Factor. q^2 + 12q + 11 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression q^2 + 12q + 11. Compare q^2 + 12q + 11 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 12, and c = 11.Find product and sum: Find two numbers whose product is ac (since a = 1, just c) and whose sum is b. We need two numbers that multiply to 11 and add up to 12. The numbers 1 and 11 satisfy these conditions because 1 * 11 = 11 and 1 + 11 = 12.Split middle term: Write the quadratic expression using the two numbers found in Step 2 to split the middle term. q^2 + 12q + 11 can be rewritten as q^2 + 1q + 11q + 11.Factor by grouping: Factor by grouping. Group the terms to factor out common factors: (q^2 + 1q) + (11q + 11) Factor out a q from the first group and 11 from the second group: q(q + 1) + 11(q + 1)Factor common binomial: Factor out the common binomial factor. Since both groups contain the factor (q + 1), factor it out: (q + 1)(q + 11)

Home

Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

\newline

q^2 + 12q + 11

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $q^2 + 12q + 11$ . Compare $q^2 + 12q + 11$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Find product and sum: Find two numbers whose product is $ac$ (since $a = 1$ , just $c$ ) and whose sum is $b$ . We need two numbers that multiply to $11$ and add up to $12$ . The numbers $1$ and $11$ satisfy these conditions because $1 \times 11 = 11$ and $1 + 11 = 12$ .
Split middle term: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $q^2 + 12q + 11$ can be rewritten as $q^2 + 1q + 11q + 11$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms to factor out common factors: $\newline$ $(q^2 + 1q) + (11q + 11)$ $\newline$ Factor out a $q$ from the first group and $11$ from the second group: $\newline$ $q(q + 1) + 11(q + 1)$
Factor common binomial: Factor out the common binomial factor. $\newline$ Since both groups contain the factor $(q + 1)$ , factor it out: $\newline$ $(q + 1)(q + 11)$