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what does it mean by, one factor is?
- Thread starter jwk811
- Start date
4) Factor completely: x2 + 10x + 24. One factor is:
A) x + 2 B) x + 3 C) x + 4
D) x + 8 E) None of these
factors are:
x * x + 5 * 2 * x + 3 * 2 * 4
The answer is C: x + 4
How do you do this, I've looked up factoring and can't figure it out
The basic way you do this is by eye. you note that (x+a)(x+b) = x2 + (a+b)x + ab and you solve for a and b
here you have a+b = 10, ab=24, and you recognize that this is solved by a=6, b=4 so
x2 + 10x + 24 = (x+6)(x+4) and (x+4) is the factor on your multiple choice list.
The other way to do this is to use the quadratic formula to solve for the roots r1 and r2 and know that your polynomial will be (x-r1)(x-r2).
You'll note here the roots are -6 and -4.
4) Factor completely: x^2 + 10x + 24.
One factor is:
A) x + 2
B) x + 3
C) x + 4
D) x + 8
E) None of these
The answer is C: x + 4
jwk811, I am correcting you again to use the "^" as in "x^2" as I typed for exponents. "x2" is not used for "x squared."
And go ahead and put those answer choices on separate lines, instead of the congested way you presented it.
(Feel free to add additional vertical spaces.)
iamamadeus
New member
- Joined
- Dec 1, 2013
- Messages
- 4
Jwk,
When you factor stuff like x2 + 10x + 24,
it is not the same as factoring each part separately.
So, x*x + 10*x + 6*4 doesn't work.
What we are trying to do is represent x2 + 10x + 24 as (x + )(x + ).
For example:
(x + 1)*(x + 3) = x*x + 1*x + 3*x + 3*1 = x2 + x + 3x + 3 = x2 + 4x + 3
So we can say that x + 1 and x + 3 are factors of x2 + 4x + 3.
Now, you have to reverse-engineer the thing, because your question gives you the polynomial as x2 + 10x + 24, not as (x + something)(x + something)
You need to find two numbers that add up to 10 and whose product equals 24.
1 * 24
2 * 12
3 * 8
4 * 6
are all the possible options
4 + 6 = 10 so that works.
so x2 + 10x + 24 = (x + 4)(x + 6)
Hence, x + 4 and x + 6 are the factors.
Hope you will find it helpful,
Amadeus
When you factor stuff like x2 + 10x + 24,
it is not the same as factoring each part separately.
So, x*x + 10*x + 6*4 doesn't work.
What we are trying to do is represent x2 + 10x + 24 as (x + )(x + ).
For example:
(x + 1)*(x + 3) = x*x + 1*x + 3*x + 3*1 = x2 + x + 3x + 3 = x2 + 4x + 3
So we can say that x + 1 and x + 3 are factors of x2 + 4x + 3.
Now, you have to reverse-engineer the thing, because your question gives you the polynomial as x2 + 10x + 24, not as (x + something)(x + something)
You need to find two numbers that add up to 10 and whose product equals 24.
1 * 24
2 * 12
3 * 8
4 * 6
are all the possible options
4 + 6 = 10 so that works.
so x2 + 10x + 24 = (x + 4)(x + 6)
Hence, x + 4 and x + 6 are the factors.
Hope you will find it helpful,
Amadeus