Question

factor out the greatest common factor in the following polynomial.
$10x^2 + 25x + 15 = \square$
check
explain
problem 4
factor out the greatest common factor in the following polynomial.
$x^4 - 8x^3 + x^2 = \square$
check
explain

Explanation:

First Polynomial: \(10x^2 + 25x + 15\)

Step1: Find GCF of coefficients

Find GCF of 10, 25, 15. Factors of 10: 1,2,5,10; 25:1,5,25; 15:1,3,5,15. GCF is 5.

Step2: Factor out GCF

Factor 5 from each term: \(5(2x^2 + 5x + 3)\)

Step1: Find GCF of terms

For \(x^4\), \(-8x^3\), \(x^2\), GCF of variables: lowest power of \(x\) is \(x^2\).

Step2: Factor out GCF

Factor \(x^2\) from each term: \(x^2(x^2 - 8x + 1)\)

Answer:

\(5(2x^2 + 5x + 3)\)

Second Polynomial: \(x^4 - 8x^3 + x^2\)