Factor x³ - 7x² - 5x + 35 by grouping. What is the resulting expression?

Solution:

Given, the function is x³ - 7x² - 5x + 35.

We have to find the resultant expression by grouping.

By grouping,

x³ - 7x² - 5x + 35 = x²(x - 7) - 5(x - 7)

Taking out common term,

x³ - 7x² - 5x + 35 = (x - 7)(x² - 5)

Therefore, the resulting expression is (x - 7)(x² - 5).

Example: Factor x⁴ + x³ + x² + x by grouping. What is the resulting expression?

Solution:

Given, the equation is x⁴ + x³ + x² + x

We have to find the resulting expression by grouping.

Grouping first and second terms,

x⁴ + x³ + x² + x = ( x⁴ + x³) + (x² + x)

Taking out common term,

= x³(x + 1) + x(x + 1)

= x (x² + 1)(x + 1)

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

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Factor x³ - 7x² - 5x + 35 by grouping. What is the resulting expression?

Summary:

The resulting expression by grouping the function x³ - 7x² - 5x + 35 is (x - 7)(x² - 5).