if the polynomial 4x^3 - 16x^2 + ax + 7, is exactly divisible by x - 1 then find the - Maths - Polynomials

Question

if the polynomial 4x^3 - 16x^2 + ax + 7, is exactly divisible by x
- 1 then find the value of a hence factorise the polynomial

Varun.Rawat · Accepted Answer

Let px = 4x3 - 16x2 + ax + 7Now, x - 1 exactly divides px, so x-1 is a factor of px
Now, p1 = 0⇒413 - 1612 + a1 + 7 = 0⇒4 - 16 + a + 7 = 0⇒-12 + 7 + a = 0⇒a = 5Now, px = 4x3-16x2+5x+7Now, x - 1 is one of the factor of px
To obtain the remaining factors of px, we will divide px by x - 1

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_57e28c6894c4d%20png"
style="width: 280px; height: 149px;">
Now, px = 4x3 - 16x2 + 5x + 7=x - 14x2 - 12x  - 7=x - 14x2 - 14x + 2x - 7=x - 12x2x - 7 + 12x - 7=x - 12x + 12x - 7

if the polynomial 4x^3 - 16x^2 + ax + 7, is exactly divisible by x - 1 then find the value of a. hence factorise the polynomial