How do you factor expressions like 3(x + h)^4 - 48(x + h)^2?

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In summary, in Chapter 1, Section 1.3 of Precalculus by David Cohen, 3rd Edition, we are introduced to factoring expressions. Specifically, we are presented with a problem involving factoring the expression 3(x + h)^4 - 48(x + h)^2. We start by factoring out 3(x + h)^2, which results in 3(x + h)^2[(x + h)^2 - 16]. Then, we simplify the quantity in the brackets by factoring it into two binomials, resulting in 3(x + h)^2[(x + h) - 4][(x - h) + 4]. This is a tricky factoring problem
  • #1
mathdad
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Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 32c.

Factor the expression.

3(x + h)^4 - 48(x + h)^2

Solution:

Factor out 3(x + h)^2.

3(x + h)^2[(x + h)^2 - 16]

Simplify the quantity in the brackets.

3(x + h)^2[(x + h) - 4][(x - h) + 4]

Is this right?
 
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  • #2
RTCNTC said:
Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 32c.

Factor the expression.

3(x + h)^4 - 48(x + h)^2

Solution:

Factor out 3(x + h)^2.

3(x + h)^2[(x + h)^2 - 16]

Simplify the quantity in the brackets.

3(x + h)^2[(x + h) - 4][(x - h) + 4]

Is this right?

right
 
  • #3
Section 1.3 has what appears to be endless factoring questions. I will post many factoring problems in the coming days. I am talking about "tricky" factoring problems not factor 3a + a.
 

Related to How do you factor expressions like 3(x + h)^4 - 48(x + h)^2?

1. What does it mean to "factor" an expression?

Factoring an expression means to break it down into smaller parts or factors that can be multiplied together to get the original expression. It is a method of simplifying and solving equations.

2. Why is factoring important in mathematics?

Factoring is important in mathematics because it allows us to solve equations and simplify expressions in a more efficient way. It also helps us to identify common patterns and relationships between numbers and variables.

3. What are the steps to factor an expression?

The steps to factor an expression vary depending on the type of expression and the techniques used. Generally, the steps involve identifying the greatest common factor (GCF), using the distributive property, and grouping like terms together.

4. Can all expressions be factored?

No, not all expressions can be factored. Some expressions may not have any common factors or may require advanced techniques such as the quadratic formula to be factored.

5. How can factoring be useful in real-life situations?

Factoring can be useful in real-life situations such as budgeting, calculating interest and discounts, and solving problems related to area and volume. It can also help in understanding and analyzing data in fields such as economics, finance, and science.

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