Question

selected response

1. which expression is equivalent to (\frac{x - 2}{x^2 + 10x - 24}) if (x

eq 2)?
a (x - 20)
b (12 - x)
c (x - 12)
d (x + 12)
constructed response

1. factor the expression completely. (625a^4 - 16b^4) show your work.

extended response

1. consider the equation (-2x^3 + 8x^2 - 9x = -9).

a. test several values to find the real - number solution of the equation. use your solution to find a binomial factor of the polynomial (p(x)) where (p(x)=0).
b. find the quadratic quotient when you divide the binomial factor in part (a) into (p(x)).
c. from parts (a) and (b), what are the real and complex solutions of (p(x)) where (p(x)=0)?

Explanation:

1.

Step1: Factor numerator

Numerator: $x^2 + 10x - 240 = (x + 20)(x - 12)$
Denominator: $x + 12$ (typo correction: original denominator likely $x + 12$ for equivalence)

Step2: Simplify expression

$\frac{(x + 20)(x - 12)}{x + 12}$ correction: If denominator is $x + 20$, then $\frac{(x + 20)(x - 12)}{x + 20} = x - 12$ correction: Original problem likely has denominator $x + 20$, so answer is $x - 12$ (Option A).

2.

Step1: Recognize difference of squares

$625a^4 - 169^4 = (25a^2)^2 - (13^2)^2$

Step2: Apply difference of squares

$=(25a^2 - 13^2)(25a^2 + 13^2)$

Step3: Factor again

$=(5a - 13)(5a + 13)(25a^2 + 169)$

3a.

Step1: Test x=3

$P(3) = -2(3)^3 + 8(3)^2 - 9(3) - 9 = -54 + 72 - 27 - 9 = 0$

Step2: Identify factor

Since $P(3)=0$, factor is $x - 3$.

3b.

Answer:

A. $x - 20$