Which of the following is equivalent to 2x^(2)+4x+3 ? Choose 1 answer: (A) 2(x+1)^(2)+1 (B) 2(x+1)^(2)+3 (C) 2(x+1)^(2)+5 (D) 2(x+1)^(2)+4x+1

Factor Quadratic Expression: First, let's try to factor the quadratic expression 2x^2 + 4x + 3 to see if it matches any of the given options. We look for two numbers that multiply to 2*3 (which is 6) and add up to 4.No Integer Factors: Unfortunately, there are no two integers that multiply to 6 and add up to 4, so we cannot factor the quadratic expression in this way. This means we need to try another method to see which option is equivalent.Expand Option (A): Let's expand each of the given options to see if any of them simplify to 2x^2 + 4x + 3. Starting with option (A): 2(x+1)^2 + 1 Expanding (x+1)^2 gives x^2 + 2x + 1. Then multiplying by 2 gives 2x^2 + 4x + 2. Finally, adding 1 gives 2x^2 + 4x + 3.

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Which of the following is equivalent to
2x^(2)+4x+3 ?
Choose 1 answer:
(A)
2(x+1)^(2)+1
(B)
2(x+1)^(2)+3
(C)
2(x+1)^(2)+5
(D)
2(x+1)^(2)+4x+1

Which of the following is equivalent to $2 x^{2}+4 x+3$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $2(x+1)^{2}+1$ $\newline$ (B) $2(x+1)^{2}+3$ $\newline$ (C) $2(x+1)^{2}+5$ $\newline$ (D) $2(x+1)^{2}+4 x+1$

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which of the following is equivalent to

2 x^{2}+4 x+3

\newline

Choose

1

answer:

\newline

(A)

2(x+1)^{2}+1

\newline

(B)

2(x+1)^{2}+3

\newline

(C)

2(x+1)^{2}+5

\newline

(D)

2(x+1)^{2}+4 x+1

Factor Quadratic Expression: First, let's try to factor the quadratic expression $2x^2 + 4x + 3$ to see if it matches any of the given options. $\newline$ We look for two numbers that multiply to $2\times 3$ (which is $6$ ) and add up to $4$ .
No Integer Factors: Unfortunately, there are no two integers that multiply to $6$ and add up to $4$ , so we cannot factor the quadratic expression in this way. This means we need to try another method to see which option is equivalent.
Expand Option (A): Let's expand each of the given options to see if any of them simplify to $2x^2 + 4x + 3$ . $\newline$ Starting with option (A): $2(x+1)^2 + 1$ $\newline$ Expanding $(x+1)^2$ gives $x^2 + 2x + 1$ . Then multiplying by $2$ gives $2x^2 + 4x + 2$ . Finally, adding $1$ gives $2x^2 + 4x + 3$ .