How would you find the Linear Factor of 2Xsquared-X-6?

Question

I know that the answer is 2X+3 but I can not figure out how to get to that answer.

Answer 1

I would use factoring by grouping.

Multiply 2 and -6, which is -12, and find the pair of factors that give a sum of -1, the coefficient of -x. The magic pair is +3 and -4.

Because +3x - 4x = -x, then expand the polynomial as 2x^2 +3x - 4x - 6.

Now factor out the x in the first pair of terms. Then factor out the -2 in the second pair of terms. At this point, you should have.............

x(2x + 3) - 2(2x + 3) which can be factored again as (x-2)(2x+3). As you can see, 2x + 3 is one of the linear factors.

Instead of factoring, you can also use synthetic division.

Hope this helps! :-)

Answer 2

2x^2 -x -6
b^2-4ac = 1-4(2)(-6) = 49 which is a perfect square with root equal to 7.
So the values of the roots are (1+/- 7)/4 = 2 or -3/2
So factors are (x-2) and (x+3/2). Now you may rewrite the answer (x+3/2) as (2x +3) because either factor when set to zero will give you x = -3/2
2x^2-x-6 = (x-2)(2x+3)

Answer 3

2x^2 - x - 6
2x^2 - 4x + 3x - 6
2x(x - 2) +3(x - 2)
(2x - 3)(x - 2)

If ax^2 + bx + c, is the general eq and a,b and c are constants... to factor this, split b into two numbers that add up to b and multiply to give the product of a and c.
In the above equation, -4 and 3 add to give -1 and multiply to give -12.

Answer 4

If one factor is in fact 2x+3, then synthetic division will give the other as (x-2). Since it comes out even, this factorization is correct.

Answer 5

I would go to yahoo answers and ask the people there how to find the answer. That is what I'd do.

Answer 6

(2x+3)(?) = 2x^2-x-6

(2x+3)(x-2) = 2x^2-x-6

So multiply by (x-2)