Question

solving quadratic equations by factoring

solve the following quadratic function by factoring:

\\f(x) = x^2 + 11x + 28\\

enter the smallest value first.

\\x = ?, \\

Explanation:

Set the quadratic function to zero

Using the Solving Quadratic Equations knowledge point

$$ x^2 + 11x + 28 = 0 $$

Factor the trinomial expression

Using the Factoring Trinomials and Polynomial Factoring knowledge points

$$ (x + 7)(x + 4) = 0 $$

Solve for the individual roots

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK0
$$

Identify the smallest value first

Compare the two calculated roots:

$$ -7 < -4 $$

The smallest root is \(-7\) and the larger root is \(-4\).

Answer:

Solve the following quadratic function by factoring:
\(f(x) = x^2 + 11x + 28\)

Enter the smallest value first.
\(x =\) <blank>\(-7\)</blank>, <blank>\(-4\)</blank>