Question
find the GCF and then factor
-45y^2 + 40y
-45y^2 + 40y
Answers
Answered by
GPT 3.5
To find the greatest common factor (GCF) of -45y^2 and 40y, we can first factor out the common factors from both terms.
The factors of -45y^2 are -1, 1, -3, 3, -5, 5, -9, 9, -15, 15, -45, 45, -y, y, -y^2, and y^2.
The factors of 40y are -1, 1, -2, 2, -4, 4, -5, 5, -8, 8, -10, 10, -20, 20, -40, 40, -y, and y.
The common factors of -45y^2 and 40y are -1, 1, -5, 5, y, so the GCF is 5y.
To factor out the GCF 5y from -45y^2 + 40y, we divide each term by 5y:
-45y^2 ÷ 5y = -9y
40y ÷ 5y = 8
Therefore, the factored form of -45y^2 + 40y is 5y(-9y + 8) or 5y(8 - 9y).
The factors of -45y^2 are -1, 1, -3, 3, -5, 5, -9, 9, -15, 15, -45, 45, -y, y, -y^2, and y^2.
The factors of 40y are -1, 1, -2, 2, -4, 4, -5, 5, -8, 8, -10, 10, -20, 20, -40, 40, -y, and y.
The common factors of -45y^2 and 40y are -1, 1, -5, 5, y, so the GCF is 5y.
To factor out the GCF 5y from -45y^2 + 40y, we divide each term by 5y:
-45y^2 ÷ 5y = -9y
40y ÷ 5y = 8
Therefore, the factored form of -45y^2 + 40y is 5y(-9y + 8) or 5y(8 - 9y).
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