Question

Can someone help my with this problem
1. Which binomial is a factor of the quadratic below?
4x2 + 23x + 15

A. 4x + 3

B. 2x + 5

C. x + 3

D. 4x + 5

Answer 1

The best way that I can think of is to find the x intercept of each binomial. And then find the x intercepts of the quadratic. If one intercept of the quadratic matches up with an intercept on a binomial then that means it is divisible.

Answer 2

Would you like me to do it as an example?

Answer 3

Yes, please

Answer 4

Do you know how to find the x intercepts of a quadratic?
I will just get them off a calculator if you do

Answer 5

No I don't

Answer 6

Okay, I will do them

Answer 7

are you still there riddle?

Answer 8

riddell sorry typo

Answer 9

4x^2 + 23x + 15

There are a few ways. This is a relatively easy function to find the intercepts and in the process, you find the two factors; one of which is a binomial that is listed.

I will use the ac b method.
A quadratic is in the form ax^2 + bx + c
So a=4 b=23 and c=15 in this particular function

In the acb method you multiply a by c to give a, let's say, target number:
a=4 c=15 so a*c = 60

The second step is to try and find two numbers that multiply together to give the answer to ac (60) and add together to give c.
There is a little bit of trial and error involved here but you will get better at it with practice.
You just have to keep trying numbers so first I will try 18 and 5.

18 + 5 = 23 so that works,
18*5 = 90 which doesn't work.

Now using these results you choose two more numbers. I know that they are 20 and 3. A tip is that if you want the multiplication number to be smaller then make the two numbers that you use have a higher difference.

20 + 3 = 23 so that works,
20 * 3 = 60 which also works.

So our two numbers that we need to use are 20 and 3.
4x^2 + 23x + 15 (just bring the quadratic down the page so it's easier to read)

Now with our two numbers we can break up the middle term into two parts:
4x^2 + 20x + 3x + 15

As a side note: It is possible to get the order wrong: 4x^2 + 3x + 20x + 15 but we can see that 4 and 3 have no common factors (other than 1) so it works better the other way.

And this makes it very easy to factorise the remaining parts, therefore finding the factors and which polynomial it is divisible by.

= 4x^2 + 20x + 3x + 15
= 4x (x + 5) + 3 (x + 5)
= (x + 5) (4x + 3)

So we can see that one of the factors is 4x + 3. :)

Answer 10

Thank you so much!

Answer 11

You are welcome

Answer 12

I have other problems can I show them to you?

Answer 13

Were you the one that did the big long list of them? :P

Answer 14

it was 7 question, yes

Answer 15

Have a go at one yourself in another question and mention me, I will have a look

Answer 16

I just saw that I had to do this and its due tomorrow

Answer 17

2. What is the greatest common monomial factor of the polynomial below?
4xy2z3 + 12x3yz4

A. 12x3y2z4

B. 4xy2z3

C. 3x2yz

D. 4xyz3

Answer 18

3. Which binomial is a factor of the quadratic below?
3x2 + 13x + 4

A. 3x + 4

B. x + 1

C. x + 3

D. 3x + 1 *

Answer 19

http://www.wolframalpha.com/input/?i=4xy2z3+%2B+12x3yz4

Have a look at this site. Scroll down to other forms and it will have a factorised form there for you