Is my factoring correct for these polynomials?

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Great job! In summary, the conversation discusses factoring polynomials, specifically (A) u^2v^2 - 225 and (B) 81x^4 - x^2. The correct factored form for (A) is (uv+15)(uv-15), and for (B) it is x^2(9x+1)(9x-1). This involves using the formula for the difference of perfect squares, where a and b represent the square roots of the values being subtracted. The conversation also mentions that these problems test knowledge of factoring values that are perfect squares.
  • #1
mathdad
1,283
1
Factor each polynomial given.

(A) u^2v^2 - 225

(B) 81x^4 - x^2

For (A), I got (uv - 15)(uv + 15). Is this right?

Solution for (B):

x^2(81x^2 - 1)

I think the binomial inside the parentheses can be factored.

So, (81x^2 - 1) becomes (9x - 1)(9x + 1).

My answer for (B) is x^2(9x - 1)(9x + 1).

Is this correct?
 
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  • #2
Both are correct.
These are both problems testing your knowledge of factoring values that are "perfect squares".
Meaning,
a^2 - b^2 = (a+b)(a-b) For example,
in (a) you have u^2v^2 - 225. Using the formula, a=uv and b=15. So your answer is (a+b)(a-b)=(uv+15)(uv-15).
 
  • #3
joypav said:
Both are correct.
These are both problems testing your knowledge of factoring values that are "perfect squares".

Not perfect squares but difference of perfect squares
 
  • #4
It feels awesome to get the right answer.
 

Related to Is my factoring correct for these polynomials?

1. How can I check if my factoring is correct for these polynomials?

One way to check if your factoring is correct for a polynomial is to multiply the factors together and see if they equal the original polynomial. Another way is to use the quadratic formula to find the roots of the polynomial and see if they match the factored form.

2. What are common mistakes made when factoring polynomials?

Common mistakes when factoring polynomials include forgetting to factor out a common factor, incorrectly applying the distributive property, and making errors in the signs of the factors.

3. How can I improve my factoring skills for polynomials?

Practicing factoring regularly and familiarizing yourself with common factoring techniques, such as difference of squares and grouping, can improve your factoring skills for polynomials. Additionally, checking your factoring by multiplying the factors together can help identify any mistakes and improve your understanding.

4. Is there a specific order in which I should factor a polynomial?

There is no specific order in which you must factor a polynomial, but it is often helpful to start by looking for common factors and then using other factoring techniques, such as grouping or the quadratic formula, if necessary.

5. What are some tips for factoring complex polynomials?

When factoring complex polynomials, it is important to first look for common factors and then use techniques such as grouping or the quadratic formula to factor the remaining terms. Breaking down the polynomial into smaller, simpler parts can also make the factoring process easier. It can also be helpful to check your factoring by multiplying the factors together to ensure they equal the original polynomial.

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