Week 3.1 Nov. 10 Polynomial Long Division Concepts

When performing polynomial long division of (x^2 - 3x + 5) by (x - 2), what is the first term of the quotient?

• x^2

• x

• -3x

• 5

After multiplying the first term of the quotient (x) by the divisor (x - 2) to get (x^2 - 2x), what is the result when this is subtracted from the first part of the dividend (x^2 - 3x)?

• -5x

• -x

• x

• 5x

In polynomial long division, when is the division process considered complete?

• When the quotient becomes zero.

• When the remainder is a constant.

• When the degree of the remainder is less than the degree of the divisor.

• When the remainder is equal to the divisor.

If the quotient of a polynomial long division is (x - 1) and the remainder is 3, with the divisor being (x - 2), how is the final answer expressed?

• x - 1 - 3/(x - 2)

• x - 1 + 3/(x - 2)

• (x - 1)(x - 2) + 3

• 3/(x - 2) - (x - 1)

When dividing (2x^3 - 2x^2 + 7) by (x^2 + 1) using polynomial long division, which of the following correctly represents the dividend and divisor with placeholders for missing terms?

• Divisor: x^2 + 1, Dividend: 2x^3 - 2x^2 + 7

• Divisor: x^2 + 0x + 1, Dividend: 2x^3 - 2x^2 + 0x + 7

• Divisor: x^2 + x + 1, Dividend: 2x^3 - 2x^2 + x + 7

• Divisor: x^2 + 0x + 1, Dividend: 2x^3 - 2x^2 + 7x + 0

What is the result of subtracting (2x^3 + 0x^2 + 2x) from (2x^3 - 2x^2 + 0x + 7)?

• -2x^2 + 2x + 7

• -2x^2 - 2x + 7

• 2x^2 - 2x + 7

• 2x^2 + 2x + 7

To find the next term in the quotient for a polynomial long division problem, what is the result of dividing the leading term of the current dividend (-2x^2) by the leading term of the divisor (x^2)?

• 2x

• -2x

• 2

• -2

In polynomial long division, when is the division process considered complete?

• When the remainder is zero.

• When the degree of the remainder is greater than or equal to the degree of the divisor.

• When the degree of the remainder is less than the degree of the divisor.

• When the quotient has no more terms.

When performing polynomial long division for (x^3 - 8) / (x - 2), what is the correct way to write the dividend to ensure all terms are accounted for?

• x^3 - 8

• x^3 + 0x^2 - 8

• x^3 + 0x^2 + 0x - 8

• x^3 + 0x - 8

What is the quotient when (x^3 - 8) is divided by (x - 2)?

• x^2 + 2x + 4

• x^2 - 2x + 4

• x^2 + 4

• x^2 - 4