Question

Which of the binomials below is a factor of this trinomial?

-2x^2 - 16x + 40

A. x - 5
B. x + 10
C. x - 10
D. x + 5

Answer 1

Take a polynomial function f(x) of degree 2 or more.
If a binomial x - a is a factor of f(x), then f(a) = 0.

Answer 2

uuhhhh

Answer 3

Now look at the options.
For binomial x - 5, a = 5
For binomial x + 10, a = -10
Do the same for the other two options.
Then evaluate the polynomial at each a.
If the polynomial evaluates to zero, that is the factor.

Answer 4

Here is another way of explaining this.
Look at each option and compare it with x - a.

Answer 5

i still do not understand

Answer 6

A: x - 5 compare to x - a; a = 5
B: x + 10 compared to x - a: a = -10
C: x - 10 compared to x - a: x = 10
D: x + 5 compared to x - a: a = -5

Do you understand it so far?

Answer 7

not really

Answer 8

You need to have a binomial in the form x - a, where a number.

Answer 9

You must have x followed by a subtraction, then a number.

Answer 10

Look at option A: x - 5
Since you already have x followed by a subtraction, then the number 5, then for option A, which is x - 5, you can see that a = 5.

Answer 11

Option B has x + 10.
In this case, x is followed by an addition, but we need the form x - a, so we write
x + 10 as x - (-10)
This hows that in this case, a = -10

Answer 12

We need each option to be in the form x - a

A. x - 5 = x - a, so a = 5
B. x + 10 = x - (-10) = x - a, so a = -10
C. x - 10 = x - a, so a = 10
D. x + 5 = x - (-5) = x - a, so a = -5

Answer 13

Now we evaluate the given polynomial at each value of a.
If it evaluates to zero, then that is the option that is a factor.

Answer 14

A. a = 5

-2x^2 - 16x + 40 = -2(5)^2 - 16(5) + 40 = -50 - 80 + 40 = -90
It does not evaluate to zero, so this is not it.

B. a = -10

-2x^2 - 16x + 40 = -2(-10)^2 - 16(-10) + 40 = -200 + 160 + 40 = 0
It does evaluate to zero, so this is it.

C. a = 10

-2x^2 - 16x + 40 = -2(10)^2 - 16(10) + 40 = -200 - 160 + 40 = -320
It does not evaluate to zero, so this is not it.

D. a = -5

-2x^2 - 16x + 40 = -2(-5)^2 - 16(-5) + 40 = -50 + 80 + 40 = 70
It does not evaluate to zero, so this is not it.