Factor. f^2 + 6f + 5 ____

Identify Variables: Identify a, b, and c in the quadratic expression f^2 + 6f + 5. Compare f^2 + 6f + 5 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 6, and c = 5.Find Multiplying Numbers: Find two numbers that multiply to c (which is 5) and add up to b (which is 6). We need to find two numbers m and n such that: m * n = 5 and m + n = 6. The numbers 1 and 5 satisfy these conditions because: 1 * 5 = 5 and 1 + 5 = 6.Write Factored Form: Write the factored form using the numbers found in Step 2. The factored form of the quadratic expression is: (f + 1)(f + 5)

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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 + 6f + 5

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $f^2 + 6f + 5$ . Compare $f^2 + 6f + 5$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 6$ , and $c = 5$ .
Find Multiplying Numbers: Find two numbers that multiply to $c$ (which is $5$ ) and add up to $b$ (which is $6$ ). $\newline$ We need to find two numbers $m$ and $n$ such that: $\newline$ $m \times n = 5$ and $m + n = 6$ . $\newline$ The numbers $1$ and $5$ satisfy these conditions because: $\newline$ $5$ $0$ and $5$ $1$ .
Write Factored Form: Write the factored form using the numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is: $\newline$ $(f + 1)(f + 5)$