Remainder Theorem & Synthetic Division...1

[nycmathguy]

Section 2.3
Question 52 (a)

Can you do 52 (a) as notes for me to try a few more on my own?

 

[MathLover1]

52.
g(x)=2x^6+3x^4-x^2+3

a. g(2)

g(2)=2*2^6+3*2^4-2^2+3
g(2)=128+48-4+3
g(2)=175

 

[nycmathguy]

52.
g(x)=2x^6+3x^4-x^2+3

a. g(2)

g(2)=2*2^6+3*2^4-2^2+3
g(2)=128+48-4+3
g(2)=175

You simply did an evaluation. The instructions say to use the Remainder Theorem and synthetic division to find each function value.

 

[MathLover1]

g(x)=2x^6+3x^4-x^2+3
g(2) =>x=2

factor will be (x-2)

........(2x^5+4x^4+11x^3+22x^2+43x +86
(x-2)|2x^6+0*x^5+3x^4+0*x^3-x^2+0*x+3
........2x^6-4x^5
.................4x^5+3x^4
.................4x^5-8x^4
..........................11x^4+0*x^3
..........................11x^4-22x^3
.....................................22x^3-x^2
.....................................22x^3-44x^2
.................................................43x^2+0*x
.................................................43x^2-86x
.............................................................86x+3
.............................................................86x-172
....................................................................172->reminder

which proves that g(2) =172

 

[nycmathguy]

g(x)=2x^6+3x^4-x^2+3
g(2) =>x=2

factor will be (x-2)

........(2x^5+4x^4+11x^3+22x^2+43x +86
(x-2)|2x^6+0*x^5+3x^4+0*x^3-x^2+0*x+3
........2x^6-4x^5
.................4x^5+3x^4
.................4x^5-8x^4
..........................11x^4+0*x^3
..........................11x^4-22x^3
.....................................22x^3-x^2
.....................................22x^3-44x^2
.................................................43x^2+0*x
.................................................43x^2-86x
.............................................................86x+3
.............................................................86x-172
....................................................................172->reminder

which proves that g(2) =172

It's easier to read long division on paper or when done on the board. Thanks anyway. Moving on.