A2 - 3.3 Long Division & Synthetic Division

Front

What is long division in polynomial division?

Back

Long division is a method used to divide polynomials similar to numerical long division, where the dividend is divided by the divisor step by step.

Tags

CCSS.HSA.APR.D.6

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c). It is faster and requires less writing than long division.

Tags

CCSS.HSA.APR.D.6

Front

What is the quotient in polynomial division?

Back

The quotient is the result of dividing one polynomial by another, excluding the remainder.

Tags

CCSS.HSA.APR.D.6

Front

How do you find the remainder when dividing a polynomial by a linear factor?

Back

You can find the remainder by evaluating the polynomial at the value that makes the linear factor zero (using the Remainder Theorem).

Tags

CCSS.HSA.APR.B.2

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial p(x) by (x - c) is equal to p(c).

Tags

CCSS.HSA.APR.B.2

Front

What does it mean to write an answer in factored form?

Back

Writing an answer in factored form means expressing a polynomial as a product of its factors, which can help in identifying roots and simplifying expressions.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial, representing how many times the variable is multiplied.

Tags

CCSS.6.EE.A.2B

Front

What is the significance of placing a zero as a coefficient in a polynomial?

Back

Placing a zero as a coefficient for a missing exponent ensures that the polynomial maintains its proper degree and structure.

Front

How do you perform long division with polynomials?

Back

To perform long division with polynomials, divide the leading term of the dividend by the leading term of the divisor, multiply the entire divisor by this result, subtract, and repeat with the new polynomial.

Tags

CCSS.HSA.APR.D.6

Front

What is the leading term of a polynomial?

Back

The leading term of a polynomial is the term with the highest degree, which determines the polynomial's end behavior.