Apex Algebra 1 Final Flashcards

Polynomial Degree

• The degree of the polynomial x² + x + 3 is 2.
• For the polynomial 3x² + x + 33, the degree is also 2.

Polynomial Operations

• The sum of (2x² + 6x + 5) and (3x² − 2x − 1) results in 5x² + 4x + 4.
• Subtracting (3x³ − 8x² − 5x + 6) from (x³ + 3x² + 5x - 4) gives -2x³ + 11x² + 10x - 1.

Binomial Multiplication

• The product of the binomials (x - 5)(x + 5) simplifies to x² - 25.
• Multiplying (7x² + 3)(7x² + 3) results in 49x⁴ + 42x² + 9.

Polynomial Multiplication

• The polynomial 3x²(4x² - 5x + 7) expands to 12x⁴ - 15x³ + 21x².
• The product of (4x - 5)(2x² + 3x - 6) simplifies to 8x³ + 2x² - 39x + 30.

Factoring

• The greatest common factor (GCF) of 6x + 4 is 2(3x + 2).
• The polynomial 5x(2x - 4) - 3(2x - 4) factors to (2x - 4)(5x - 3).
• Factoring by grouping leads to 2x(x² + 9x + 5) for the expression 2x³ + 18x² + 10x.

Solving Quadratic Equations

• The solutions for the equation 3x² + 8x + 4 = 0 are x = -2 and x = -2/3.

Additional Polynomial Multiplication

• Multiplying (x + 2)(x² + 3x + 4) yields x³ + 5x² + 10x + 8.
• Factoring the expression 3x² + 6x + 4x + 8 gives (x + 2)(3x + 4).

Simplification

• The expression (t + 6)² simplifies to t² + 12t + 36.
• The perfect square trinomial 4x² - 16x + 16 factors to (2x - 4)².

Difference of Perfect Squares

• The expression 4x² - 81y² factors into (2x - 9y)(2x + 9y).

Finding Zeros and Vertex

• The zeros of the equation x² + 3x + 2 = 0 are found from factors x + 2 = 0 and x + 1 = 0.
• The vertex of the parabola represented by y = (x - 3)² + 2 is at the point (3, 2).

Inverse Functions

• The inverse of the function f(x) = 2x - 1 is f⁻¹(x) = ½x + ½.
• For the function f(x) = 4x - 5, its inverse is f⁻¹(x) = x/4 + 5/4.