Question

If (x+1) is the factor of polynomial p(x) = ax²+x+1, then find a.

Answer 1

a = 1

Explanation:

Factors are what we can multiply to get the number.

x² + x + 1

Factor the polynomial.

x(x+1) + 1

ax² + x = x(x + 1)

ax² + x = x² + x

`a=(x^2 +x)/(x^2 +x)`

a = 1

Answer 2

a = 0

Explanation:

p(x) = ax²+x+1

Let x+1 = 0 => x = -1

Putting in the above polynomial

=> p(-1) = a(-1)^2+(-1)+1

By Remainder Theorem, Remainder will be zero

=> 0 = a(1) -1+1

=> 0 = a

OR

=> a = 0