Question

1. which expression is a factor of $10z^2 - 120z + 320$?

a. $z - 32$
b. $z + 4$
c. $z - 8$
d. $z + 16$

open - ended

1. the expression $3p^2 - 15p - 72$ can be written in factored form $f(p + 3)(p + k)$, where $f$ and $k$ represent two different numbers. what is the value of $f$ and $k$?

$f = $
$k = $

1. a factorys storage capacity is modeled by the expression $2m^2 - 24m + 72$, where $m$ is the maximum load variable. the efficiency expert needs the expression in its completely factored form. write an expression to represent the capacity factored completely.

1. a contractor is installing a custom rectangular patio stone. the area of the stone is given by the expression $s^2 - 7s - 30$ square feet, where $s$ is a variable length. write two binomial factors that represent the length and width of the patio stone.

1. the area of a rectangular poster board is modeled by the expression $p^2 + 15p + 56$ square inches. write two binomial factors that represent the length and width of the poster board.

1. the area of the rectangular base of a new storage container is modeled by the expression $7b^2 - 70b + 175$ square meters. a factor manager needs to factor the expression completely to determine the dimensions. write an expression to represent the area factored completely.

Explanation:

Step1: Factor out GCF of Q6

$10z^2 - 120z + 320 = 10(z^2 - 12z + 32)$

Step2: Factor quadratic of Q6

$z^2 - 12z + 32 = (z-8)(z-4)$

Step3: Match factor to options of Q6

Compare to given options.

Step4: Factor out GCF of Q7

$3p^2 -15p -72 = 3(p^2 -5p -24)$

Step5: Factor quadratic of Q7

$p^2 -5p -24 = (p+3)(p-8)$

Step6: Identify f and k of Q7

Match to $f(p+3)(p+k)$.

Step7: Factor out GCF of Q8

$2m^2 -24m +72 = 2(m^2 -12m +36)$

Step8: Factor perfect square of Q8

$m^2 -12m +36 = (m-6)^2$

Step9: Factor quadratic of Q9

$s^2 -7s -30 = (s-10)(s+3)$

Step10: Factor quadratic of Q10

$p^2 +15p +56 = (p+7)(p+8)$

Step11: Factor out GCF of Q11

$7b^2 -70b +175 =7(b^2 -10b +25)$

Step12: Factor perfect square of Q11

$b^2 -10b +25 = (b-5)^2$

Answer:

1. C. $z - 8$
2. $f=3$, $k=-8$
3. $2(m-6)^2$
4. $(s-10)$ and $(s+3)$
5. $(p+7)$ and $(p+8)$
6. $7(b-5)^2$