What is the expression in factored form? 6x4+3x3−9x2
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To factor the expression 6x^4 + 3x^3 - 9x^2, we look for common factors among the terms.
Step 1: Factor out the greatest common factor.
The greatest common factor among the terms is 3x^2, so we factor that out:
3x^2(2x^2 + x - 3)
Step 2: Factor the quadratic expression.
To factor the quadratic expression, we look for two numbers that multiply to give -6 (the last term -3 multiplied by the first term 2) and add up to 1 (the coefficient of the middle term).
The numbers are 3 and -2, since 3 * -2 = -6 and 3 + (-2) = 1.
So, we can rewrite the quadratic expression as:
3x^2 (2x^2 + 3x - 2x - 3)
Step 3: Grouping and factoring by grouping.
We group the terms inside the parentheses and factor by grouping:
3x^2[(2x^2 + 3x) + (-2x - 3)]
3x^2 [x(2x + 3) - 1(2x + 3)]
3x^2 (x - 1)(2x + 3)
Therefore, the expression 6x^4 + 3x^3 - 9x^2 in factored form is 3x^2 (x - 1)(2x + 3).