Question

Find the value of c so that (x-2) left parenthesis, x, minus, 2, right parenthesis is a factor of the polynomial p(x), left parenthesis, x, right parenthesis. p(x) = x^3 -4x^2 +3x+c

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{(x-2)\;is\;a\;factor\;of\;P(x) = x^3 -4x^2 +3x+c}$

$\underline{\textbf{To find:}}$

$\textsf{The value of c}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Factor theorem:}}$

$\boxed{\textbf{(x-a) is a factor of P(x) if and only if P(a)=0}}$

$\mathsf{P(x)=x^3 -4x^2 +3x+c}$

$\textsf{Since (x-2) is a factor of P(x), we have P(2)=0}$

$\implies\mathsf{2^3 -4(2)^2 +3(2)+c=0}$

$\implies\mathsf{8 -4(4)+3(2)+c=0}$

$\implies\mathsf{8 -16+6+c=0}$

$\implies\mathsf{8 -10+c=0}$

$\implies\mathsf{-2+c=0}$

$\implies\boxed{\mathsf{c=2}}$

$\underline{\textbf{Find more:}}$

If x-2 is factor of polynomial 5x²+mx, then value of m is​

https://brainly.in/question/48051029

Answer 2

x - 2 = 0

⇒ x = 2

x³ - 4x² + 3x + c = 0

⇒ (2)³ - 4(2)² + 3(2) + c = 0

⇒ 8 - 16 + 6 + c = 0

⇒ c = 2