Question
Which is a common factor of 6d^2 + 5d - 6
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Answers
GPT 3.5
To find the common factor of the quadratic expression 6d^2 + 5d - 6, we need to factor the expression using the AC method or by inspection.
1. Factor the quadratic expression:
The quadratic expression is in the form of ax^2 + bx + c.
The factors of ac = 6(-6) = -36.
To find two numbers that multiply to -36 and add up to 5:
The numbers are 9 and -4.
9 * (-4) = -36 and 9 + (-4) = 5.
Therefore, we can rewrite the quadratic expression as:
6d^2 + 9d - 4d - 6
2. Factor by grouping:
(6d^2 + 9d) + (-4d - 6)
3d(2d + 3) - 2(2d + 3)
Factor out the common factor "2d + 3":
(3d - 2)(2d + 3)
Therefore, the common factor of the quadratic expression 6d^2 + 5d - 6 is (3d - 2).
1. Factor the quadratic expression:
The quadratic expression is in the form of ax^2 + bx + c.
The factors of ac = 6(-6) = -36.
To find two numbers that multiply to -36 and add up to 5:
The numbers are 9 and -4.
9 * (-4) = -36 and 9 + (-4) = 5.
Therefore, we can rewrite the quadratic expression as:
6d^2 + 9d - 4d - 6
2. Factor by grouping:
(6d^2 + 9d) + (-4d - 6)
3d(2d + 3) - 2(2d + 3)
Factor out the common factor "2d + 3":
(3d - 2)(2d + 3)
Therefore, the common factor of the quadratic expression 6d^2 + 5d - 6 is (3d - 2).