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vampirchik [111]
3 years ago
15

Find the value of c so that the polynomial p(x) is divisible by (x-3). p(x) =-x^3+cx^2-4x+3. c=?

Mathematics
1 answer:
Vilka [71]3 years ago
4 0

Answer:

\boxed{\textsf {The value of c is $\sf \dfrac{-14}{3}$. }}

Step-by-step explanation:

A polynomial is given to us . We need to find the value of c so that it is divisible by (x-3 ) .The given polynomial to us is ,

\sf \implies p(x)=- x^3+cx^2-4x+3

And the factor is ,

\sf \implies g(x) = x + 3

Now , according to factor theorem , p(x) will be divisible by g(x) if p(-3) = 0

\sf \implies p(x)= - x^3+cx^2-4x+3 \\\\\implies\sf p(-3) = 0 \\\\\sf\implies -(-3)^3+c(-3)^2-4(-3)+3 = 0 \\\\\sf\implies 27 + 9c +12+3=0 \\\\\sf\implies 9c +42=0 \\\\\sf\implies 9c = (-42) \\\\\sf\implies c = \dfrac{-42}{9}\\\\\sf\implies \boxed{\pink{\sf c = \dfrac{-14}{3}}}

<h3><u>Hence </u><u>the </u><u>value </u><u>of </u><u>c </u><u>is </u><u>(</u><u>-</u><u>1</u><u>4</u><u>)</u><u>/</u><u>3</u><u> </u><u>.</u></h3>
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