Distributive Property

Multiply and Divide polynomials by a constant worksheet

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Dividing Monomials Be able to divide polynomials Be able to simplify expressions involving powers of monomials by applying the division properties of powers.

Vocabulary Monomial: A number, a variable, or the product of a number and one or more variables Constant: A monomial that is a real number. Power: An expression in the form xn. Base: In an expression of the form xn, the base is x. Exponent: In an expression of the form xn, the exponent is n. Quotient: The number resulting by the division of one number by another.

Quotient of Powers Simplify: Step 1: Rewrite the expression in expanded form Step 2: Simplify. For all real numbers a, and integers m and n: Remember: A number divided by itself is 1.

Power of a Quotient Simplify: Step 1: Write the exponent in expanded form. For all real numbers a and b, and integer m: Step 2: Multiply and simplify.

Division by a Monomial Step 1: Divide the coefficients together Step 2: When you divide the variables together, subtract the exponents of LIKE BASES Step 3: Do this to each term in the numerator

Things to Remember When dividing Polynomials by a monomial, remember to divide each term in the numerator by the term in the denominator. Remember your exponent laws for dividing. You subtract the exponents if the base is the same. Remember your answer can have a fraction. You may only have to reduce the fraction in some cases.

Step 1: Create “Fractions” by dividing each term in numerator by Step 1: Create “Fractions” by dividing each term in numerator by the denominator Step 2: Divide the coefficients Step 2: Divide the variables, subtract exponents of LIKE BASES Step 4: Simplify the expression (if possible)

Step 1: Create “Fractions” by dividing each term in numerator by Step 1: Create “Fractions” by dividing each term in numerator by the denominator Step 2: Divide the coefficients Step 2: Divide the variables, subtract exponents of LIKE BASES Step 4: Simplify the expression (if possible) Simplify When Dividing a Polynomial by a monomial, you are simplifying the expression. 5x2 – 10x 5 Simplify, Divide each term in the numerator by the term in the denominator. 5x2 5 10x = - = x2 – 2x

Simplify = - + = 3b3 – 6b2 + 9b 6b 3b3 6b 6b2 9b b2 2 - b + 3 Step 1: Create “Fractions” by dividing each term in numerator by the denominator Step 2: Divide the coefficients Step 2: Divide the variables, subtract exponents of LIKE BASES Step 4: Simplify the expression (if possible) Simplify When Dividing a Polynomial by a monomial, you are simplifying the expression. 3b3 – 6b2 + 9b 6b Simplify, Divide each term in the numerator by the term in the denominator. 3b3 6b 6b2 = - + 9b = b2 2 - b + 3 Remember that you can have a fraction in your answer, just reduce.

Simplify Step 1: Create “Fractions” by dividing each term in numerator by the denominator Step 2: Divide the coefficients Step 2: Divide the variables, subtract exponents of LIKE BASES Step 4: Simplify the expression (if possible)

Step 1: Create “Fractions” by dividing each term in numerator by Step 1: Create “Fractions” by dividing each term in numerator by the denominator Step 2: Divide the coefficients Step 2: Divide the variables, subtract exponents of LIKE BASES Step 4: Simplify the expression (if possible) Division

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