Factor. x^2 + 20x + 19 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression x^2 + 20x + 19. The quadratic expression is in the form ax^2 + bx + c, where 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 numbers are 1 and 19.Write Factored Form: Write the factored form using the numbers found in Step 2. The factored form of the quadratic expression is (x + m)(x + n), where m = 1 and n = 19. Therefore, the factored form is (x + 1)(x + 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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x^2 + 20x + 19

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $x^2 + 20x + 19$ . $\newline$ The quadratic expression is in the form $ax^2 + bx + c$ , where $a = 1$ , $b = 20$ , and $b$ $0$ .
Find Factors and Sum: Find two numbers that multiply to $c$ ( $19$ ) and add up to $b$ ( $20$ ). $\newline$ We need to find two numbers $m$ and $n$ such that $m \times n = 19$ and $m + n = 20$ . $\newline$ Since $19$ is a prime number, the only factors of $19$ are $19$ $0$ and $19$ itself. $\newline$ $19$ $2$ and $19$ $3$ , so the numbers are $19$ $0$ and $19$ .
Write Factored Form: Write the factored form using the numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(x + m)(x + n)$ , where $m = 1$ and $n = 19$ . $\newline$ Therefore, the factored form is $(x + 1)(x + 19)$ .