Question

factor completely.

\\6r^5 - 5r^2 + 5r^3 - 6r^4\\

Explanation:

⚡ Using what you learned: Factoring by Grouping

Step 1: Rearrange terms

Rearrange the terms to group those with common coefficients:

$$ 6r^5 - 6r^4 + 5r^3 - 5r^2 $$

Step 2: Factor by grouping

Group the first two terms and the last two terms:

$$ (6r^5 - 6r^4) + (5r^3 - 5r^2) $$

Factor out the greatest common factor (GCF) from each group:

$$ 6r^4(r - 1) + 5r^2(r - 1) $$

Factor out the common binomial term \( (r - 1) \):

$$ (r - 1)(6r^4 + 5r^2) $$

Step 3: Factor completely

Factor out the remaining GCF, \( r^2 \), from the second binomial:

$$ r^2(r - 1)(6r^2 + 5) $$

Answer:

$$ r^2(r - 1)(6r^2 + 5) $$