Problem 52
Question
Factor each polynomial using the negative of the greatest common factor. $$-18 x^{4}+9 x^{3}+6 x^{2}$$
Step-by-Step Solution
Verified Answer
The factored form of the polynomial is \(-3x^2(6x^2 - 3x - 2)\).
1Step 1: Identify the Greatest Common Factor (GCF)
First, identify the GCF of all terms. The GCF needs to be negative since it is asked in the problem. For \(-18x^4, 9x^3\), and \(6x^2\), they each have an \(x^2\) factor, therefore, the greatest common factor is -3\(x^2\).
2Step 2: Divide each term by the GCF
Next, divide each term by the common factor \(-3x^2\). This gives \(-18x^4/-3x^2 = 6x^2\), \(9x^3/-3x^2 = -3x\), and \(6x^2/-3x^2 = -2\).
3Step 3: Combine Results
Combine the results in order from highest to lowest degrees. \(6x^2 - 3x - 2\) gives us the final factored form.
Other exercises in this chapter
Problem 52
Factor completely. $$2 r^{3}+8 r^{2}+6 r$$
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Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$y(y+9)=4(2 y+5)$$
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Factor any perfect square trinomials, or state that the polynomial is prime. $$x^{2}+24 x+144$$
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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 x^{2}-31
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