7.2 Factor Trinomials of the Form x 2 +bx+c

Before you get started, take this readiness quiz.

Multiply: $\left(x + 4\right) \left(x + 5\right) .$
If you missed this problem, review the reference.

Simplify: ⓐ $−9 + \left(−6\right)$ ⓑ $−9 + 6 .$
If you missed this problem, review the reference.

Simplify: ⓐ $−9 \left(6\right)$ ⓑ $−9 \left(−6\right) .$
If you missed this problem, review the reference.

Factor: $x^{2} + 6 x + 8$.

Factor: $y^{2} + 8 y + 15$.

Factor: $u^{2} + 11 u + 24$.

Factor: $q^{2} + 10 q + 24$.

Factor: $t^{2} + 14 t + 24$.

Factor: $y^{2} + 17 y + 60$.

Factor: $x^{2} + 19 x + 60$.

Factor: $v^{2} + 23 v + 60$.

Factor: $t^{2} - 11 t + 28$.

Factor: $u^{2} - 9 u + 18$.

Factor: $y^{2} - 16 y + 63$.

Factor: $z^{2} + 4 z - 5$.

Factor: $h^{2} + 4 h - 12$.

Factor: $k^{2} + k - 20$.

Factor: $z^{2} - 4 z - 5$.

Factor: $x^{2} - 4 x - 12$.

Factor: $y^{2} - y - 20$.

Factor: $q^{2} - 2 q - 15$.

Factor: $r^{2} - 3 r - 40$.

Factor: $s^{2} - 3 s - 10$.

Factor: $y^{2} - 6 y + 15$.

Factor: $m^{2} + 4 m + 18$.

Factor: $n^{2} - 10 n + 12$.

Factor: $2 x + x^{2} - 48$.

Factor: $9 m + m^{2} + 18$.

Factor: $−7 n + 12 + n^{2}$.

Factor: $x^{2} + 12 x y + 36 y^{2}$.

Factor: $u^{2} + 11 u v + 28 v^{2}$.

Factor: $x^{2} + 13 x y + 42 y^{2}$.

Factor: $r^{2} - 8 r s - 9 s^{2}$.

Factor: $a^{2} - 11 a b + 10 b^{2}$.

Factor: $m^{2} - 13 m n + 12 n^{2}$.

Factor: $u^{2} - 9 u v - 12 v^{2}$.

Factor: $x^{2} - 7 x y - 10 y^{2}$.

Factor: $p^{2} + 15 p q + 20 q^{2}$.

Factor each trinomial of the form $x^{2} + b x + c$.

$x^{2} + 4 x + 3$

Factor each trinomial of the form $x^{2} + b x + c$.

$m^{2} + 12 m + 11$

Factor each trinomial of the form $x^{2} + b x + c$.

$a^{2} + 9 a + 20$

Factor each trinomial of the form $x^{2} + b x + c$.

$p^{2} + 11 p + 30$

Factor each trinomial of the form $x^{2} + b x + c$.

$n^{2} + 19 n + 48$

Factor each trinomial of the form $x^{2} + b x + c$.

$a^{2} + 25 a + 100$

Factor each trinomial of the form $x^{2} + b x + c$.

$x^{2} - 8 x + 12$

Factor each trinomial of the form $x^{2} + b x + c$.

$y^{2} - 18 y + 45$

Factor each trinomial of the form $x^{2} + b x + c$.

$x^{2} - 8 x + 7$

Factor each trinomial of the form $x^{2} + b x + c$.

$p^{2} + 5 p - 6$

Factor each trinomial of the form $x^{2} + b x + c$.

$y^{2} - 6 y - 7$

Factor each trinomial of the form $x^{2} + b x + c$.

$x^{2} - x - 12$

Factor each trinomial of the form $x^{2} + b x + c$.

$a^{2} - 3 a - 28$

Factor each trinomial of the form $x^{2} + b x + c$.

$w^{2} - 5 w - 36$

Factor each trinomial of the form $x^{2} + b x + c$.

$x^{2} + x + 5$

Factor each trinomial of the form $x^{2} + b x + c$.

$8 - 6 x + x^{2}$

Factor each trinomial of the form $x^{2} + b x + c$.

$x^{2} - 12 - 11 x$

Factor each trinomial of the form $x^{2} + b x y + c y^{2}$. If the trinomial cannot be factored, answer “Prime.”

$p^{2} + 3 p q + 2 q^{2}$

Factor each trinomial of the form $x^{2} + b x y + c y^{2}$. If the trinomial cannot be factored, answer “Prime.”

$r^{2} + 15 r s + 36 s^{2}$

Factor each trinomial of the form $x^{2} + b x y + c y^{2}$. If the trinomial cannot be factored, answer “Prime.”

$m^{2} - 12 m n + 20 n^{2}$

Factor each trinomial of the form $x^{2} + b x y + c y^{2}$. If the trinomial cannot be factored, answer “Prime.”

$x^{2} - 2 x y - 80 y^{2}$

Factor each trinomial of the form $x^{2} + b x y + c y^{2}$. If the trinomial cannot be factored, answer “Prime.”

$m^{2} - 64 m n - 65 n^{2}$

Factor each trinomial of the form $x^{2} + b x y + c y^{2}$. If the trinomial cannot be factored, answer “Prime.”

$a^{2} + 5 a b - 24 b^{2}$

Factor each trinomial of the form $x^{2} + b x y + c y^{2}$. If the trinomial cannot be factored, answer “Prime.”

$x^{2} - 3 x y - 14 y^{2}$

Factor each trinomial of the form $x^{2} + b x y + c y^{2}$. If the trinomial cannot be factored, answer “Prime.”

$m^{2} - 5 m n + 30 n^{2}$

Factor each expression.

$u^{2} - 12 u + 36$

Factor each expression.

$x^{2} - 14 x - 32$

Factor each expression.

$r^{2} - 20 r s + 64 s^{2}$

Factor each expression.

$k^{2} + 34 k + 120$

Factor each expression.

$y^{2} + 10 y + 15$

Factor each expression.

$m^{2} + m n - 56 n^{2}$

Factor each expression.

$u^{2} - 17 u v + 30 v^{2}$

Factor each expression.

$c^{2} - 8 c d + 26 d^{2}$

Consecutive integers Deirdre is thinking of two consecutive integers whose product is 56. The trinomial $x^{2} + x - 56$ describes how these numbers are related. Factor the trinomial.

Many trinomials of the form $x^{2} + b x + c$ factor into the product of two binomials $\left(x + m\right) \left(x + n\right)$. Explain how you find the values of m and n.

Will factored $x^{2} - x - 20$ as $\left(x + 5\right) \left(x - 4\right)$. Bill factored it as $\left(x + 4\right) \left(x - 5\right)$. Phil factored it as $\left(x - 5\right) \left(x - 4\right)$. Who is correct? Explain why the other two are wrong.