Write a polynomial function of less degree with integral coefficients that has the given zero square root of two, 1+2 square root of two

Answered question

2022-01-11

Write a polynomial function of less the group for integral coefficients that has the given zero square root of two, 1+2 square root of two

Answer & Explanation

nick1337

nick1337

Expert2022-02-08Added 777 answers

Remove parentheses.

f(x)=(x0)(x2)(x+2)(x(1+22))(x+(1+22))

f(x)=(x2+x(2))(x+2)(x(1+22))(x+1+22)

Expand (x2+2(2))(x+2) using the FOIL Method.

f(x)=(x2x+x22+x(2)x+x(2)2)(x(1+22))(x+1+22)

Simplify and combine like terms.

f(x)=(x32x)(x(1+22))(x+1+22)

Simplify each term.

f(x)=(x32x)(x122)(x+1+22)

Expand (x32x)(x122) by multiplying each term in the first expression by each term in the second expression.

f(x)=(x3x+x31+x3(22)2xx2x12x(22))(x+1+22)

Simplify each term.

f(x)=(x4x3+x3(22)2x2+2x+4x2)(x+1+22)

Expand (x4x3+x3(22)2x2+2x+4x2)(x+1+22) by multiplying each term in the first expression by each term in the second expression.

f(x)=x4x+x41+x4(22)x3xx31x3(22)+x3(22)x+x3(22)1+x3(22)(22)2x2x

2x212x2(22)+2xx+2x1+2x(22)+4x2x+4x21+4x2(22)

Simplify terms.

f(x)=x511x32x32+x3(22)+2x+4x2+4x2+16x

Add 2x32 and x3(22)

f(x)=x511x34x32+2x+4x2+4x2+16x

Add 2x and 16x

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?