We appreciate your visit to Factor the expression completely tex x 4 4x 2 45 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We need to factor the expression
[tex]$$
x^4 + 4x^2 - 45.
$$[/tex]
A useful strategy is to treat this as a quadratic in terms of [tex]$x^2$[/tex]. Follow these steps:
1. Let
[tex]$$
u = x^2.
$$[/tex]
Then the expression becomes:
[tex]$$
u^2 + 4u - 45.
$$[/tex]
2. Now, we need to factor the quadratic [tex]$u^2 + 4u - 45$[/tex]. We look for two numbers that multiply to [tex]$-45$[/tex] and add to [tex]$4$[/tex]. These numbers are [tex]$9$[/tex] and [tex]$-5$[/tex] because:
[tex]$$
9 \cdot (-5) = -45 \quad \text{and} \quad 9 + (-5) = 4.
$$[/tex]
3. Using these numbers, we factor the quadratic as:
[tex]$$
u^2 + 4u - 45 = (u - 5)(u + 9).
$$[/tex]
4. Substitute back [tex]$x^2$[/tex] for [tex]$u$[/tex]:
[tex]$$
(u - 5)(u + 9) = (x^2 - 5)(x^2 + 9).
$$[/tex]
Thus, the complete factorization of the original expression is:
[tex]$$
(x^2 - 5)(x^2 + 9).
$$[/tex]
[tex]$$
x^4 + 4x^2 - 45.
$$[/tex]
A useful strategy is to treat this as a quadratic in terms of [tex]$x^2$[/tex]. Follow these steps:
1. Let
[tex]$$
u = x^2.
$$[/tex]
Then the expression becomes:
[tex]$$
u^2 + 4u - 45.
$$[/tex]
2. Now, we need to factor the quadratic [tex]$u^2 + 4u - 45$[/tex]. We look for two numbers that multiply to [tex]$-45$[/tex] and add to [tex]$4$[/tex]. These numbers are [tex]$9$[/tex] and [tex]$-5$[/tex] because:
[tex]$$
9 \cdot (-5) = -45 \quad \text{and} \quad 9 + (-5) = 4.
$$[/tex]
3. Using these numbers, we factor the quadratic as:
[tex]$$
u^2 + 4u - 45 = (u - 5)(u + 9).
$$[/tex]
4. Substitute back [tex]$x^2$[/tex] for [tex]$u$[/tex]:
[tex]$$
(u - 5)(u + 9) = (x^2 - 5)(x^2 + 9).
$$[/tex]
Thus, the complete factorization of the original expression is:
[tex]$$
(x^2 - 5)(x^2 + 9).
$$[/tex]
Thanks for taking the time to read Factor the expression completely tex x 4 4x 2 45 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
