Dividing Polynomials: Long Division Techniques

What is the first step in dividing polynomials by long division?

• Subtract the polynomials

• Add the polynomials

• Multiply the polynomials

• Identify the dividend and divisor

In the given problem, what is the dividend?

• 9x - 36

• 4x^2 - 9x + 9

• 4x^3 - 17x^2 + 13x - 41

• X - 4

What should you do if there are missing degree terms in the dividend?

• Ignore them

• Insert a placeholder with zero as the coefficient

• Add a new term

• Multiply the terms

How many times does X go into 4x^3?

• 4

• 4x

• 4x^3

• 4x^2

What is the result of distributing 4x^2 into the divisor X - 4?

• 4x^2 + 16x

• 4x^3 - 16x^2

• 4x^3 + 16x^2

• 4x^2 - 16x

What is the next step after distributing and subtracting the first term?

• Bring down the next term

• Add the terms

• Divide the terms

• Multiply the terms

How many times does X go into -1x^2?

• -1x

• -x

• 1x

• x

What is the result of distributing -x into the divisor X - 4?

• -x^2 + 4x

• x^2 - 4x

• x^2 + 4x

• -x^2 - 4x

What is the final quotient in the given problem?

• 4x^2 - x + 9

• 4x^2 + x + 9

• 4x^2 - 9x + 9

• 4x^2 - x - 9

Is X - 4 a factor of the dividend 4x^3 - 17x^2 + 13x - 41?

• No, because the divisor is not a factor

• Yes, because the quotient is a polynomial

• No, because the remainder is not zero

• Yes, because the remainder is zero