Question

Find the zeros of the polynomial function.

f(x) = x3 + 5x2 - 4x - 20

A. x = -5, x = 4

B. x = -2, x = 2

C. x = -5, x = -2, x = 2

D. x = 5, x = -2, x = 2

Answer 1

Hint:

x^3 + 5x^2 = x^2(x + 5)
-4x - 20 = -4(x + 5)

Answer 2

B

Answer 3

Well, that was definitely a guess.

Answer 4

SORRY a

Answer 5

Yet another guess. I suppose my hint was not helpful enough for you

Answer 6

Trust me. Guessing is not the way.

Answer 7

OK Explain Please

Answer 8

ok

Answer 9

wow it disappeared

Answer 10

The best way to figure it out is to factor it. The best factoring method is "factor by grouping". With factor by grouping, you factor the first two terms x^2 + 5x^2, then then last two terms -4x - 20

When you factor each pair of terms you get:

x^2(x + 5) and -4(x + 5)


Notice that x + 5 is common to both factorizations. So then you factor out x + 5 to get

(x + 5)(x^2 - 4)

Now since x^2 - 4 is a difference of squares that factors to (x + 2)(x - 2) so the complete factorization of f(x) is

f(x) = (x + 5)(x + 2)(x - 2)

Then you set f(x) = 0

0 = (x + 5)(x + 2)(x - 2)

And then set each factor equal to zero:

0 = x + 5
0 = x + 2
0 = x - 2

From there, you solve each for x.

Answer 11

x=5 x=2 x=2

Answer 12

x=-2 ast one

Answer 13

You did not solve for x.

Answer 14

i am confused

Answer 15

I find it strange that I have to do every single step for you.

Answer 16

0 = x + 5

Subtract 5 from both sides

x = -5

0 = x + 2

Subtract 2 from both sides
x = -2

0 = x - 2

Add 2 to both sides
x = 2

So x = {-5, -2, 2}

Answer 17

i did the same but the opposite way i subtracted 0 from both sides

Answer 18

Thank you

Answer 19

You have to ask yourself if it makes sense to subtract 0 from both sides. What will subtracting zero from both sides accomplish? I don't know if you are joking or not.