Question

write a polynomial in standard form with the following zeros: -3, 2, and 5

Answer 1

First let's put them into their factorizations. Those numbers alone mean that x = -3, x = 2 and x = 5. But if we work backwards from factoring we would have (x + 3) = 0, (x - 2) = 0, and (x - 5) = 0. Those are the roots now of the polynomial. Working backwards still we have (x + 3)(x - 2)(x - 5). Multiply all those together by FOIL-ing a couple of times and you will have you answer. BTW, you might should know that if a polynomial has 3 roots, it is an x^3 equation. The number of roots a polynomial has defines the degree of the polynomial. Any other questions on this or anything else, feel free to ask!

Answer 2

thank you so much! im going to try to solve it and then ill tell you my answer. when i send it, could you tell me if its right?

Answer 3

If -3, 2, and 5 are the zeroes of the polynomial, then

x = -3
x = 2
x = 5

Moving everything to the left side:
x + 3 = 0
x - 2 = 0
x - 5 = 0

By zero Product Property
(x + 3)(x - 2)(x - 5) = 0

After multiplying you end up with a cubic polynomial
f(x) = (x + 3)(x - 2)(x - 5)

Answer 4

hero, is f(x) = (x+3)(x-2)(x-5) the polynomial in standard form? or do i need to foil this
to get to the standard form? if so, how do you foil with three terms?

Answer 5

Use the distributive property rather than FOIL. This is an anti-FOIL community:

f(x) = (x(x - 2) + 3(x - 2))(x - 5)

Answer 6

where did you get the 3 on the outside of (x-2) and where did you get the x on the outside of (x-2) ?

Answer 7

From x + 3...

I'm sure you remember the distributive property:
(b + c)a = ba + ca

In this case, when you distribute (x + 3)(x - 2), you treat (x - 2) as \(a\) , then \(x\) as \(b\) and \(3\) as \(c\)

So
(x + 3)(x - 2) = x(x - 2) + 3(x - 2)

Answer 8

so, would the answer be,
x squared +x-6

Answer 9

(x + 3)(x - 2) = x(x - 2) + 3(x - 2)
= x^2 - 2x + 3x - 6
= x^2 + x - 6

Answer 10

But now you have to perform the same distributive process for
(x^2 + x - 6)(x - 5)

But this time, when you do it, show your work.

Answer 11

ok thank you ill send you my answer when im done

Answer 12

Along with your steps. I'm more interested in your steps than the answer.

Answer 13

ok

Answer 14

x(x^3+x-6) -5(x^2+x-6) distribute the x to 1st parenthesis, -5 to the second parenthesis

x^3+x^2-6x-5x^2-5x+30 combine like terms

x^3-4x^2-11x+30 the final answer

Answer 15

Interesting, you made a slight mistake at the beginning. You wrote:
x(x^3 + x - 6) - 5(x^2 + x - 6)

But you meant to write:
x(x^2 + x - 6) - 5(x^2 + x - 6)

Answer 16

oh ok i see where i did that. on my paper its copied down right. so thanks :) can i ask another math question?

Answer 17

if yes, here it is:

Divide and express the result in the form
P(x) = D(x)Q(X) + R(X)

(4x^3 + 2x^2 + 3x + 4) divided by (x+4)

Answer 18

@beachbum1996, you still here?