Factor the following expression.
2 x squared plus 7 x minus 30
(1 point)
Responses
left parenthesis 2 x minus 5 right parenthesis left parenthesis x plus 6 right parenthesis
Image with alt text: left parenthesis 2 x minus 5 right parenthesis left parenthesis x plus 6 right parenthesis
left parenthesis 2 x minus 5 right parenthesis left parenthesis x minus 6 right parenthesis
Image with alt text: left parenthesis 2 x minus 5 right parenthesis left parenthesis x minus 6 right parenthesis
left parenthesis 2 x plus 5 right parenthesis left parenthesis x minus 6 right parenthesis
Image with alt text: left parenthesis 2 x plus 5 right parenthesis left parenthesis x minus 6 right parenthesis
left parenthesis 2 x plus 5 right parenthesis left parenthesis x plus 6 right parenthesis
Image with alt text: left parenthesis 2 x plus 5 right parenthesis left parenthesis x plus 6 right parenthesis
The correct factorization of the expression 2x^2 + 7x - 30 is:
(2x - 5)(x + 6)
To factor the expression 2x^2 + 7x - 30, we need to find two numbers that multiply to -60 and add up to 7.
The factors of -60 are: (-1, 60), (-2, 30), (-3, 20), (-4, 15), (-5, 12), (-6, 10).
Out of these pairs, the numbers that add up to 7 are (-5, 12).
So we can rewrite the middle term of the expression as 7x = -5x + 12x.
Now, let's factor by grouping:
2x^2 - 5x + 12x - 30
Taking the common factors from the first two terms and last two terms:
x(2x - 5) + 6(2x - 5)
Now we can see that we have a common factor, which is (2x - 5).
Factoring out (2x - 5):
(2x - 5)(x + 6)
Therefore, the factored form of the expression 2x^2 + 7x - 30 is:
(2x - 5)(x + 6)