Factor. p^2 + 20p + 19 ____

Identify Coefficients: Identify the coefficients for p^2, p, and the constant term in the quadratic expression p^2 + 20p + 19. The quadratic expression is in the form p^2 + bp + c, where b is the coefficient of p, and c is the constant term. For p^2 + 20p + 19, b = 20 and c = 19.Find Multiplying Numbers: Find two numbers that multiply to give c (19) and add up to give 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 we are looking for are 1 and 19.Write Factored Form: Write the factored form of the quadratic expression using the numbers found in the previous step. The factored form will be (p + m)(p + n), where m and n are the numbers found. Substitute m = 1 and n = 19 into the factored form to get (p + 1)(p + 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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p^2 + 20p + 19

Identify Coefficients: Identify the coefficients for $p^2$ , $p$ , and the constant term in the quadratic expression $p^2 + 20p + 19$ . The quadratic expression is in the form $p^2 + bp + c$ , where $b$ is the coefficient of $p$ , and $c$ is the constant term. For $p^2 + 20p + 19$ , $b = 20$ and $c = 19$ .
Find Multiplying Numbers: Find two numbers that multiply to give $c (19)$ and add up to give $b (20)$ . 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 numbers we are looking for are $1$ and $19$ .
Write Factored Form: Write the factored form of the quadratic expression using the numbers found in the previous step. $\newline$ The factored form will be $(p + m)(p + n)$ , where $m$ and $n$ are the numbers found. $\newline$ Substitute $m = 1$ and $n = 19$ into the factored form to get $(p + 1)(p + 19)$ .