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Chapter 6: Problem 34

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. $$15 y^{2}-3 y+9$$

Short Answer

Expert verified
The factored form of the polynomial \(15 y^{2}-3 y+9\) is \(3(5y^2 - y + 3)\).

Step by step solution

01

Find the GCF

Identify the largest number that each coefficient in the polynomial has in common. In this case, the coefficients are 15, -3, and 9. The greatest common factor of these numbers is 3.
02

Rewrite the polynomial

Write each term as a product of the GCF and the remaining factor. We get the following:\[3(5y^2 - y + 3)\]
03

Check the result

Check if the expression can be factored further. In this case, \(5y^2 - y + 3\) can't be factored further, so we're done.

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