Problem 42
Question
Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$12 x^{2}-25$$
Step-by-Step Solution
Verified Answer
The given polynomial, \(12x^{2} - 25\), cannot be factored further using the GCF method as the GCF in this case is 1.
1Step 1: Identify the Terms in the Polynomial
Identify the terms in the polynomial, which are \(12x^{2}\) and \(-25\) in this case.
2Step 2: Find the Greatest Common Factor
Determine the greatest common factor (GCF) of these terms. For \(12x^{2}\) and \(-25\), 1 is the GCF since there is no other number or variable that the two terms have in common.
3Step 3: Factor the Polynomial
Factor the polynomial using the GCF. However, since our GCF in this case is 1 and factorizing the polynomial with 1 will result in the original polynomial itself, it cannot be factored further using GCF method.
Other exercises in this chapter
Problem 42
Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$25 x^{2}=49$$
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Factor completely, or state that the polynomial is prime. $$-4 x^{2}+4$$
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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}-19
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Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations usin
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