Question

1. $3x^2 + 26x + 35$

a. $(x + 5)(3x + 7)$
b. $(3x + 7)(x - 5)$
c. $(3x + 5)(x - 7)$
d. $(3x + 5)(x + 7)$

1. use factoring. what is the solution of $2x^2 = 14x + 60$?

a. $x = -10, x = 3$
b. $x = -15, x = 4$
c. $x = 10, x = -3$
d. $x = 15, x = -4$

1. what are the interval(s) on which the function $y = x^2 - 2x - 48$ is positive?

a. $x < 6$ and $x > 8$
b. $-6 < x < 8$
c. $x > 6$ and $x < -8$
d. $6 < x < 8$
simplify the expression.

1. $(3 + i) - (2 - 2i)$

a. $1 + 3i$
b. $5 - i$
c. $4i$
d. $-1 - 3i$

1. $(i)(-7i)$

a. $7i$
b. $-7$
c. $7$
d. $-7i$

1. $(4 - i)(2 + 5i)$

a. $2(4 + 9i)$
b. $(13 + 18i)$
c. $3 + 18i$
d. $(8 + 18i)$

1. $\frac{-2 + i}{-4 - 5i}$

a. $-\frac{1}{3} + 1\frac{5}{9}i$
b. $\frac{3}{41} - \frac{14}{41}i$
c. $\frac{3}{41} - \frac{6}{41}i$
d. $\frac{13}{41} - \frac{14}{41}i$

1. $\frac{-2 - 3i}{6i}$

a. $\frac{1}{2} - \frac{1}{3}i$
b. $\frac{1}{2} + \frac{1}{3}i$
c. $-\frac{1}{2} + \frac{1}{3}i$
d. $-\frac{1}{2} + \frac{1}{3}i$

Explanation:

Question 21

Step1: Expand each option

For option a: \((x + 5)(3x + 7)=3x^2+7x + 15x+35 = 3x^2+22x + 35\) (not equal to \(3x^2+26x + 35\))

Step2: Expand option d

\((3x + 5)(x + 7)=3x^2+21x+5x + 35=3x^2+26x + 35\) (matches the given quadratic)

Question 22

Step1: Rearrange the equation

\(2x^2-14x - 60=0\), divide by 2: \(x^2 - 7x-30 = 0\)

Step2: Factor the quadratic

\(x^2 - 7x - 30=(x - 10)(x + 3)=0\), so \(x = 10\) or \(x=-3\)

Question 23

Step1: Find roots of \(y=x^2-2x - 48\)

Factor: \((x - 8)(x + 6)=0\), roots \(x = 8\) and \(x=-6\)

Step2: Analyze the parabola

Since the coefficient of \(x^2\) is positive, the parabola opens upwards. So \(y>0\) when \(x < - 6\) or \(x>8\)

Question 24

Answer:

d. \((3x + 5)(x + 7)\)