Question: Find the factors. If the polynomial is prime, state so. 2. $z^2 + 9z + 8$

Find the factors. If the polynomial is prime, state so.

2. $z^2 + 9z + 8$

Solution

The image shows a math problem asking for the factors of a polynomial: \[ x^2 + 9x + 8 \] To factor the quadratic polynomial, we look for two numbers that multiply to 8 (the constant term) and add to 9 (the coefficient of the middle term). The numbers that satisfy these conditions are 1 and 8. Rewrite the middle term 9x using these numbers: \[ x^2 + 1x + 8x + 8 \] Group the terms: \[ (x^2 + 1x) + (8x + 8) \] Factor out the greatest common factor from each group: \[ x(x + 1) + 8(x + 1) \] Notice that \(x + 1\) is a common factor: \[ (x + 1)(x + 8) \] Therefore, the factors of the polynomial \(x^2 + 9x + 8\) are \((x + 1)\) and \((x + 8)\).