Question

Without actual division, prove that the polynomial 2x3+4x2+x-34 is exactly
divisible by (x-2)

Answer 1

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Answer 2

Step-by-step explanation:

Hey!

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\begin{gathered}p(x) = > 2x {}^{3} + 4x {}^{2} + x - 34 \\ \\ g(x) = > (x - 2) \\ \\ = > > x - 2 = 0 \\ \\ = > > x = 2 \\ \\ put \: x = 2 \: in \: p(x) \\ \\ = > 2(2) {}^{3} + 4(2) {}^{2} + 2 - 34 \\ \\ = > 2 \times 8 + 4 \times 4 + 2 - 34 \\ \\ = > 16 + 16 + 2 - 34 \\ \\ = > 32 + 2 - 34 \\ = > 34 - 34 = 0 \\ \\ \end{gathered}

p(x)=>2x

3

+4x

2

+x−34

g(x)=>(x−2)

=>>x−2=0

=>>x=2

putx=2inp(x)

=>2(2)

3

+4(2)

2

+2−34

=>2×8+4×4+2−34

=>16+16+2−34

=>32+2−34

=>34−34=0

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