Q&A for How to Factor Algebraic Equations

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How do I factor simple addition?

Community Answer

Find a common factor for the two numbers. For example, for 6 + 8, 6 and 8 share a factor of two. You can then rewrite it as 2 (3 + 4).

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Question

How would I factor -24x+4x^2?

Donagan

Top Answerer

Both terms have 4x as a factor. Therefore, -24x + 4x² = 4x(-6 + x) = 4x(x - 6).

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Question

Can you demonstrate an easier problem? I have problems like 42r - 18 to factor.

Community Answer

Find a common factor of 42r and 18, e.g. 6. This number will go on the outside of the bracket so 6(...). Then divide the original number(s) you had by 6. We end up with 7r-3. This will go on the inside of the bracket to make the final answer: 6(7r-3). You can check your answer by expanding the brackets again: if the answer matches what you started with, then the answer is correct!

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Sqrt[2(ab)^2+(ac)^2+(bc)^2)-a^4-b^4-c^4]/4. This equation is part of the proof of Heron's Formula. Could you show, step by step, how to factor it?

Community Answer

Use the "guess a root" method. Saying what it's from is a huge hint. Your expression should equal 0 whenever a + b = c (degenerate triangle). That means (a+b-c) is a factor. By symmetry (a-b+c) and (-a+b+c) are also factors. Divide those out and see what's left.

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Question

How do I factorize 4x^3 + 8x?

Donagan

Top Answerer

4x(x² + 2).

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Question

How do I factorize x^2 + 6x + 9?

Donagan

Top Answerer

x² + 6x + 9 = (x + 3) (x + 3) = (x + 3)²

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Question

How do I factor -3 - p?

Donagan

Top Answerer

The only factor common to both terms is -1. So -3 - p = -1(3 + p). You could also write it as -(3 + p). Either way the value is the same.

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Question

How do I factorize 5a + ax - 2b + by?

Donagan

Top Answerer

a(5 + x) - b(2 - y).

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Question

What are the factors of 2x^2 - 7x-6 = 0? I can't make it work to any of the above rules.

Donagan

Top Answerer

You're right, it doesn't factor.

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Question

How do I do 5a - 10av?

Cluster_Ducky

Community Answer

Both terms can be factorized as 5 and a, therefore we keep a 5a outside the bracket: 5a(1x - 2v).

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Question

How do I factor 8x^2 - 14x - 15?

Donagan

Top Answerer

8x² - 14x - 15 = (4x + 3)(2x - 5).

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Question

How do I factorize 8wx + 12xyz - 24wxyz?

Donagan

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8wx + 12xyz - 24wxyz = 4x (2w + 3yz - 6wyz).

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Question

How do I I factor x squared -x-30+0?

Community Answer

So you have x^2 - x - 30 + 0. This factors nicely into (x-6)(x+5). To double check, multiply the factors together to make sure you get what you started with.

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Question

How do I answer 3m(b - m)?

Donagan

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3bm - 3m².

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Question

How can I solve an algebraic expression involving a perfect square?

Community Answer

If the question is the difference of perfect squares, such as (x^2-4), you would square root both numbers and put it in this formula (x+4)(x-4).

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Question

How do I factor powers in algebraic equations?

Community Answer

Try to factor out common factors like 2x^2 +x; you can factor this to be x(2x+1). Do your best to simplify and cancel.

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Question

How do l factorize when doing algebra?

Community Answer

When you factorize, you are trying to find the greatest common factor. For example, take 4=2x. 2 is the is the greatest common factor because its the highest possible number BOTH numbers can be divided with.

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Question

How can I factorize x^2-9?

Community Answer

x² - 9 = (x - 3)(x + 3).

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Question

How do I factor an equation that doesn’t equal zero (ex: 5zma=a+2)?

I_l1ke_gam3s

Community Answer

First, you cannot solve this equation because there are a total of 3 variables in one equation, and you need three separate equations in terms of z, m, and a. But if you set it equal to zero by subtracting a and 2 from both sides, you get 5zma - a - 2 = 0. You can factor out a, making it a(5zm - 1) - 2 = 0.

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