Factor -7x³ + 21x² + 3x - 9 by grouping. What is the resulting expression?

Solution:

Given, the function is -7x³ + 21x² + 3x - 9.

We have to find the resultant expression by grouping.

By grouping,

-7x³ + 21x² + 3x - 9 = -7x²(x - 3) + 3(x - 3)

Taking out common term,

-7x³ + 21x² + 3x - 9 = (x - 3)(-7x² + 3)

Therefore, the resulting expression is (x - 3)(-7x² + 3).

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 -7x³ + 21x² + 3x - 9 by grouping. What is the resulting expression?

Summary:

The resulting expression by grouping the function -7x³ + 21x² + 3x - 9 is (x - 3)(-7x² + 3).