Problem 55
Question
Factor each polynomial using the negative of the greatest common factor. $$-12 x^{3} y^{2}-18 x^{3} y+24 x^{2} y$$
Step-by-Step Solution
Verified Answer
The factorized form of this polynomial is \(-6x^{2}y (2xy +3x -4)\.
1Step 1: Identify the Greatest Common Factor (GCF)
Examine all of the terms in the polynomial to identify the greatest common factor. For this polynomial, the GCF is \(6x^{2}y\).
2Step 2: Factor out the GCF
Divide each term in the polynomial by the GCF and rewrite the polynomial as the product of the GCF and the resulting expression. In this case, the polynomial becomes \(-2x y -3x + 4\) (after dividing each term by GCF). Now the factored form is \(6x^{2}y(-2x y -3x + 4)\).
3Step 3: Writing out the Final Simplified Expression
The final simplified factorized form of the polynomial is \(-6x^{2}y (2xy +3x -4)\.
Other exercises in this chapter
Problem 55
Factor completely. $$2 r^{3}+8 r^{2}-64 r$$
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Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$64 w^{2}=48 w-9$$
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Factor any perfect square trinomials, or state that the polynomial is prime. $$25 y^{2}-10 y+1$$
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Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$15 a^{2}-a b
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