Question

for what values of p is (-4)a zero of the polynomial x2-2x-(7p+3)

Answer 1

x²-2x-(7p+3)=0
(-4)²-2(-4)-7p-3=0
16+8-3-7p=0
21-7p=0
-7p=-21
p=21/7
p=3
If p = 3 , then (-4) is a factor of p(x)

Answer 2

The value of p is 3 in  given polynomial function: $\bold{x^{2}-2 x-(7 p+3)}$

Given: $x^{2}-2 x-(7 p+3)$ is a polynomial.

Now, we need to find the value of p.

Let, f(x)=$x^{2}-2 x-(7 p+3)$  

Given that x+4 is a factor, applying f(-4) in the above equation, we get f(-4) = 0

Substitute x=-4 in the given equation,  

Now we get,f(-4) = (-4)2-2(-4)-(7p+3)

On substituting the above equation, we get,16 + 8 –(7p + 3) = 0

Now, simplifying the above equation,

24 = 7p+3

7p = 21

p=3

Hence, the value of p is found to be 3, ∴p = 3