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Questions and Answers
Which of the following represents the correct factors of the polynomial $21x^2 + 7x$?
Which of the following represents the correct factors of the polynomial $21x^2 + 7x$?
- 7(3x + 1)
- 7x(3x + 1) (correct)
- 3x(7 + 21x)
- 2x(10 + 21x)
What type of factoring is used in the expression $16x^2 - 81$?
What type of factoring is used in the expression $16x^2 - 81$?
- Difference of two squares (correct)
- Perfect square trinomial
- Factoring by grouping
- Sum of cubes
How can the polynomial $x^2 - 10x + 25$ be classified?
How can the polynomial $x^2 - 10x + 25$ be classified?
- Sum of two cubes
- Difference of two squares
- General trinomial
- Perfect square trinomial (correct)
Which of the following expressions is a factored form of $x^3 - 27$?
Which of the following expressions is a factored form of $x^3 - 27$?
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Which statement is true when x = 4 for the expressions $A: 16x^2 - 81$ and $B: (4x - 9)(4x + 9)$?
Which statement is true when x = 4 for the expressions $A: 16x^2 - 81$ and $B: (4x - 9)(4x + 9)$?
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Study Notes
Competency Overview
- Learners will master the complete factoring of various polynomial types.
- Focus areas include common monomial factors, difference of two squares, sum and difference of two cubes, perfect square trinomials, and general trinomials.
Module Expectations
- Designed to enhance skills in factoring polynomials.
- Mastery of different factoring techniques will be achieved through this module.
- Key expectations include:
- Enumeration of various factoring types.
- Differentiation between distinct factoring techniques.
- Identification of factorable expressions.
- Complete factoring of polynomials.
Factoring Techniques
- Greatest Common Monomial Factor: Identify and factor out the highest common factor from all terms.
- Difference of Two Squares: Applies to expressions in the form (a^2 - b^2) which factor as ((a + b)(a - b)).
- Sum and Difference of Two Cubes:
- Sum: (a^3 + b^3) factors to ((a + b)(a^2 - ab + b^2)).
- Difference: (a^3 - b^3) factors to ((a - b)(a^2 + ab + b^2)).
- Perfect Square Trinomial: Form (a^2 + 2ab + b^2) factors to ((a + b)^2) and (a^2 - 2ab + b^2) factors to ((a - b)^2).
- Factoring by Grouping: Group terms with common factors, then factor out shared elements.
Pre-Test Sample Questions
- Question on Factors: Identify the correct factoring of the expression (21x^2 + 7x).
- Expression Comparison: Evaluate statements about the expressions (A: 16x^2 - 81) and (B: (4x - 9)(4x + 9)) when (x = 4).
Key Terms
- Polynomials: Algebraic expressions composed of variables raised to whole number powers.
- Factorable Expressions: Algebraic expressions that can be rewritten as a product of simpler expressions.
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