Questions: Decide which is the correct factored form of the polynomial. 8 y^2+65 y-63 Choose the correct factored form. A. (2 y-7)(4 y+9) B. (8 y+7)(y-9) C. (8 y-7)(y+9) D. (2 y+9)(4 y-7)

Solution Steps

To determine the correct factored form of the polynomial \(8y^2 + 65y - 63\), we can expand each of the given options and see which one matches the original polynomial.

We start with the polynomial given in the problem: \[ 8y^2 + 65y - 63 \]

We expand each of the given options to see which one matches the original polynomial.

\[ (2y - 7)(4y + 9) = 2y \cdot 4y + 2y \cdot 9 - 7 \cdot 4y - 7 \cdot 9 = 8y^2 + 18y - 28y - 63 = 8y^2 - 10y - 63 \]

\[ (8y + 7)(y - 9) = 8y \cdot y + 8y \cdot (-9) + 7 \cdot y + 7 \cdot (-9) = 8y^2 - 72y + 7y - 63 = 8y^2 - 65y - 63 \]

\[ (8y - 7)(y + 9) = 8y \cdot y + 8y \cdot 9 - 7 \cdot y - 7 \cdot 9 = 8y^2 + 72y - 7y - 63 = 8y^2 + 65y - 63 \]

\[ (2y + 9)(4y - 7) = 2y \cdot 4y + 2y \cdot (-7) + 9 \cdot 4y + 9 \cdot (-7) = 8y^2 - 14y + 36y - 63 = 8y^2 + 22y - 63 \]

We compare the expanded forms with the original polynomial \(8y^2 + 65y - 63\).

• Option A: \(8y^2 - 10y - 63\) (does not match)
• Option B: \(8y^2 - 65y - 63\) (does not match)
• Option C: \(8y^2 + 65y - 63\) (matches)
• Option D: \(8y^2 + 22y - 63\) (does not match)

Final Answer