Factoring Expressions with Negative Exponents

This video tutorial covers various techniques for factoring algebraic expressions, focusing on the greatest common factor (GCF), negative and fractional exponents, and quadratic forms. It demonstrates how to identify and extract the GCF, handle negative and fractional exponents, and use substitution for quadratic expressions. The tutorial also explores advanced factoring techniques for more complex expressions, providing step-by-step examples to enhance understanding.

What is the first step in factoring an expression like 2x to the negative 2 plus 8x to the negative 5?

• Find the greatest common factor

• Add the exponents

• Multiply the coefficients

• Subtract the exponents

When factoring 3x to the negative 4 plus 6x to the negative 5, what is the GCF?

• 6

• 3

• x to the negative 5

• x to the negative 4

How do you handle negative fractional exponents when factoring?

• Subtract them directly

• Ignore them

• Convert them to positive exponents

• Add them directly

How do you simplify the expression 4x to the negative one half minus 8x to the negative three halves?

• Factor out 8

• Factor out 4

• Factor out x to the negative one half

• Factor out x to the negative three halves

In the expression x to the minus 2 plus 7x to the minus 1 plus 12, what substitution can be used?

• a = x to the minus 1

• a = x to the minus 2

• a = x

• a = x squared

What is the result of factoring x to the minus 4 plus 5x to the minus 2 plus 4?

• (x to the minus 2 + 5)(x to the minus 2 + 4)

• (x to the minus 2 + 4)(x to the minus 2 + 1)

• (x to the minus 1 + 5)(x to the minus 1 + 4)

• (x to the minus 1 + 4)(x to the minus 1 + 1)

What is the result of factoring x to the minus 4 minus 25x to the minus 2 plus 144?

• (x to the minus 2 - 25)(x to the minus 2 + 144)

• (x to the minus 1 - 9)(x to the minus 1 - 16)

• (x to the minus 1 - 25)(x to the minus 1 + 144)

• (x to the minus 2 - 9)(x to the minus 2 - 16)

What substitution is used for x to the minus 4 plus 5x to the minus 2 plus 4?

• a = x

• a = x to the minus 4

• a = x to the minus 2

• a = x squared

What is the GCF in the expression 2x to the minus 3 minus 2x to the minus 4 minus 24x to the minus 5?

• 2x to the minus 3

• 2x to the minus 4

• 2x

• 2x to the minus 5

What is the final step in factoring 2x to the minus 3 minus 2x to the minus 4 minus 24x to the minus 5?

• Add x to the fifth power

• Multiply by x to the fifth power

• Divide by x to the fifth power

• Subtract x to the fifth power