Factor. f^2 + 20f + 19 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression f^2 + 20f + 19. Compare f^2 + 20f + 19 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 20, and c = 19.Find Factors and Sum: Find two numbers that multiply to c (19) and add up to b (20). We need to find two numbers m and n such that m * n = 19 and m + n = 20. Since 19 is a prime number, the only factors of 19 are 1 and 19 itself. 1 * 19 = 19 and 1 + 19 = 20. So, the two numbers are 1 and 19.Write Factored Form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (f + m)(f + n), where m and n are the numbers found in Step 2. Substitute m = 1 and n = 19 into the factored form to get (f + 1)(f + 19).

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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 + 20f + 19

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $f^2 + 20f + 19$ . Compare $f^2 + 20f + 19$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Find Factors and Sum: Find two numbers that multiply to $c (19)$ and add up to $b (20)$ . We need to find two numbers $m$ and $n$ such that $m \times n = 19$ and $m + n = 20$ . Since $19$ is a prime number, the only factors of $19$ are $1$ and $19$ itself. $b (20)$ $0$ and $b (20)$ $1$ . So, the two numbers are $1$ and $19$ .
Write Factored Form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(f + m)(f + n)$ , where $m$ and $n$ are the numbers found in Step $2$ . $\newline$ Substitute $m = 1$ and $n = 19$ into the factored form to get $(f + 1)(f + 19)$ .