Question

Find all positive and negative integers b such that x^2+bx+9 factors.

Answer 1

4x + b

Explanation:

The derivative of a polynomial is the sum of the derivative of it's terms. The derivative of a constant term is 0. The derivative of the ( ax to the n) is ( nax to the n-1 )

2 x 2x(²minus¹ )+ bx(¹minus¹)

multiple 2x2

4x²–¹ + bx¹–¹

subtract 1 from 2

4x¹ + bx¹–¹

subtract 1 from 1

4x¹ + bx⁰

for any term t, t¹ = t

4x + bx⁰

for any term t except 0

t⁰ = 1

4x + b x 1

for any term t, t x 1 = t

and 1t = t

4x + b