Dividing by Factoring: Key Concepts and Techniques

What is the first step in dividing a polynomial by a monomial?

• Factor the polynomial

• Identify the GCF

• Divide each term individually

• Simplify the expression

What method is used to divide a polynomial by a binomial?

• Factoring

• Synthetic division

• Long division

• Partial fractions

What is created to help find the factors of a polynomial during division?

• A quadratic equation

• A Venn diagram

• A pie chart

• An X puzzle

What must be true for factors to be canceled out in polynomial division?

• They must be prime numbers

• They must be opposites

• One must be the derivative of the other

• They must be identical

What does factoring by grouping involve?

• Separating the polynomial into two groups and finding the GCF of each

• Multiplying adjacent terms together

• Adding all terms of the polynomial

• Dividing the polynomial by its highest degree term

How can you identify a factor of the numerator from the denominator?

• By recognizing a common factor

• By using the distributive property

• Through long division

• By applying the quadratic formula

What is a key step in simplifying a division problem involving polynomials?

• Multiplying the highest degree terms

• Adding all the coefficients

• Subtracting the polynomials

• Canceling out common factors

Why can't terms be canceled just because they appear in both the numerator and denominator?

• Because they might not be factors

• Because it violates algebraic principles

• Because they are not like terms

• Because it would change the degree of the polynomial

What is a 'difference of two squares'?

• Two polynomials added together

• A polynomial divided by a monomial

• The subtraction of two square roots

• A binomial squared minus another binomial squared

How is the 'difference of two squares' factored?

• Into a sum and a difference

• Into two identical binomials

• By finding the square root of each term

• By dividing each term by 2