Question

which of the binomials below is a factor of this trinomial x^2-x-12
a.x-3
b.x-6
c.x+3
d.x+6

Answer 1

Do you know how to factor a binomial of this type?

Answer 2

no

Answer 3

I'll show you, then you'll be able to answer the question.

Answer 4

thank you

Answer 5

You have a trinomial of the type
\(x^2 + ax + b\)
a and b are just numbers, but notice that there is no number with the x^2.

Answer 6

The first rule of factoring is always try to factor a common factor out of all terms.

Answer 7

In your case, the coefficients (the number parts of the terms) are 1, -1, and -12.
They don't have a common factor, so there is no common factor we can take out.

Answer 8

That means we start factoring.

Answer 9

okay how do you factor

Answer 10

This is the procedure.
Look at the last number.
In this case it's -12.
You need to find two numbers that multiply to -12.
Also, these two numbers must add to the middle number, -1.

Answer 11

Here are all the sets of two integers whose product is -12:
-1 * 12 = -12
-12 * 1 = -12
-2 * 6 = -12
-6 * 2 = -12
-3 * 4 = -12
-4 * 3 = -12
Ok so far?

Answer 12

Im thinking it is B?

Answer 13

You mean B from my choices or B from the problem's choices?

Answer 14

yes i understand.. thank you for helping. B from the problem

Answer 15

No. It isn't. Follow me to the end of my explanation. It's almost done.
Then you'll choose the correct choice.

Answer 16

okay thanks

Answer 17

You saw my listing of 6 different sets of integers that multiply to -12, right?

Answer 18

yes

Answer 19

Now you need to choose the correct one.
The correct one is the one in which the two numbers add to the middle coefficient.
The middle coefficient is -1.
Of all 6 choices I gave you, which one has two numbers that add to -1?

Answer 20

-4+3

Answer 21

-1 + 12 = 11
-12 + 1 = -11
-2 + 6 = 4
-6 + 2 = -4
-3 + 4 = 1
-4 + 3 = -1

Answer 22

Exactly. That's correct.
Now all you need to do is set up two sets of parentheses.
( )( )

Answer 23

Then insert x in the left side of each one
(x )(x )

Finally insert each number in the right side of each parentheses.

(x - 4)(x + 3)

We need to call 3, +3 to show an operation.

Answer 24

What is a polynomial?¿

Answer 25

That's it.
That is how you factor a trinomial of the type
\(x^2 + ax + b\)

In summary:
1. Try to factor a common factor.
2. Find two numbers that multiply to b and add to a.
3. Call these numbers p and q.
4. The factorization is (x + p)(x + q)

Answer 26

A ploynomial is a sum of terms.
Each term is a number multiplied by 0 or more variables.

Answer 27

Thank you for your help. Im doing apex thats why i needed help.So the answer will be C

Answer 28

A monomial is one term.
A binomial is two-term polynomial.
A trinomial is a three-term polynomial.

Answer 29

x + 3 is correct.

Answer 30

I love you

Answer 31

Thank you so much

Answer 32

You're welcome.
Keep studying and asking questions.
That's how you learn.

Answer 33

When a trinomial is factored as (x+m)(x+n) what is the sum of m and n?

Answer 34

Look at my summary above.
I'll copy it below to make it easier to see.

Answer 35

Factor trinomial \(x^2 + ax + b\)

Procedure:
1. Try to factor a common factor.
2. Find two numbers that multiply to b and add to a.
3. Call these numbers p and q.
4. The factorization is (x + p)(x + q)

Answer 36

Notice that the numbers you call m and n, I called p and q.

Answer 37

so it would be the coefficient term?

Answer 38

m and n are numbers that add to the middle coefficient of the trinomial.

Answer 39

The sum of m and n is the coefficient of the x-term.

Answer 40

so it would be the constant term or the degree of the trinomial

Answer 41

No.
Not the constant term.
The constant term is the last number that has no variable.
Also, it's not the degree.
The degree is the exponent of x, which in this case is 2.

Answer 42

thank you

Answer 43

Once again, the sum of m and n is the coefficient of the x-term.

Answer 44

You're welcome.