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Directions: Factor each polynomial. Check your answer by distributing. 24x^4y^2+30x^2y^2 6x^2y^2(4x^2+5) 3x^2y^2(8x^2+10) 6x^2y(4x^2+5) 6xy^2(4x^2+5)

Pergunta

Directions: Factor each polynomial. Check your answer by
distributing.
24x^4y^2+30x^2y^2
6x^2y^2(4x^2+5)
3x^2y^2(8x^2+10)
6x^2y(4x^2+5)
6xy^2(4x^2+5)

Directions: Factor each polynomial. Check your answer by distributing. 24x^4y^2+30x^2y^2 6x^2y^2(4x^2+5) 3x^2y^2(8x^2+10) 6x^2y(4x^2+5) 6xy^2(4x^2+5)

Solução

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LuísElite · Tutor por 8 anos

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The factored form of the polynomial \(24x^{4}y^{2}+30x^{2}y^{2}\) is \(6x^{2}y^{2}(4x^{2}+5)\).

Explicação

## Step 1<br />The given polynomial is \(24x^{4}y^{2}+30x^{2}y^{2}\). We need to factorize this polynomial.<br /><br />## Step 2<br />To factorize the polynomial, we need to find the greatest common factor (GCF) of the two terms. The GCF of \(24x^{4) and \(30x^{2}y^{2}\) is \(6x^{2}y^{2}\).<br /><br />## Step 3<br />Next, we divide each term by the GCF to get the remaining factors. So, \(24x^{4}y^{2}\) divided by \(6x^{2}y^{2}\) gives \(4x^{2}\), and \(30x^{2}y^{2}\) divided by \(6x^{2}y^{2}\) gives \(5\).<br /><br />## Step 4<br />Therefore, the factored form of the polynomial is \(6x^{2}y^{2}(4x^{2}+5)\).<br /><br />## Step 5<br />To verify the factoring, we distribute \(6x^{2}y^{2}\) across the terms in gives us the original polynomial \(24x^{4}y^{2}+30x^{2}y^{2}\), confirming that the factoring is correct.
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