Factor. d^2 + 10d + 9 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is d^2 + 10d + 9. In the standard form of a quadratic expression, ax^2 + bx + c, the coefficient a is the coefficient of d^2, which is 1. The coefficient b is the coefficient of d, which is 10. The coefficient c is the constant term, which is 9.Find Multiplying Numbers: Find two numbers that multiply to c (9) and add up to b (10). We need to find two numbers that multiply together to give 9 and add together to give 10. The numbers 1 and 9 satisfy these conditions because 1 * 9 = 9 and 1 + 9 = 10.Write Factored Form: Write the factored form using the two numbers found. The factored form of the quadratic expression is (d + 1)(d + 9), because when we expand this, we get d^2 + d + 9d + 9, which simplifies to d^2 + 10d + 9.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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d^2 + 10d + 9

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is $d^2 + 10d + 9$ . In the standard form of a quadratic expression, $ax^2 + bx + c$ , the coefficient $a$ is the coefficient of $d^2$ , which is $1$ . The coefficient $b$ is the coefficient of $d$ , which is $10$ . The coefficient $c$ is the constant term, which is $9$ .
Find Multiplying Numbers: Find two numbers that multiply to $c$ ( $9$ ) and add up to $b$ ( $10$ ). We need to find two numbers that multiply together to give $9$ and add together to give $10$ . The numbers $1$ and $9$ satisfy these conditions because $1 \times 9 = 9$ and $1 + 9 = 10$ .
Write Factored Form: Write the factored form using the two numbers found. $\newline$ The factored form of the quadratic expression is d + \(1)(d + $9$ )\, because when we expand this, we get d^\(2 + d + $9$ d + $9$ )\, which simplifies to d^\(2 + $10$ d + $9$ )\.