# Remainder Theorem & Synthetic Division...1

Discussion in 'Other Pre-University Math' started by nycmathguy, Sep 11, 2021.

1. ### nycmathguy

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Section 2.3
Question 52 (a)

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

nycmathguy, Sep 11, 2021
2. ### MathLover1

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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

MathLover1, Sep 11, 2021
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3. ### nycmathguy

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

nycmathguy, Sep 11, 2021
4. ### MathLover1

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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

MathLover1, Sep 12, 2021
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