Yes, that is correct! Great job factoring the expression.

  • MHB
  • Thread starter mathdad
  • Start date
In summary, factoring is a mathematical process used to simplify complex expressions and make them easier to solve. It is typically used when solving equations with variables and can also be used to simplify algebraic expressions and find the roots of a polynomial equation. The general steps for factoring include identifying the greatest common factor, looking for patterns within the terms, using factoring techniques, and checking the factoring by multiplying the factors together. An example of factoring an expression is 2x² + 8x + 6, which can be factored into (2x + 3)(x + 2). To check your factoring, you can multiply the factors together or plug in different values for the variable.
  • #1
mathdad
1,283
1
Factor the expression.

t^4 - 9t^2 + 20

My Solution

(t^2)^2 - 9t^2 + 20

Let u = t^2

u^2 - 9u + 20

(u - 5)(u - 4)

I can back-substitute for u.

(t^2 - 5)(t^2 - 4)

I see that t^2 - 4 is the difference of two perfect squares.

Answer: (t^2 - 5)(t - 2)(t + 2)

Correct?
 
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  • #2
Looks good. (Yes)
 
  • #3
MarkFL said:
Looks good. (Yes)

Very good. Good night. More factoring questions on Friday.
 

FAQ: Yes, that is correct! Great job factoring the expression.

What is factoring and why is it important?

Factoring is a mathematical process of breaking down an expression into smaller factors. It is important because it helps simplify complex expressions and makes them easier to solve.

How do I know when to use factoring?

Factoring is typically used when solving equations with variables, such as quadratic equations. It can also be used to simplify algebraic expressions and find the roots of a polynomial equation.

What are the steps for factoring an expression?

The general steps for factoring an expression are as follows:
1. Identify the greatest common factor (GCF) of the coefficients.
2. Look for patterns within the terms, such as perfect squares or the difference of squares.
3. Use factoring techniques, such as the distributive property or grouping, to further simplify the expression.
4. Check your factoring by multiplying the factors together and making sure they equal the original expression.

Can you provide an example of factoring an expression?

Sure! Let's factor the expression 2x² + 8x + 6.
Step 1: The GCF of the coefficients is 2.
Step 2: The first two terms have a common factor of 2x, and the last two terms have a common factor of 3.
Step 3: Using the distributive property, we can rewrite the expression as 2x(x + 4) + 3(x + 2).
Step 4: Now we have a common factor of (x + 2), so we can rewrite the expression as (2x + 3)(x + 2).
This is the factored form of the expression.

How can I check my factoring?

To check your factoring, you can multiply the factors together and see if they equal the original expression. You can also plug in different values for the variable and make sure the factored expression and the original expression give the same result.

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