Question

if (2x-1) be a factor of the polynomial p(x) = kx^3 + 23x^2 + 71x + 30 then find k and hence factorize the polynomial p(x)​

Answer 1

the answere would be k=-570

oh and answere me :()

Answer 2

k=-570

Explanation:

P(x) = kx^3+23x^2+71x+30

If 2x-1 is a factor of p(x)

Then,

2x-1 =0

2x=1

x=1/2 and at this value, p(x) =0

Substitute x = 1/2 for x in p(x)

p(1/2) = k(1/2)^3 + 23(1/2)^2;+71(1/2)+30

k(1/8)+23/4 +71/2+30=0

k/8= -23/4 -71/2-30

k/8 = -285/4

k= -(285*8)/4

k=-570

Thus, the polynomial p(x) = -570x^3 +23x^2 +71x +30

Factorization of p(x)

(2x-1) (-285x^2 +131x-30).