Chapter 1.2.3-1.2.5: Multiplying Polynomials, Power of Monomials and Binomials, and Dividing Polynomial

How do you multiply a binomial by a binomial?

applying the Distributive Property twice.
(a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd

multiply the First terms, Outer terms, Inner terms and Last terms.
This is abbreviated FOIL

How do you multiply a polynomial by a polynomial?

1. Distribute each term of the first polynomial to every term of the second polynomial.

2. Multiply constants and apply exponent rules (add exponents for like terms).

3. Combine like terms if needed.

How do you multiply conjugate pairs?

Use the difference of squares formula:

(a + b)(a - b) = a^2 - b^2

How do you find the gfc?

1. Find the prime factorization of each number.

2. Enter the prime factors of the first number in separate columns in the first row of the chart.

3. List the prime factors of the second number in the second row, matching factors in the same column.

4. Bring down all full columns (where both numbers share prime factors).

The product of the factors brought down is the GCF.

What is a dividend and a divisor?

• Dividend: The polynomial being divided.

• Divisor: The polynomial dividing the dividend.

2x^2 + 3x + 1 / x + 1

• Dividend: 2x^2 + 3x + 1

• Divisor: x + 1

How do you Divide a Polynomial by a Monomial?

• Divide each term of the polynomial by the monomial.

• Distribute the division over addition and subtraction.

What is one way to Divide a Polynomial by a Binomial?

Dividing Polynomials (Cancellation Method)

• Factor both the numerator and denominator.

• Cancel common factors.

• Simplify the remaining expression.

What is another way to divide a polynomial by a binomial?

long division:

1. Ensure descending order of the dividend and divisor.

2. Divide the leading term of the dividend by the leading term of the divisor.

3. Multiply the quotient by the divisor and subtract from the dividend.

4. Repeat until the degree of the remainder is less than the divisor.