Complete each factored form. 5x^(2)+22 x+8=(5x+2)(quad)

Recognize the structure: Recognize the structure of the quadratic expression. The given quadratic expression is in the form of ax^2 + bx + c, where a = 5, b = 22, and c = 8. We need to find two numbers that multiply to ac (5 * 8 = 40) and add up to b (22).Find two numbers: Find two numbers that multiply to 40 and add up to 22. The numbers that satisfy these conditions are 20 and 2 because 20 * 2 = 40 and 20 + 2 = 22.Write middle term: Write the middle term of the quadratic expression as a sum of two terms using the numbers found in Step 2. 5x^2 + 22x + 8 can be rewritten as 5x^2 + 20x + 2x + 8.Factor by grouping: Factor by grouping. Group the terms to factor out common factors: (5x^2 + 20x) + (2x + 8) 5x(x + 4) + 2(x + 4)Factor out common binomial: Factor out the common binomial factor. Since both groups contain the binomial (x + 4), we can factor it out: (5x + 2)(x + 4)

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Complete each factored form.

5x^(2)+22 x+8=(5x+2)(quad)

Complete each factored form. $\newline$ $5x^{2}+22x+8=(5x+2)(\quad)$

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Algebra 2

Factor sums and differences of cubes

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Q. Complete each factored form.

\newline

5x^{2}+22x+8=(5x+2)(\quad)

Recognize the structure: Recognize the structure of the quadratic expression. $\newline$ The given quadratic expression is in the form of $ax^2 + bx + c$ , where $a = 5$ , $b = 22$ , and $c = 8$ . $\newline$ We need to find two numbers that multiply to $ac$ ( $5 \times 8 = 40$ ) and add up to $b$ ( $22$ ).
Find two numbers: Find two numbers that multiply to $40$ and add up to $22$ . The numbers that satisfy these conditions are $20$ and $2$ because $20 \times 2 = 40$ and $20 + 2 = 22$ .
Write middle term: Write the middle term of the quadratic expression as a sum of two terms using the numbers found in Step $2$ . $\newline$ $5x^2 + 22x + 8$ can be rewritten as $5x^2 + 20x + 2x + 8$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms to factor out common factors: $\newline$ $(5x^2 + 20x) + (2x + 8)$ $\newline$ $5x(x + 4) + 2(x + 4)$
Factor out common binomial: Factor out the common binomial factor. $\newline$ Since both groups contain the binomial $(x + 4)$ , we can factor it out: $\newline$ $(5x + 2)(x + 4)$