What is the factored form of x^2 - 4x - 32?

What is the factored form of x^2 - 4x - 32?

• A. (x + 8)(x - 4)
• B. (x - 4)(x + 8)
• C. (x - 8)(x + 4)
• D. (x + 4)(x + 8)

Answer: (C)

To factor a quadratic with a leading coefficient of 1, find two numbers that multiply to the constant term and add to the middle coefficient. Here, we want two numbers that multiply to -32 and add to -4. Those numbers are -8 and 4. Rewriting -4x as -8x + 4x and factoring by grouping gives x^2 - 8x + 4x - 32 = x(x - 8) + 4(x - 8) = (x - 8)(x + 4). The order of the factors doesn’t matter, so (x - 8)(x + 4) is the correct factored form. Other pairings would produce a different middle term (for example, (x + 8)(x - 4) gives +4x, and (x + 4)(x + 8) gives +12x), which don’t match the original expression.

To factor a quadratic with a leading coefficient of 1, find two numbers that multiply to the constant term and add to the middle coefficient. Here, we want two numbers that multiply to -32 and add to -4. Those numbers are -8 and 4. Rewriting -4x as -8x + 4x and factoring by grouping gives x^2 - 8x + 4x - 32 = x(x - 8) + 4(x - 8) = (x - 8)(x + 4). The order of the factors doesn’t matter, so (x - 8)(x + 4) is the correct factored form. Other pairings would produce a different middle term (for example, (x + 8)(x - 4) gives +4x, and (x + 4)(x + 8) gives +12x), which don’t match the original expression.