Write a polynomial function f of least degree

Answered question

2022-01-19

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form. 7, 1+i

Answer & Explanation

xleb123

xleb123

Skilled2022-01-30Added 181 answers

Simplify each term.

Apply the distributive property.

(x7)(x11i)(x(1i))

Multiply −1 by 1.

(x7)(x1i)(x(1i))

Expand (x7)(x1i) by multiplying each term in the first expression by each term in the second expression.

(xx+x1+x(i)7x717(i))(x(1i))

Simplify terms.

(x2x+x(i)7x+7+7i)(x(1i))

Subtract 7x from x.

(x2+x(i)8x+7+7i)(x(1i))

Simplify each term.

Apply the distributive property.

(x2+x(i)8x+7+7i)(x11i)

Multiply -1 by 1

(x2+x(i)8x+7+7i)(x1i)

Multiply -1 by -1

(x2+x(i)8x+7+7i)(x1+1i)

Multiply i by 1.

(x2+x(i)8x+7+7i)(x1+i)

Expand (x2+x(i)8x+7+7i)(x1+i) by multiplying each term in the first expression by each term in the second expression.

x2x+x21+x2i+x(i)x+x(i)1+x(i)i8xx8x18xi+7x+71+7i+7ix+7i1+7ii

Simplify terms.

x3x2+x2i+x2(i)+xi+x8x2+8x8xi+7x7+7i+7ix7i7

Simplify by adding terms.

x39x2+16x14

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