Factor 15x³ - 5x² + 6x - 2 by grouping. What is the resulting expression?

Solution:

Given, the function is 15x³ - 5x² + 6x - 2.

We have to find the resultant expression by grouping.

By grouping,

15x³ - 5x² + 6x - 2 = 5x²(3x - 1) + 2(3x - 1)

Taking out common term,

15x³ - 5x² + 6x - 2 = (3x - 1)(5x² + 2)

Therefore, the resulting expression is (3x - 1)(5x² + 2).

Example: Factor x³ + x² + x + 1 by grouping. What is the resulting expression?

Solution:

Given, the equation is x³ + x² + x + 1

We have to find the resulting expression by grouping.

Grouping first and second terms,

x³ + x² + x + 1 = ( x³ + x²) + (x + 1)

Taking out common term,

= x²(x + 1) + (x + 1)

= (x² + 1) (x + 1)

Therefore, the resulting expression is (x² + 1) (x + 1).

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Factor 15x³ - 5x² + 6x - 2 by grouping. What is the resulting expression?

Summary:

The resulting expression by grouping the function 15x³ - 5x² + 6x - 2 is (3x - 1)(5x² + 2).