The polynomial p(x)=x^ 4 -5x^ 3 +ax^ 2 +bx+12 is divisible by both and

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

Problem

The polynomial

p(x)=x^{4}-5x^{3}+ax^{2}+bx+12

is divisible by both

x-2

and

x-3

. (i) Find the values of

a

and

b

. (ii) Using the values of

a

and

b

found in part (i), factorise

p(x)

completely.