Question

if the polynomial 4x³-16x²+ax+7is exactly divisible by (x-1),then find the value of a. hence factorise the polynomial​

Answer 1

SOLUTION:-

Given:

The polynomial 4x³ -16x² +ax +7 exactly divisible by (x-1).

To find:

The value of a & factorise the polynomial.

Explanation:

The roots of the given polynomial is;

x-1=0

=) x= 1

Putting in above the polynomial:

=) 4(1)³ -16(1)² +a(1) +7=0

=) 4×1 -16 ×1 + a +7=0

=) 4 - 16 + a +7 =0

=) -12 + a +7 =0

=) a -5 =0

=) a= 0+5

=) a= 5

And, divide in the attachment a figure.

Factorise the polynomial;

(x-1)(4x² - 12x -7)

=) (x-1)(4x² -14x+2x -7)

=) (x-1) [2x(2x -7) +1 (2x-7)]

=) (x-1) (2x-7) (2x +1)

Thank you.