Question

1 which of the following shows the polynomial factored complete? $4y^4 - 16y$ a $4y(y - 2)(y + 2)$ b $y(2y - 4)(2y + 4)$ c $4y(y + 2)(y + 2)$ d $4y(y - 2)(y - 2)$ 2 which of the following is a factor of the polynomial $4x^2 - 20x + 25$ a $(2x + 5)$ b $(2x - 5)$ c $(5 - 2x)$ d $(5 + 2x)$ 3 sophie is making a friendship bracelet and has a bag containing 20 beads of different colors. there are 10 purple beads, 6 green beads and 4 silver beads. if sophie randomly selects two beads from the bag without replacing the first bead, what is the probability that the first bead is silver? a $\frac{1}{2}$ b $\frac{2}{19}$ c $\frac{1}{5}$ d $\frac{2}{5}$ 4 a survey was conducted with a 150 randomly selected high school students to see if they play a sport or play an instrument. what is the probability that a randomly selected student only plays a sport? | play instrument | do not play instrument | total | |---|---|---| | play sport | 25 | 15 | 40 | | do not play sport | 70 | 40 | 110 | | total | 95 | 55 | 150 | a $\frac{1}{2}$ b $\frac{13}{30}$ c $\frac{1}{6}$ d $\frac{7}{15}$ 5 factor the polynomial completely $81 - 16x^4$ a $(9 + 4x^2)(9 - 4x^2)$ b $(9 + 4x^2)(3 + 2x)(3 - 2x)$ c $(3 - 2x)^4$ d $(3 + 2x)^2(3 - 2x)^2$ 6 which of the following is not a factor of the polynomial $5b^2 - 20$ a $5(b^2 - 4)$ b $(b - 2)$ c $(b + 4)$ d $(b + 2)$

Explanation:

Problem 1

Step1: Factor out GCF

Factor $4y$ from $4y^3-16y$:
$4y(y^2 - 4)$

Step2: Factor difference of squares

Factor $y^2-4$ as $(y-2)(y+2)$:
$4y(y-2)(y+2)$

Problem 2

Step1: Recognize perfect square trinomial

$4x^2-20x+25=(2x-5)^2$

Step2: Identify matching factor

The factor is $(2x-5)$

Problem 3

Step1: Count total and silver beads

Total beads: $10+6+4=20$, silver beads: $4$

Step2: Calculate probability

Probability first bead is silver: $\frac{4}{20}=\frac{1}{5}$

Problem 4

Step1: Find "only plays sport" count

Only plays sport = Play sport - Play both: $95-70=25$

Step2: Calculate probability

Total students: $150$, probability: $\frac{25}{150}=\frac{1}{6}$

Problem 5

Step1: Factor difference of squares

$81-16x^4=(9+4x^2)(9-4x^2)$

Step2: Factor remaining difference of squares

Factor $9-4x^2=(3+2x)(3-2x)$:
$(9+4x^2)(3+2x)(3-2x)$

Problem 6

Step1: Factor the polynomial

$5b^2-20=5(b^2-4)=5(b-2)(b+2)$

Step2: Identify non-factor

The non-factor is $(b+4)$

Answer:

1. A. $4y(y-2)(y+2)$
2. B. $(2x - 5)$
3. A. $\frac{1}{5}$
4. C. $\frac{1}{6}$
5. B. $(9+4x^2)(3+2x)(3-2x)$
6. C. $(b + 4)$