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what is the expression in factored form x^2+13x+42 show all the stepsQuestion
what is the expression in factored form
3x^2+6x-24
show all your steps
3x^2+6x-24
show all your steps
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GPT 3.5
To find the factored form of the expression 3x^2 + 6x - 24, we need to factor out the greatest common factor (GCF) from the coefficients and then factor the remaining quadratic expression.
1. First, calculate the GCF of the coefficients 3, 6, and 24, which is 3.
3 * (x^2 + 2x - 8)
2. Now, focus on factoring the quadratic expression within the parentheses: x^2 + 2x - 8.
To find two numbers that multiply to -8 and add up to 2, we can use trial and error:
- (-4) * (+2) = +8 and (-4) + (+2) = -2
So, x^2 + 2x - 8 can be factored as (x - 2)(x + 4).
3. Substitute this factored form back into the original expression:
3 * (x^2 + 2x - 8) = 3 * (x - 2)(x + 4)
Therefore, the expression in factored form is 3(x - 2)(x + 4).
1. First, calculate the GCF of the coefficients 3, 6, and 24, which is 3.
3 * (x^2 + 2x - 8)
2. Now, focus on factoring the quadratic expression within the parentheses: x^2 + 2x - 8.
To find two numbers that multiply to -8 and add up to 2, we can use trial and error:
- (-4) * (+2) = +8 and (-4) + (+2) = -2
So, x^2 + 2x - 8 can be factored as (x - 2)(x + 4).
3. Substitute this factored form back into the original expression:
3 * (x^2 + 2x - 8) = 3 * (x - 2)(x + 4)
Therefore, the expression in factored form is 3(x - 2)(x + 4).
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