Factor. 2n^2 + 17n + 8 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2n^2 + 17n + 8 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 17, c = 8Find numbers for multiplication: Find two numbers that multiply to a*c (2*8 = 16) and add up to b (17). The numbers that satisfy these conditions are 1 and 16 because 1*16 = 16 and 1+16 = 17.Rewrite middle term: Rewrite the middle term 17n using the two numbers found in the previous step: 1n and 16n. The expression becomes 2n^2 + 1n + 16n + 8.Group terms into pairs: Group the terms into two pairs: (2n^2 + 1n) and (16n + 8).Factor out common factors: Factor out the greatest common factor from each pair. From the first pair (2n^2 + 1n), factor out n: n(2n + 1). From the second pair (16n + 8), factor out 8: 8(n + 1).Correct math error: Notice that there is a mistake in the previous step. The common factor for the second pair (16n + 8) should be 8, but the term inside the parentheses should be (2n + 1) to match the first pair. This is a math error.

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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2n^2 + 17n + 8

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2n^2 + 17n + 8$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 17$ , $c = 8$
Find numbers for multiplication: Find two numbers that multiply to $a*c$ ( $2*8 = 16$ ) and add up to $b$ ( $17$ ). $\newline$ The numbers that satisfy these conditions are $1$ and $16$ because $1*16 = 16$ and $1+16 = 17$ .
Rewrite middle term: Rewrite the middle term $17n$ using the two numbers found in the previous step: $1n$ and $16n$ . The expression becomes $2n^2 + 1n + 16n + 8$ .
Group terms into pairs: Group the terms into two pairs: $2n^2 + 1n$ and $16n + 8$ .
Factor out common factors: Factor out the greatest common factor from each pair. $\newline$ From the first pair $(2n^2 + 1n)$ , factor out $n$ : $n(2n + 1)$ . $\newline$ From the second pair $(16n + 8)$ , factor out $8$ : $8(n + 1)$ .
Correct math error: Notice that there is a mistake in the previous step. The common factor for the second pair $16n + 8$ should be $8$ , but the term inside the parentheses should be $(2n + 1)$ to match the first pair. This is a math error.