Question

What polynomial has roots of -5, -4, and 1 ?

x3 - 8x2 - 11x + 20

x3 - x2 + 22x + 40

x3 + x2 - 22x - 40

x3 + 8x2 + 11x - 20

Answer 1

@mathstudent55

Answer 2

The polynomial that has roots m, n, p, is
(x - k)(x - n)(x - p)

Answer 3

Your roots are -5, -4, and 1.
You write 3 binomials, each one being x minus the root. Then multiply them together to find the polynomial.

Answer 4

Notice that your first 2 roots are negative and the binomials are written with x MINUS the root.

Answer 5

So -5 times -4 times 1?

Answer 6

First write out the 3 binomials.
Then multiply them together.

Answer 7

A binomial has to have x in it.

Answer 8

x - (-5)
x - (-4)
x - 1
The first two binomials above can be simplified since each one has two negative signs.

Answer 9

So then they change to x + 5, x + 4, and x - 1?

Answer 10

Great. So far so good.
Now you need to multiply them together.
(x + 5)(x + 4)(x - 1)

Answer 11

Before you multiply them together, you can save some time by looking at the constant term of each binomial.
The product of these 3 binomials is going to be of the form:
Ax^3 + Bx^2 + Cx + D
The D is a constant term (number only, no variable)
It comes from the product of 5, 4 and -1.
What is 5 * 4 * (-1) = ?

Answer 12

Ok so, x^3 +8x^2 -11 + 20?

Answer 13

Once again, what is 5 * 4 * (-1) = ?

Answer 14

-20*

Answer 15

That's better.
Since only one of the choices has -20 as the constant term, that has to be the answer.

Answer 16

Perfect! Thank you! I hate to be a bother but could you help me with another? You make me understand more than my teacher

Answer 17

We can check by multiplying, of course:

(x + 5)(x + 4)(x - 1) =
= (x^2 + 5x + 4x + 20)(x - 1)
= (x^2 + 9x + 20)(x - 1)
= x^3 + 9x^2 + 20x - x^2 - 9x - 20
= x^3 + 8x^2 + 11x - 20

Answer 18

Sure enough, the constant term is -20.

Answer 19

Go ahead, but pls start anew post. I'll help you there.

Answer 20

Got it!