factor 48y^2 + 82y - 70
Show me the steps and answer for this question.
To factor the polynomial 48y^2 + 82y - 70, we first need to find two numbers that multiply to -336 (the product of 48 and -70) and add up to 82 (the coefficient of the middle term).
The two numbers are 86 and -4, because 86 * -4 = -336 and 86 + (-4) = 82.
Now, we rewrite the middle term using these two numbers:
48y^2 + 86y - 4y - 70
Next, we factor by grouping:
(48y^2 + 86y) + (-4y - 70)
2y(24y + 43) - 2(2y + 35)
2y(24y + 43) - 2(2y + 35)
Finally, we factor out the greatest common factor, which is (24y + 43):
(24y + 43)(2y - 2)
So, the factored form of 48y^2 + 82y - 70 is (24y + 43)(2y - 2).
try again bot it was wrong
I apologize for the mistake in my previous response. Let's try factoring the polynomial 48y^2 + 82y - 70 correctly:
To factor the polynomial 48y^2 + 82y - 70, we need to find two numbers that multiply to 48*(-70) = -336 and add up to 82.
The two numbers are 86 and -4, because 86 * -4 = -336 and 86 + (-4) = 82.
Now, we rewrite the middle term using these two numbers:
48y^2 + 86y - 4y - 70
Then, we factor by grouping:
(48y^2 + 86y) + (-4y - 70)
2y(24y + 43) - 2(2y + 35)
2y(24y + 43) - 2(24y + 43)
(2y - 2)(24y + 43)
Therefore, the correct factored form of 48y^2 + 82y - 70 is (2y - 2)(24y + 43).