Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q...

Brittney Lord

Brittney Lord

Answered

2021-02-08

Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q ae the same Px=3x4-5x3+x2-3x+5 Qx=3x-5x+1x-3x+5 Make an effort to mentally evaluate P(2) and Q(2) using the provided forms. What is simpler? Now write the polynomial Rx=x52x4+3x32x3+3x+4 in “nested” form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how using the nested form has the same arithmetic steps as using synthetic division to determine a polynomial's value?

Answer & Explanation

StrycharzT

StrycharzT

Expert

2021-02-09Added 102 answers

Given

P(x)=3x45x3+x23x+5

Q(x)=(((3x5)x+1)x3)x+5

R(x)=x52x4+3x32x2+3x+4

Expand Q

Q(x)=(((3x5)x+1)x3)x+5

=((3x25x+1)x3)x+5

=(3x35x2+x3)x+5

=3x45x3+x23x+5

So, P(x)=Q(x)=3x45x3+x23x+5

Hence proved Evaluate P(2) and Q(2)

P(x)=3x45x3+x23x+5

P(2)=3(2)45(2)3+(2)23(2)+5

=4840+46+5

=11

Q(2)=(((3(2)5)2+1)23)2+5

=((3(2)+1)23)2+5

=((3(2))3)2+5

=(3)2+5

=11
Nested form of R(x)

R(x)=x52x4+3x32x2+3x+4

R(x)=(x42x3+3x22x+3)x+4

=((x32x2+3x2)x+3)x+4

Jeffrey Jordon

Jeffrey Jordon

Expert

2022-01-15Added 2575 answers

Answer is given below (on video)

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