Question

Factor each expression.
6t2+7t−5
step by step

Answer 1

First, let's factor the common factor of the expression, which is 1:

1(6t^2 + 7t - 5)

Next, we need to find two numbers that multiply to -30 (the product of 6 and -5) and add up to 7 (the coefficient of the middle term). These numbers are 10 and -3.

Now, we can rewrite the middle term with 10t and -3t:

1(6t^2 + 10t - 3t - 5)

Now, we can group the terms and factor by grouping. Factor out a 2t from the first two terms and factor out a -1 from the last two terms:

1(2t(3t + 5) - 1(3t + 5))

Now, factor out the common factor of (3t + 5):

1(2t - 1)(3t + 5)

Therefore, the factored form of the expression 6t^2 + 7t - 5 is (2t - 1)(3t + 5).