Question

16. If p(x) = 2x® - 11x2 - 4x +5 and g(x) = 2x + 1, show that g(x) is not a
factor of p(x).​

Answer 1

$\huge {\underline {\bf {Question}}}$

If p(x) = 2x3 - 11x2 - 4x +5 and g(x) = 2x + 1, show that g(x) is not a factor of p(x).

$\huge {\underline {\bf {Answer}}}$

• Given :

p(x) = 2x3 - 11x2 - 4x +5

g(x) = 2x + 1

• Show that :

g(x) is not a factor of p(x).

• Solution :

g(x) = 2x + 1 = 0

g(x) => x = -1/2

Now , putting x = -1/2 in given p (x) , we get

$p(x) = 2x^3 - 11x^2 - 4x + 5 \\ = 2 (\frac{-1}{2})^3 - 11 (\frac {-1}{2})^2 - 4 (\frac {-1}{2}) + 5 \\ = 2 (\frac {-1}{8}) - 11 (\frac {-1}{4}) - (\frac {-4}{2}) + 5 \\ = (\frac {-2}{4}) +(\frac{11}{4}) - (-2) + 5 \\ = \frac{-1}{4} + \frac{11}{4} + 2 + 5 \\ = \frac{-1 + 11 + 8 + 20}{4} \\ = \frac{38}{4} \\ = 9.5$

Since, p(x) = 2x^3 - 11x^2 - 4x + 5 is not equal to zero (0) , so g(x) is not a factor of p(x).