# How do you divide #(x^5 - 2x^2 + 4) ÷ (x - 4)#?

It is basically just long division, but remember to include terms with

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To divide ( (x^5 - 2x^2 + 4) ) by ( (x - 4) ), you can use polynomial long division or synthetic division. Let's use polynomial long division here.

Step 1: Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient.

[ \frac{x^5}{x} = x^4 ]

Step 2: Multiply the entire divisor ( (x - 4) ) by the term you found in step 1, then subtract this from the dividend.

[ (x - 4)(x^4) = x^5 - 4x^4 ]

[ (x^5 - 2x^2 + 4) - (x^5 - 4x^4) = -4x^4 - 2x^2 + 4 ]

Step 3: Repeat the process with the result from step 2.

[ \frac{-4x^4}{x} = -4x^3 ]

[ (x - 4)(-4x^3) = -4x^4 + 16x^3 ]

[ (-4x^4 - 2x^2 + 4) - (-4x^4 + 16x^3) = 16x^3 - 2x^2 + 4 ]

Step 4: Repeat until the degree of the remainder is less than the degree of the divisor.

[ \frac{16x^3}{x} = 16x^2 ]

[ (x - 4)(16x^2) = 16x^3 - 64x^2 ]

[ (16x^3 - 2x^2 + 4) - (16x^3 - 64x^2) = 62x^2 + 4 ]

Since the degree of the remainder (2) is less than the degree of the divisor (1), we stop.

Therefore, ( (x^5 - 2x^2 + 4) ) divided by ( (x - 4) ) equals ( x^4 - 4x^3 + 16x^2 + \frac{62x^2 + 4}{x - 4} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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