Factor 5x^2-13x-6
I got (5x-3)(x-2) as the answer, but I know that is wrong. Can someone please explain this to me? Thank-you.
You just need to switch the numerals and make one positive.
(5x+2)(x-3) = 5x^2-13x-6
I hope this helps. Thanks for asking.
To factor the quadratic expression 5x^2 - 13x - 6, we will use the method of factoring by grouping.
First, let's write down the expression:
5x^2 - 13x - 6
We want to split the middle term, -13x, into two terms such that their coefficients multiply to give the product of the first and last term, which is 5x^2 * (-6) = -30x^2.
To do this, we need to find two numbers whose sum is -13 and whose product is -30.
If we consider the factors of -30, we have:
-30 = 1 * (-30)
-30 = 2 * (-15)
-30 = 3 * (-10)
-30 = 5 * (-6)
Among these pairs of numbers, the pair that adds up to -13 is 2 and -15.
Now, we rewrite the -13x term as 2x - 15x:
5x^2 + 2x - 15x - 6
Next, we group the terms:
(5x^2 + 2x) + (-15x - 6)
Now, factor out the greatest common factors from each group:
x(5x + 2) - 3(5x + 2)
Notice that we have a common factor of (5x + 2) in both terms.
Now, we can factor out (5x + 2):
(5x + 2)(x - 3)
So, the factored form of 5x^2 - 13x - 6 is (5x + 2)(x - 3).