Factoring Polynomials: Techniques and Strategies

What pattern identifies a difference of two squares in a polynomial?

• a^3 - b^3

• a^2 - b^2

• a + b

• a^2 + b^2

Tags

CCSS.HSA.APR.C.4

What is essential to recognize patterns in factoring techniques?

• Memorizing formulas

• Mastering the multiplication table

• Using a calculator

• Understanding calculus

How is the greatest common factor used in factoring polynomials?

• By adding it to each term

• By dividing each term by it

• By multiplying it with each term

• By subtracting it from each term

How do you determine the greatest common factor (GCF) of a polynomial?

• By finding the difference of the coefficients

• By adding the coefficients

• By identifying the highest common factor that divides the terms

• By dividing the polynomial by its leading coefficient

What is the result of factoring by grouping in the polynomial y^3 + 3y^2 + 4y + 12?

• y + 3(y^2 + 4)

• y^2 + 4(y + 3)

• (y + 3)(y^2 + 4)

• y^2(y + 3) + 4(y + 3)

What technique is used to simplify the polynomial x^3 - 5x^2 + 3x - 15?

• Completing the square

• Difference of squares

• Quadratic formula

• Factoring by grouping

What is the first step in factoring a quadratic equation with a leading coefficient of one?

• Dividing each term by the leading coefficient

• Multiplying the first and last terms

• Finding the square root

• Drawing a big X

Which set of factors solves the puzzle for factoring x^2 + 7x + 12?

• 12 and 1

• 3 and 4

• 6 and 2

• 2 and 10

In advanced quadratic factoring, what additional step is taken when the leading coefficient is greater than one?

• Converting coefficients to their absolute values

• Applying the distributive property

• Multiplying the first and last terms to find new factors

• Using the quadratic formula

What is the factored form of 2x^2 + 5x + 2?

• (2x + 1)(x + 2)

• (2x + 2)(x + 1)

• (x + 1)(x + 2)

• (2x - 1)(x - 2)