Factor. 2j^2 + 9j + 10 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 2j^2 + 9j + 10. Compare 2j^2 + 9j + 10 with ax^2 + bx + c. a = 2 b = 9 c = 10Find two numbers: Find two numbers that multiply to a*c (which is 2*10 = 20) and add up to b (which is 9). The two numbers that satisfy these conditions are 5 and 4, because: 5 * 4 = 20 5 + 4 = 9Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step 2. 2j^2 + 9j + 10 can be written as 2j^2 + 5j + 4j + 10.Factor by grouping: Factor by grouping. Group the terms into two pairs: (2j^2 + 5j) and (4j + 10). Factor out the greatest common factor from each pair. From the first pair, factor out j: j(2j + 5). From the second pair, factor out 4: 4(2j + 5).Write factored form: Write the factored form of the expression. Since both groups contain the common factor (2j + 5), factor this out: j(2j + 5) + 4(2j + 5) = (j + 4)(2j + 5).

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2j^2 + 9j + 10

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2j^2 + 9j + 10$ . Compare $2j^2 + 9j + 10$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $2*10 = 20$ ) and add up to $b$ (which is $9$ ). $\newline$ The two numbers that satisfy these conditions are $5$ and $4$ , because: $\newline$ $5 \times 4 = 20$ $\newline$ $5 + 4 = 9$
Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step $2$ . $\newline$ $2j^2 + 9j + 10$ can be written as $2j^2 + 5j + 4j + 10$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $2j^2 + 5j$ and $4j + 10$ . $\newline$ Factor out the greatest common factor from each pair. $\newline$ From the first pair, factor out $j$ : $j(2j + 5)$ . $\newline$ From the second pair, factor out $4$ : $4(2j + 5)$ .
Write factored form: Write the factored form of the expression. $\newline$ Since both groups contain the common factor $(2j + 5)$ , factor this out: $\newline$ $j(2j + 5) + 4(2j + 5) = (j + 4)(2j + 5)$ .