MATH SOLVE

3 months ago

Q:
# synthetic division of 2x^3-4x+5 divided by x+3. Thanks! Please show me how to do it.

Accepted Solution

A:

Answer:[tex]\frac{2x^3-4x+5}{x+3}=2x^2-6x+14+\frac{-37}{x+3}[/tex].Step-by-step explanation:We can only do synthetic division when dividing by a linear expression. You are because you are dividing by x+3 which has degree 1.We know it has degree 1 because the one variable we have there has a power of 1.Anyways x+3 decides what we put on the outside of the division.x+3=0 when x=-3 (subtracted 3 on both sides).We put -3 on the outside.Now for the numbers that go inside are the coefficients contained in the expression that is the dividend. You need to make sure you have any zero-placeholders for any missing terms.For example you cannot just write 2 - 4 5 because we are missing the x^2 term so you would actually write 2 0 -4 5.So this is the setup for this:-3 | 2 0 -4 5 | |------------------------------First step drop down the first entry inside below the bar (kind of like doing 2+0 because we really are):-3 | 2 0 -4 5 | |------------------------------ 2Any number that you put below the bar must be multiplied to the outside number (except the last number which is the remainder). This number will go under the term that is after it inside above the bar. Like this:-3 | 2 0 -4 5 | -6 |------------------------------ 2Now any numbers inside directly underneath another number, you add:-3 | 2 0 -4 5 | -6 |------------------------------ 2 -6Do you know what we do with numbers below the bar? They get ________ by the outside number.You guessed it! They get multiplied as we said earlier:-3 | 2 0 -4 5 | -6 18 |------------------------------ 2 -6Just like when we did 0+-6 to get -6; we are going to do -4+18 to get the next number under the bar:-3 | 2 0 -4 5 | -6 18 |------------------------------ 2 -6 14Multiply and add over and over again until you get the remainder:So the result of doing 14(-3) goes directly underneath 5:-3 | 2 0 -4 5 | -6 18 -42 |------------------------------ 2 -6 14 -37So the quotient is: 2x^2-6x+14 (This is just one degree less than the dividend and goes in order of descending exponents)The remainder is -37 (This is the last number in the last column)So [tex]\frac{2x^3-4x+5}{x+3}=2x^2-6x+14+\frac{-37}{x+3}[/tex].