Factor. f^2 + 6f + 8 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression f^2 + 6f + 8. The quadratic expression is in the form af^2 + bf + c, where a = 1, b = 6, and c = 8.Find numbers multiply and add: Find two numbers that multiply to a*c (which is 8) and add up to b (which is 6). We need to find two numbers that multiply to 8 and add up to 6. The numbers 2 and 4 meet these criteria because 2 * 4 = 8 and 2 + 4 = 6.Write quadratic expression: Write the quadratic expression using the two numbers found in Step 2. We can express f^2 + 6f + 8 as f^2 + 2f + 4f + 8.Factor by grouping: Factor by grouping. Group the terms to factor by grouping: (f^2 + 2f) + (4f + 8). Factor out the common factors from each group: f(f + 2) + 4(f + 2).Factor common binomial: Factor out the common binomial factor. Since both groups contain the factor (f + 2), we can factor it out: (f + 2)(f + 4).

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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f^2 + 6f + 8

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $f^2 + 6f + 8$ . $\newline$ The quadratic expression is in the form $af^2 + bf + c$ , where $a = 1$ , $b = 6$ , and $b$ $0$ .
Find numbers multiply and add: Find two numbers that multiply to $a*c$ (which is $8$ ) and add up to $b$ (which is $6$ ). $\newline$ We need to find two numbers that multiply to $8$ and add up to $6$ . The numbers $2$ and $4$ meet these criteria because $2 \times 4 = 8$ and $2 + 4 = 6$ .
Write quadratic expression: Write the quadratic expression using the two numbers found in Step $2$ . $\newline$ We can express $f^2 + 6f + 8$ as $f^2 + 2f + 4f + 8$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms to factor by grouping: $(f^2 + 2f) + (4f + 8)$ . $\newline$ Factor out the common factors from each group: $f(f + 2) + 4(f + 2)$ .
Factor common binomial: Factor out the common binomial factor. $\newline$ Since both groups contain the factor $(f + 2)$ , we can factor it out: $(f + 2)(f + 4)$ .