Which of the following is equivalent to the expression x^(2)-5x-14 ? Choose 1 answer: (A) (x-14)(x+1) (B) (x-7)(x+2) (C) (x-2)(x+7) (D) (x-1)(x+14)

Factor the quadratic expression: Factor the quadratic expression x^2 - 5x - 14. To factor a quadratic expression of the form ax^2 + bx + c, we need to find two numbers that multiply to ac (the product of the coefficient of x^2 and the constant term) and add up to b (the coefficient of x). Here, a = 1, b = -5, and c = -14. We need two numbers that multiply to (1)(-14) = -14 and add up to -5.Find two numbers: Find two numbers that multiply to -14 and add up to -5. The numbers -7 and +2 multiply to -14 and add up to -5. -7 * 2 = -14 -7 + 2 = -5Write the factored form: Write the factored form using the two numbers found in Step 2. The quadratic expression x^2 - 5x - 14 can be factored as (x - 7)(x + 2).

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Which of the following is equivalent to the expression
x^(2)-5x-14 ?
Choose 1 answer:
(A)
(x-14)(x+1)
(B)
(x-7)(x+2)
(C)
(x-2)(x+7)
(D)
(x-1)(x+14)

Which of the following is equivalent to the expression $x^{2}-5 x-14$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $(x-14)(x+1)$ $\newline$ (B) $(x-7)(x+2)$ $\newline$ (C) $(x-2)(x+7)$ $\newline$ (D) $(x-1)(x+14)$

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Math Problems

Algebra 1

Identify equivalent linear expressions

Full solution

Q. Which of the following is equivalent to the expression

x^{2}-5 x-14

\newline

Choose

1

answer:

\newline

(A)

(x-14)(x+1)

\newline

(B)

(x-7)(x+2)

\newline

(C)

(x-2)(x+7)

\newline

(D)

(x-1)(x+14)

Factor the quadratic expression: Factor the quadratic expression $x^2 - 5x - 14$ . $\newline$ To factor a quadratic expression of the form $ax^2 + bx + c$ , we need to find two numbers that multiply to $ac$ (the product of the coefficient of $x^2$ and the constant term) and add up to $b$ (the coefficient of $x$ ). $\newline$ Here, $a = 1$ , $b = -5$ , and $c = -14$ . $\newline$ We need two numbers that multiply to $(1)(-14) = -14$ and add up to $ax^2 + bx + c$ $0$ .
Find two numbers: Find two numbers that multiply to $-14$ and add up to $-5$ . $\newline$ The numbers $-7$ and $+2$ multiply to $-14$ and add up to $-5$ . $\newline$ $-7 \times 2 = -14$ $\newline$ $-7 + 2 = -5$
Write the factored form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The quadratic expression $x^2 - 5x - 14$ can be factored as $(x - 7)(x + 2)$ .