Factor. 4m^2 + 9m + 5 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 4m^2 + 9m + 5. Compare 4m^2 + 9m + 5 with the standard form ax^2 + bx + c. a = 4 b = 9 c = 5Find Multiplying Numbers: Find two numbers that multiply to a*c (which is 4*5=20) and add up to b (which is 9). We need to find two numbers that multiply to 20 and add up to 9. After checking possible pairs of factors of 20 (1 and 20, 2 and 10, 4 and 5), we see that none of these pairs add up to 9. This means we cannot factor the quadratic expression by simple factorization methods.Use Quadratic Formula: Since the quadratic expression cannot be factored using integers, we would need to use the quadratic formula to find the roots or complete the square. However, the original question prompt asks us to factor the expression, which implies factoring over the integers. Therefore, we conclude that the expression cannot be factored over the integers.

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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4m^2 + 9m + 5

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $4m^2 + 9m + 5$ . Compare $4m^2 + 9m + 5$ with the standard form $ax^2 + bx + c$ . $a = 4$ $b$ $0$ $b$ $1$
Find Multiplying Numbers: Find two numbers that multiply to $a*c$ (which is $4*5=20$ ) and add up to $b$ (which is $9$ ). $\newline$ We need to find two numbers that multiply to $20$ and add up to $9$ . $\newline$ After checking possible pairs of factors of $20$ ( $1$ and $20$ , $2$ and $4*5=20$ $0$ , $4*5=20$ $1$ and $4*5=20$ $2$ ), we see that none of these pairs add up to $9$ . $\newline$ This means we cannot factor the quadratic expression by simple factorization methods.
Use Quadratic Formula: Since the quadratic expression cannot be factored using integers, we would need to use the quadratic formula to find the roots or complete the square. However, the original question prompt asks us to factor the expression, which implies factoring over the integers. Therefore, we conclude that the expression cannot be factored over the integers.