Q&A for How to Factor Binomials

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What if the variable has no coefficient? Or the two numbers share 1 as the greatest common factor?

Donagan

Top Answerer

Some binomials simply cannot be factored.

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Question

2x to the 2 power minus 8 factored is 2(x-2)(x+2) in my text book. But I'm confused because (x-2)(x+2) becomes x to the second power minus 4

Community Answer

This is because you can actually factor twice. X squared minus four is a difference of perfect squares, meaning you can factor it to (x-2)(x+2). The 2 in front is from the first factoring.

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Question

What if one term has the same coefficient, but no exponent?

Donagan

Top Answerer

Factor out the coefficient.

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How do you factorise (x-8) squared -5?

Community Answer

(x - 8)² - 5 = (x - 8)(x - 8) - 5 = (x² - 16x + 64) - 5 = x² - 16x + 59. That expression does not factorise (factor). If the original expression were an equation (which it isn't), you could find the value of x by using the quadratic formula.

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What is lim x to the power of 2 minus 4 as x approaches 2?

Community Answer

Find the limit by letting x = 2: 2² - 4 = 4 - 4 = 0. The limit is zero. In other words, as x approaches 2, the value of (x² - 4) approaches zero.

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How do you factor x^2 + 100?

I_l1ke_gam3s

Community Answer

Unless you want to make use of "imaginary" numbers, this cannot be factored.

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