If a polynomial has four terms, 3×3 + 5x + 6×2 + 10, which factoring method can be considered?

• a) Perfect-square trinomial
• b) Difference of squares
• c) Factor by grouping
• d) Sum of cubes

Answer c) Factor by Grouping

Answer Explanation:

Yes, the correct answer is c) Factor by grouping.

When you have a polynomial with four terms, factor by grouping is often the most appropriate method to try first. This method involves grouping the terms into pairs and factoring out the common factor from each pair, then factoring further if possible.

For the given polynomial 3×3+5x+6×2+103x^3 + 5x + 6x^2 + 103x3+5x+6x2+10:

1. You can group the terms as (3×3+6×2)+(5x+10)(3x^3 + 6x^2) + (5x + 10)(3x3+6x2)+(5x+10).
2. Factor out the common factors from each group:
   • 3×2(x+2)+5(x+2)3x^2(x + 2) + 5(x + 2)3x2(x+2)+5(x+2).
3. Now, you can factor out the common binomial factor $(x+2)$:
   • (x+2)(3×2+5)(x + 2)(3x^2 + 5)(x+2)(3x2+5).

So, factor by grouping is the appropriate method for this polynomial.

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Smirti

(Founder of Management Notes)
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I am Smirti Bam, an enthusiastic edu blogger with a passion for sharing insights into the dynamic world of business and management through this website.

I hold a MBA degree from Presidential Business School, Kathmandu, and a BBA degree with a specialization in Finance from Apex College,

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