Factor. f^2 + 18f + 17 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression f^2 + 18f + 17. Compare f^2 + 18f + 17 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 18, and c = 17.Compare with standard form: Find two numbers whose product is ac (since a = 1, just c) and whose sum is b. We need two numbers that multiply to 17 and add up to 18. The numbers 1 and 17 satisfy these conditions because 1 * 17 = 17 and 1 + 17 = 18.Find product and sum: Write the quadratic expression using the two numbers found in Step 2 to split the middle term. The expression becomes f^2 + 1f + 17f + 17.Write expression with numbers: Factor by grouping. Group the terms to factor out common factors: (f^2 + 1f) + (17f + 17) Factor out an f from the first group and 17 from the second group: f(f + 1) + 17(f + 1)Factor by grouping: Factor out the common binomial factor (f + 1). The factored form is (f + 1)(f + 17).

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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f^2 + 18f + 81

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $f^2 + 18f + 17$ . Compare $f^2 + 18f + 17$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Compare with standard form: Find two numbers whose product is $ac$ (since $a = 1$ , just $c$ ) and whose sum is $b$ . We need two numbers that multiply to $17$ and add up to $18$ . The numbers $1$ and $17$ satisfy these conditions because $1 \times 17 = 17$ and $1 + 17 = 18$ .
Find product and sum: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $\newline$ The expression becomes $f^2 + 1f + 17f + 17$ .
Write expression with numbers: Factor by grouping. $\newline$ Group the terms to factor out common factors: $\newline$ $(f^2 + 1f) + (17f + 17)$ $\newline$ Factor out an $f$ from the first group and $17$ from the second group: $\newline$ $f(f + 1) + 17(f + 1)$
Factor by grouping: Factor out the common binomial factor $(f + 1)$ . $\newline$ The factored form is $(f + 1)(f + 17)$ .