# How do you divide using synthetic division: #(2u^4 - 5u^3 - 12u^2 + 2u - 8)/(u - 4)#?

The remainder is

Let's perform the synthetic division

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with a Remainder of

#{: ([0],,,color(grey)(u^4),color(grey)(u^3),color(grey)(u^2),color(grey)(u^1),color(grey)(u^0)), ([1],," | ",2,-5,-12,+2,-8), ([2],ul(+color(white)("xxx"))," | ",ul(color(white)(0)),ul(+8),ul(+12),ul(+0),ul(+8)), ([3],xxcolor(magenta)4," | ",color(red)2,color(red)(+3),color(white)(+0)color(red)(0),color(white)("+")color(red)(2),color(white)("+")0), ([4],,,color(grey)(u^3),color(grey)(u^2),color(white)(+0)color(grey)(u^1),color(white)("+")color(grey)(u^0)color(white)("+"),color(blue)("R")) :}#

Rows [0] and [4] are not really part of the synthetic division; they are here for reference purposes only.

Row [1] are the coefficients of the variables in row [0]

Values in Row [3] are the sum of the values in the same column from Rows [1] and [2]

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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.

- How do you long divide #(x^4 - 2x^2 + 4x + 1) ÷ (x^3-x^2-x+1)#?
- What are all the possible rational zeros for #f(x)=x^3+4x^2+5x+2# and how do you find all zeros?
- What are the values of #k# when #x^4-3x^2+x-2# is divided by #x-k# and has a remainder of #2#?
- How do you use synthetic division to find the factors of #f(x)= x^4 -x^3 -19x^2+49x-30#?
- How do you use the rational root theorem to find the roots of #3x^3 + 3x^2-2x + 15 = 0#?

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