Question

The value of P if (x - 3) is a factor of
p^2x^3 - px^2 + 3px - p is
(A) 27
(B) -27
(C)1/27
(D) -1/27​

Answer 1

Answer:

$\tt{p^{2}x^{3} - px^{2} + 3px - p}$

Take 'p' common:

$\tt{p(x^{2} - x^{2} + 3x - 1}$

x - 3 is a factor.

=》 x = 3

$\tt{p(27 - 9 + 9 - 1) = 0}$

=》 $\tt{p = \frac{1}{27}}$

Answer 2

Correct Question : Find the value of p if (x - 3) is a factor of polynomial p^2x^3 - px^2 + 3px - p.

Answer : Opt. c) 1/27

Step by step explanation :

The given polynomial has factor ( x - 3 ) only if p(3) = 0

Here,

p(3) = (3)³ × p² - 3²p + 3×3p - p

0 = 27p² - 9p + 9p - p

0 = 27p² - p

27p² - p = 0

p²/p = 1/27

p = 1/27

Thus, The value of p is 1/27.

Final answer : Opt. c) 1/27