7.3 Factor Trinomials of the Form ax 2 +bx+c

Before you get started, take this readiness quiz.

Find the GCF of $45 p^{2} \text{and} 30 p^{6}$.
If you missed this problem, review the reference.

Multiply $\left(3 y + 4\right) \left(2 y + 5\right)$.
If you missed this problem, review the reference.

Combine like terms $12 x^{2} + 3 x + 5 x + 9$.
If you missed this problem, review the reference.

Identify the best method to use to factor each polynomial.

1. ⓐ $6 y^{2} - 72$
2. ⓑ $r^{2} - 10 r - 24$
3. ⓒ $p^{2} + 5 p + p q + 5 q$

Identify the best method to use to factor each polynomial:

1. ⓐ $4 y^{2} + 32$
2. ⓑ $y^{2} + 10 y + 21$
3. ⓒ $y z + 2 y + 3 z + 6$

Identify the best method to use to factor each polynomial:

1. ⓐ $a b + a + 4 b + 4$
2. ⓑ $3 k^{2} + 15$
3. ⓒ $p^{2} + 9 p + 8$

Factor completely: $2 n^{2} - 8 n - 42$.

Factor completely: $4 m^{2} - 4 m - 8$.

Factor completely: $5 k^{2} - 15 k - 50$.

Factor completely: $4 y^{2} - 36 y + 56$.

Factor completely: $3 r^{2} - 9 r + 6$.

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

Factor completely: $4 u^{3} + 16 u^{2} - 20 u$.

Factor completely: $5 x^{3} + 15 x^{2} - 20 x$.

Factor completely: $6 y^{3} + 18 y^{2} - 60 y$.

Factor completely: $2 a^{2} + 5 a + 3$.

Factor completely: $4 b^{2} + 5 b + 1$.

Factor completely: $8 x^{2} - 14 x + 3$.

Factor completely: $10 y^{2} - 37 y + 7$.

Factor completely: $8 a^{2} - 3 a - 5$.

Factor completely: $6 b^{2} - b - 15$.

Factor completely: $18 x^{2} - 3 x - 10$.

Factor completely: $30 y^{2} - 53 y - 21$.

Factor completely: $15 n^{3} - 85 n^{2} + 100 n$.

Factor completely: $56 q^{3} + 320 q^{2} - 96 q$.

Factor: $6 x^{2} + 13 x + 2$.

Factor: $4 y^{2} + 8 y + 3$.

Factor: $20 h^{2} + 13 h - 15$.

Factor: $6 g^{2} + 19 g - 20$.

Factor: $10 t^{2} + 19 t - 15$.

Factor: $3 u^{2} + 8 u + 5$.

Factor: $16 x^{2} - 32 x + 12$.

Factor: $18 w^{2} - 39 w + 18$.

Identify the best method to use to factor each polynomial.

1. ⓐ $10 q^{2} + 50$
2. ⓑ $a^{2} - 5 a - 14$
3. ⓒ $u v + 2 u + 3 v + 6$

Identify the best method to use to factor each polynomial.

1. ⓐ $x^{2} + 4 x - 21$
2. ⓑ $a b + 10 b + 4 a + 40$
3. ⓒ $6 c^{2} + 24$

Factor completely.

$5 x^{2} + 35 x + 30$

Factor completely.

$2 z^{2} - 2 z - 24$

Factor completely.

$7 v^{2} - 63 v + 56$

Factor completely.

$p^{3} - 8 p^{2} - 20 p$

Factor completely.

$3 m^{3} - 21 m^{2} + 30 m$

Factor completely.

$5 x^{4} + 10 x^{3} - 75 x^{2}$

Factor.

$2 t^{2} + 7 t + 5$

Factor.

$11 x^{2} + 34 x + 3$

Factor.

$4 w^{2} - 5 w + 1$

Factor.

$6 p^{2} - 19 p + 10$

Factor.

$4 q^{2} - 7 q - 2$

Factor.

$4 p^{2} + 17 p - 15$

Factor.

$16 x^{2} - 32 x + 16$

Factor.

$30 q^{3} + 140 q^{2} + 80 q$

Factor.

$5 n^{2} + 21 n + 4$

Factor.

$9 z^{2} + 15 z + 4$

Factor.

$4 k^{2} - 16 k + 15$

Factor.

$5 s^{2} - 9 s + 4$

Factor.

$6 y^{2} + y - 15$

Factor.

$2 n^{2} - 27 n - 45$

Factor.

$3 x^{2} + 5 x + 4$

Factor.

$60 y^{2} + 290 y - 50$

Factor.

$48 z^{3} - 102 z^{2} - 45 z$

Factor.

$16 s^{2} + 40 s + 24$

Factor.

$48 y^{2} + 12 y - 36$

Factor.

$12 y^{2} - 29 y + 14$

Factor.

$a^{2} - a - 20$

Factor.

$6 n^{2} + 5 n - 4$

Factor.

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

Factor.

$13 z^{2} + 39 z - 26$

Factor.

$x^{2} + 3 x - 28$

Factor.

$3 p^{2} + 21 p$

Factor.

$6 r^{2} + 30 r + 36$

Factor.

$24 n^{2} + 20 n + 4$

Factor.

$x^{2} + 2 x - 24$

Height of a toy rocket The height of a toy rocket launched with an initial speed of 80 feet per second from the balcony of an apartment building is related to the number of seconds, t, since it is launched by the trinomial $−16 t^{2} + 80 t + 96$. Completely factor the trinomial.

List, in order, all the steps you take when using the “ac” method to factor a trinomial of the form $a x^{2} + b x + c .$

What are the questions, in order, that you ask yourself as you start to factor a polynomial? What do you need to do as a result of the answer to each question?