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1. Factorise: 54x2 + 42x3 – 30x4

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As a registered tutor on UrbanPro.com specializing in Class 7 Tuition, I understand the importance of providing clear and structured explanations for mathematical problems. Let's delve into the factorization of the given polynomial expression: Problem Statement Factorize the polynomial expression: 54x²...
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As a registered tutor on UrbanPro.com specializing in Class 7 Tuition, I understand the importance of providing clear and structured explanations for mathematical problems. Let's delve into the factorization of the given polynomial expression:

Problem Statement

Factorize the polynomial expression: 54x² + 42x³ – 30x⁴

Solution Steps

Step 1: Identify the Common Factor

The first step in factoring a polynomial is to identify the common factor of all the terms. In this case, the common factor is 6x².

  • Expression after factoring out the common factor: 6x2(9+7x−5x2)6x2(9+7x−5x2)

Step 2: Factorize the Quadratic Expression

Now, we need to factorize the quadratic expression inside the parentheses. For this, we can use methods like grouping or the quadratic formula.

  • Quadratic expression after factoring: 6x2(3−x)(3+5x)6x2(3−x)(3+5x)

Step 3: Final Factorization

Combine the factored common factor with the factored quadratic expression:

  • Final factorization of the given polynomial: 6x2(3−x)(3+5x)6x2(3−x)(3+5x)

    In conclusion, the factorization of the given polynomial expression is 6x2(3−x)(3+5x)6x2(3−x)(3+5x). When considering Class 7 Tuition, online coaching provides a conducive learning environment with personalized attention, flexibility, abundant resources, technology integration, and expert guidance.
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