Question

17 multiple answer 1 point solve. select all solutions. $2x^3 - 32x = 0$ 5 2i -2 0 4 2 -2i -4 18 multiple choice 1 point how many real solutions are there to the equation? $y = x^4 + 2x^2 - 8$ 2 3 4 1 clear my selection 19 fill in the blank 1 point solve by factoring. find all solutions. $4x^2 + 19x - 5 = 0$ factored form is (enter with no spaces). the solutions, from largest to smallest, are and. enter as an improper fraction in the form a/b, if applicable.

Explanation:

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Question 17

Step1: Factor out common term

$2x(x^2 - 16) = 0$

Step2: Factor difference of squares

$2x(x-4)(x+4) = 0$

Step3: Set factors to 0

$2x=0 \implies x=0$; $x-4=0 \implies x=4$; $x+4=0 \implies x=-4$
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Question 18

Step1: Substitute $u=x^2$

$y = u^2 + 2u - 8$

Step2: Factor quadratic

$(u+4)(u-2) = 0$

Step3: Solve for $u$

$u=-4$ or $u=2$

Step4: Solve for real $x$

$x^2=-4$ (no real solutions); $x^2=2 \implies x=\sqrt{2}, -\sqrt{2}$ (2 real solutions)
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Question 19

Step1: Factor quadratic

$(4x-1)(x+5) = 0$

Step2: Set factors to 0

$4x-1=0 \implies x=\frac{1}{4}$; $x+5=0 \implies x=-5$

Step3: Order solutions

Largest: $\frac{1}{4}$, Smallest: $-5$

Answer:

1. 0, 4, -4
2. 2
3. Factored form: (4x-1)(x+5); Solutions: $\frac{1}{4}$, $-5$