Basic Algebra - Factorising

[moonlighthunter]

Hi,

The numerator is 9x^2 - 4. According to the exam board the correct answer is b = 4. I think b = 2.
What do you think?

 

[HallsofIvy]

[math]ax^2- b^2= (x\sqrt{a}- b)(x\sqrt{a}+ b)[/math]. That COULD be (3x- 2)(3x+ 2) with a= 9 and b= 2.

In order that [math]9x^2- 4[/math] reduce to 3x- 2, the denominator must have a factor of 3x+ 2 so must be --- [math](3x+ 2)(4x- 1)= 12x^2 + 5x- 2[/math].

The fraction is [math]\frac{9x^2- 4}{12x^2+ 5x- 2}[/math] with a= 9, b= 4, c= 12, d= 5, and e= -2.

 

[ROBERTMILLS]

The expression [math]ax^2 - b^2 = (x\sqrt{a} - b)(x\sqrt{a} + b)[/math] represents the factored form of a quadratic equation, where [math]a[/math] and [math]b[/math] are constants. This can be demonstrated as (3x - 2)(3x + 2) with [math]a = 9[/math] and [math]b = 2[/math].

To ensure that [math]9x^2 - 4[/math] can be factored to 3x - 2, the denominator must contain a factor of 3x + 2. This implies that the denominator should be in the form of [math](3x + 2)(4x - 1) = 12x^2 + 5x - 2[/math].

Thus, the given fraction is [math]\frac{9x^2 - 4}{12x^2 + 5x - 2}[/math], where [math]a = 9[/math], [math]b = 4[/math], [math]c = 12[/math], [math]d = 5[/math], and [math]e = -2[/math].


Such type of problems are not easy. It require a lot of practice with samples and assignments. But sometimes one may get stuck with their assignments. If you also stuck with the assignment, I would suggest you to visit MathsAssignmentHelp.com for their samples and assignment solution. You can also contact them at +1 (315) 557-6473.

 

[RobertSmart]

To factorize ax^2−b^2, we use the difference of squares formula:

ax^2−b^2=(x√a−b)(x√a+b).

Given that ax^2−b^2=9x2−4,

we identify a=9 and b=2.

This expression can be factored as (3x−2)(3x+2).

For 9x^2−4 to reduce to 3x−2, the denominator must contain a factor of 3x+2.

So, it should be of the form (3x+2)(4x−1)=12x^2+5x−2.

Thus, the fraction becomes 9x^2−4/12x^2+5x−2, where a=9, b=2, c=12, d=5, and e=−2.


By the way, if you need further assistance with math assignments or want to explore more problems, you might find useful resources at website of MathsAssignmentHelp.com. You can contact them at +1 (315) 557-6473.

 

[moonlighthunter]

Thank you for your replies. It made sense.

 

[solo_guitar]

Hi,
View attachment 4141
View attachment 4141 The numerator is 9x^2 - 4. According to the exam board the correct answer is b = 4. I think b = 2.
What do you think?

I hope you are doing great. I am considering a chapter by chapter, section by section review of College Algebra. The textbook I will be using is College Algebra by Michael Sullivan Edition 9, which you can free download by simply searching online.

Come along with me as I cover every chapter, every section in the Michael Sullivan Edition 9 textbook. It's going to be fun. We are going to learn so much from each other. Knowledge is power.

My name is Feliz. What is yours? So, are you going to take this ride with me through college algebra on our way to precalculus and finally calculus l, ll, and lll? You say?

Feliz

 

[solo_guitar]

To factorize ax^2−b^2, we use the difference of squares formula:

ax^2−b^2=(x√a−b)(x√a+b).

Given that ax^2−b^2=9x2−4,

we identify a=9 and b=2.

This expression can be factored as (3x−2)(3x+2).

For 9x^2−4 to reduce to 3x−2, the denominator must contain a factor of 3x+2.

So, it should be of the form (3x+2)(4x−1)=12x^2+5x−2.

Thus, the fraction becomes 9x^2−4/12x^2+5x−2, where a=9, b=2, c=12, d=5, and e=−2.


By the way, if you need further assistance with math assignments or want to explore more problems, you might find useful resources at website of MathsAssignmentHelp.com. You can contact them at +1 (315) 557-6473.

I hope you are doing great. I am considering a chapter by chapter, section by section review of College Algebra. The textbook I will be using is College Algebra by Michael Sullivan Edition 9, which you can free download by simply searching online.

Come along with me as I cover every chapter, every section in the Michael Sullivan Edition 9 textbook. It's going to be fun. We are going to learn so much from each other. Knowledge is power.

My name is Feliz. What is yours? So, are you going to take this ride with me through college algebra on our way to precalculus and finally calculus l, ll, and lll? You say?

Feliz

 

[conway]

Is this what you really want? Pretend for a moment you are the greatest mathematician to have ever lived. What is that next to the value of love?

 

[solo_guitar]

Is this what you really want? Pretend for a moment you are the greatest mathematician to have ever lived. What is that next to the value of love?

I give up. Take care of yourself. Blocking time.

 

[conway]

Lol be blessed

 

[conway]

If you wish to only talk of mathematics....you must live in and remain....in college. Such a thing is very sad. Such a thing has no beaches....no entertainment....no love....good luck...if that is what you wish....good luck...you will find many friends among robots!

 

[Oculus8596]

Hi,
View attachment 4141
View attachment 4141 The numerator is 9x^2 - 4. According to the exam board the correct answer is b = 4. I think b = 2.
What do you think?

What have you tried?