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Which of the following is equivalent to the expression
3x^(2)+21 x+18 ?
Choose 1 answer:
(A)
3(x+1)(x+6)
(B)
3(x+2)(x+3)
(C)
3(x+2)(x+9)
(D)
3(x+3)(x+4)

Which of the following is equivalent to the expression $3 x^{2}+21 x+18$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $3(x+1)(x+6)$ $\newline$ (B) $3(x+2)(x+3)$ $\newline$ (C) $3(x+2)(x+9)$ $\newline$ (D) $3(x+3)(x+4)$

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Quadratic equation with complex roots

Full solution

Q. Which of the following is equivalent to the expression

3 x^{2}+21 x+18

?

\newline

Choose

1

answer:

\newline

(A)

3(x+1)(x+6)

\newline

(B)

3(x+2)(x+3)

\newline

(C)

3(x+2)(x+9)

\newline

(D)

3(x+3)(x+4)

Identify coefficients: Identify the coefficients of the quadratic expression $3x^2 + 21x + 18$ . The coefficients are $a=3$ , $b=21$ , and $c=18$ .
Factor out GCF: Factor out the greatest common factor (GCF) from the expression. $\newline$ The GCF of $3x^2$ , $21x$ , and $18$ is $3$ . Factoring out $3$ , we get: $\newline$ $3(x^2 + 7x + 6)$
Factor quadratic expression: Factor the quadratic expression inside the parentheses. $\newline$ We need to find two numbers that multiply to $6$ (the constant term) and add up to $7$ (the coefficient of $x$ ). $\newline$ The numbers that satisfy these conditions are $1$ and $6$ . $\newline$ So, we can write the factored form as: $\newline$ $3(x + 1)(x + 6)$
Match with options: Match the factored expression with the given options. $\newline$ The factored expression $3(x + 1)(x + 6)$ matches option (A).

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