Question

Find the value of c so that (x+1) is a factor of the polymonial p(x)=5x^4+7x^3-2x^2-3x+c

Answer 1

Answer:

c = - 3

Step-by-step explanation:

$\because$ (x+1) is a factor of the polymonial $p(x)=5x^4+7x^3-2x^2-3x+c$

Let (x + 1) =0$\implies$ x = - 1

$\therefore$ at x = - 1, p(x) =0.

$p(x)=5x^4+7x^3-2x^2-3x+c \\ \\ 0 = 5( { - 1})^{4} + 7( { - 1})^{3} - 2( { - 1})^{2} - 3( - 1) + c \\ \\ 0 = 5 \times 1 + 7( - 1) - 2 \times 1 + 3 + c \\ \\ 0 = 5 - 7 - 2 + 3 + c \\ \\ 0 = 7 - 7 + 3 + c \\ \\ 0 = 3 + c \\ \\ c = - 3$

Answer 2

Answer:

BRAINLIEST PLZZZZ

Step-by-step explanation:

Also given that (x+1) is factor of given polynomial p(x).

Need to determine value of constant c.

We will be solving above problem using factor theorem.

Factor theorem says that if ( x – a) is a factor of any polynomial f(x) , then f(a) = 0.

As in our case f(x) = p(x) and factor of p(x) is (x + 1) , which can be rewritten as (x – ( -1)) , so "a" in our case is -1 .

According to factor theorem p(-1) = 0

On substituting x = -1 , in given expression of p(x) we get

Hence value of c in the given polynomial is 1