Factor the polynomial 4x⁴ - 20x² - 3x² + 15 by grouping. What is the resulting expression?
(4x² + 3)(x² - 5)
(4x² - 3)(x² - 5)
(4x² - 5)(x² + 3)
(4x² + 5)(x² - 3)

Solution:

It is given that, factor the polynomial 4x⁴ - 20x² - 3x² + 15 by grouping means separation of the polynomial in two addends, each of them consists of two addends:

So, 4x⁴ - 20x² - 3x² + 15

= (4x⁴ - 20x²) + (-3x² + 15)

In the first two terms, the common factor is 4x⁴ and in the third and the fourth terms, the common factor is -3.

Taking them out as common, we get

= 4x²(x² - 15) – 3(x² - 5)

= (x² - 5)(4x² - 3)

Therefore, the resulting expression is (x² - 5)(4x² - 3).

Factor the polynomial 4x⁴ - 20x² - 3x² + 15 by grouping. What is the resulting expression?

Summary:

Factor the polynomial 4x⁴ - 20x² - 3x² + 15 by grouping. The resulting expression is (x² - 5)(4x² - 3).