Answer:
The factored form of the expression (5x^3 - 10x^2) + (7x - 14) is (x - 2)(5x^2 + 7).
Step-by-step explanation:
To factor the expression (5x^3 - 10x^2) + (7x - 14) by grouping, we can follow these steps:
Step 1: Group the terms in the expression.
(5x^3 - 10x^2) + (7x - 14)
Step 2: Look for the greatest common factor (GCF) in each group separately.
In the first group (5x^3 - 10x^2), the GCF is 5x^2:
5x^2(x - 2)
In the second group (7x - 14), the GCF is 7:
7(x - 2)
Step 3: Now, we have a common factor of (x - 2) in both groups.
Combine the two groups using the common factor:
5x^2(x - 2) + 7(x - 2)
Step 4: Factor out the common factor (x - 2) from both terms.
(x - 2)(5x^2 + 7)
Therefore, the factored form of the expression (5x^3 - 10x^2) + (7x - 14) is (x - 2)(5x^2 + 7).
