Question

Factor completely r^2 -7r-18

Answer 1

(r + 2)(r - 9)

Explanation:

To factor the quadratic expression
`\(r^2 - 7r - 18\)`, we look for two numbers that multiply to the product of the coefficient of
`\(r^2\) (1)` and the constant term (-18), and add up to the coefficient of
`\(r\) (-7)`.

These numbers are -2 and 9 because:

`\[ -2 * 9 = -18 \]` (product)

`\[ -2 + 9 = -7 \]` (sum)

Now, we can express the quadratic expression as the product of two binomials:

`\[ r^2 - 7r - 18 = (r - 9)(r + 2) \]`