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

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2u^2 + 17u + 8 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 17, c = 8Find suitable numbers: 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 17u using the two numbers found in the previous step: 2u^2 + 17u + 8 = 2u^2 + 1u + 16u + 8.Group terms into pairs: Group the terms into two pairs: (2u^2 + 1u) and (16u + 8).Factor out common factors: Factor out the greatest common factor from each pair. From the first pair, factor out u: u(2u + 1). From the second pair, factor out 8: 8(u + 1).Correct previous step: Notice that there is a mistake in the previous step. The common factor in the second pair should be 8, but the expression inside the parentheses should be the same as the first pair for the expression to be factorable. We need to correct this.

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2u^2 + 17u + 8

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2u^2 + 17u + 8$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 17$ , $c = 8$
Find suitable numbers: 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 $17u$ using the two numbers found in the previous step: $2u^2 + 17u + 8 = 2u^2 + 1u + 16u + 8$ .
Group terms into pairs: Group the terms into two pairs: $2u^2 + 1u$ and $16u + 8$ .
Factor out common factors: Factor out the greatest common factor from each pair. From the first pair, factor out $u$ : $u(2u + 1)$ . From the second pair, factor out $8$ : $8(u + 1)$ .
Correct previous step: Notice that there is a mistake in the previous step. The common factor in the second pair should be $8$ , but the expression inside the parentheses should be the same as the first pair for the expression to be factorable. We need to correct this.