Question

Use the grouping method to factor the polynomial below completely 10x^3 - 35x^2 + 6x - 21

Answer 1

(5x² + 3)(2x - 7)

Step-by-step explanation:

First, we need to group the first two terms and the last two terms, so:

10x³ - 35x² + 6x - 21

(10x³ - 35x²) + (6x - 21)

We can write each term as follows:

10x³ = 5x²(2x)

35x² = 5x²(7)

6x = 3(2x)

21 = 3(7)

So, we can factor 5x² from the first term (10x³ - 35x²) and we can factor 3 from the second term (6x - 21). Then, we get:

5x²(2x - 7) + 3(2x - 7)

Now, we need to factor (2x -7), so:

(5x² + 3)(2x - 7)

So, the factorization of the polynomial 10x³ - 35x² + 6x - 21 is:

(5x² + 3)(2x - 7)