Write Quadratic Equation: Write down the quadratic equation. The given quadratic equation is 3x^2 - 8x - 180 = 0.Factor Quadratic Equation: Factor the quadratic equation, if possible. To factor the quadratic equation, we need to find two numbers that multiply to give the product of the coefficient of x^2 term (3) and the constant term (-180), which is -540, and add up to the coefficient of the x term (-8).Find Numbers for Factoring: Find two numbers that multiply to -540 and add up to -8. The numbers -20 and 27 multiply to -540 (since -20 * 27 = -540) and add up to 7 (since -20 + 27 = 7). However, we need the sum to be -8, not 7. This indicates that we cannot factor the quadratic equation easily. We will need to use the quadratic formula instead.

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$3 x^{2}-8 x-180=0$

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Algebra 2

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3 x^{2}-8 x-180=0

Write Quadratic Equation: Write down the quadratic equation. $\newline$ The given quadratic equation is $3x^2 - 8x - 180 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation, if possible. $\newline$ To factor the quadratic equation, we need to find two numbers that multiply to give the product of the coefficient of $x^2$ term $(3)$ and the constant term $(-180)$ , which is $-540$ , and add up to the coefficient of the $x$ term $(-8)$ .
Find Numbers for Factoring: Find two numbers that multiply to $-540$ and add up to $-8$ . The numbers $-20$ and $27$ multiply to $-540$ (since $-20 \times 27 = -540$ ) and add up to $7$ (since $-20 + 27 = 7$ ). However, we need the sum to be $-8$ , not $7$ . This indicates that we cannot factor the quadratic equation easily. We will need to use the quadratic formula instead.