Algebraic factoring?

Question

I'm taking calculus this year and I've already forgotten how to factor from College Algebra! Please help!

2x^2+7x-15

Thanks in advance!

Answer 1

= 2x^2 +10x- 3x-15

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

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

Answer 2

When you are factorising you multiply the two end numbers ( 2 & -15 in your question) and then you find two factors of the number that you got (-30) that when added gives you the middle term. Then you replace the middle term with the two factors. You then factor out any common terms between the first two items and the last two items. Finally you write your result as a product of the terms outside of the brackets multiplied by the terms inside the brackets.

so 2x^2 + 7x -15
= 2x^2 +10x - 3x -15
= 2x(x+5) -3(x+5)
= (2x-3)(x+5)

Answer 3

Here is how you should do the factorisation......

2x^2+7x-15

=2x^2+10x-3x-15

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

=(2x-3)(x+5) and the sum is done.

In case u have doubts about how to proceed,here's an easy method :
First multiply the coefficients of x^2 and the constant at the end of the quadratic expression.In this case u get (2X15)= 30. Now try to split up this no into two of it's factors.
What are the possible pairs of factors in this case?They are, quite obviously (1,30), (3,10), (6,5), and (15,2).
Now, try to identify the pair (a,b) such that (a-b)=the coefficient of x, when the last term is negative OR try to identify the (a,b) such that (a+b)= coefficient of x when the last term is positive.
Here the last term was negative, so u should choose the pair (3,10) because (10-3)=7.
If you follow these steps, hopefully u will be able to factor any quadratic expression provided it has rational roots.

If you are in doubt about anything in maths, you can e-mail directly to me.I will be happy to share my knowledge with you.

Answer 4

Here u go, in ur problem find the factors of the 1st and 3rd numbers; 2,3,5, now u have to check how can u add or subtract these three numbers to get ur midde term i.e 7.

here u should take 10 and 3, i.e 2*5 and 3 so if u do +10x - 3X u get +7x and also -30X^2(+10x*-3x).

Hence, ur problem stands as
2x^2 +10x - 3x - 15
= 2x(x+5)-3(x+5)
=(2x-3)(x+5)

I hope u understood

Answer 5

the answer is (x+5)(2x - 3)

You find two numbers that add up to 7 and multiply to 2(-15), or -30. In this case, the numbers are 10 and -3. You the seven with them.

2x^2 - 3x + 10x - 15

Factor the two sides.....
x(2x - 3) + 5(2x - 3)

and take the parentheses and the x + 5 (distributive)

(x + 5)(2x - 3) and there it is

Answer 6

Factoring is a bit hit-and-miss sometimes, but here's how I would do it:

Assume that it factors into something like:

(2x + a)(x + b)

(The reason for the "2x" in one factor and the "x" in the other, is that I know that those will multiply to "2x²", which is part of the original expression)

So:
(2x + a)(x + b) = 2x² + (a+2b)x + ab

So now try to find some values for "a" and "b" so that:
(a+2b) = 7
and:
ab = –15

Answer 7

2x^2+10x-3x-15
2x(x+5)-3(x+5)
(2x-3)(x+5)


Good luck with Calc

Answer 8

(2x - 3)(x + 5)
Check
(2x)(x + 5) - 3(x + 5)
2x² + 10x - 3x - 15
2x² + 7x - 15 as required.

Answer 9

(2x-3)(x+5) is the answer

Answer 10

(2x-3)(x+5)