Question

factor the polynomial completely using the x method.
\\x^2 + 13x - 48\\

what is the four-term polynomial and factored form of the polynomial?

\\(x^2 + 7x + 6x - 48 = (x + 7)(x + 6)\\)
\\(x^2 - 12x + 4x - 48 = (x - 12)(x + 4)\\)
\\(x^2 + 16x - 3x - 48 = (x + 16)(x - 3)\\)
\\(x^2 - 16x + 3x - 48 = (x - 16)(x + 3)\\)

Explanation:

Identify coefficients

$$ a = 1, \quad b = 13, \quad c = -48 $$

$$ ac = -48 $$

Find factors of ac that sum to b

$$ 16 \times (-3) = -48 $$

$$ 16 + (-3) = 13 $$

Rewrite trinomial as four-term polynomial and factor

$$ x^2 + 16x - 3x - 48 = x(x + 16) - 3(x + 16) = (x + 16)(x - 3) $$

Answer:

• (A) \(x^2 + 7x + 6x - 48 = (x + 7)(x + 6)\)
• (B) \(x^2 - 12x + 4x - 48 = (x - 12)(x + 4)\)
• (C) \(x^2 + 16x - 3x - 48 = (x + 16)(x - 3)\) (Correct answer)
• (D) \(x^2 - 16x + 3x - 48 = (x - 16)(x + 3)\)