+qx+10

. The following information is given: •

x=1

is a zero of

F(x)

. •

x=-2

is a zero of

F(x)

. •

x=3

is a zero of

F(x)

. • When

F(x)

is divided by

(x+1)

, the remainder is

-12

. (i) Form the four equations involving

m, n, p,

and

q

that arise from the above conditions. (ii) Solve the simultaneous equations obtained in part (i) to find the values of

m, n, p,

and

q