Question

7. p(x) = 2x4 + x3 – 8x? – X+6, g(x) = 2x – 3 please verify that using factor throrem​

Answer 1

GIVEN :

$p(x) = 2x^4 + x^3 - 8x^2 - x+6$, g(x) = 2x - 3 please verify that using factor theorem​

TO VERIFY :

The factor theorem for the given polynomial

SOLUTION :

Given polynomials are $p(x) = 2x^4 + x^3 - 8x^2 - x+6$, g(x) = 2x - 3

By using the Factor theorem we have that,

2x-3=0  

$x=\frac{3}{2}$

Now put  in p(x) we get,

$p(\frac{3}{2})=2(\frac{3}{2})^4+(\frac{3}{2})^3-8(\frac{3}{2})^2-\frac{3}{2}+6$

$=2(\frac{81}{16})+\frac{27}{8}-8(\frac{9}{4})-\frac{3}{2}+6$

$=\frac{81}{8}+\frac{27}{8}-18-\frac{3}{2}+6$

$=\frac{81+27-144-12+48}{8}$

$=\frac{156-156}{8}$

$=\frac{0}{8}$

= 0

$p(\frac{3}{2})=0$

⇒ 2x-3 is a factor for the given polynomial p(x)

Hence the factor theorem is verified.