University:
Miami University
Course:
MTH 125 | Precalculus
Academic year:

2023
Views:

80

Pages:

1
Author:

Alma Stephenson

Prerequisites Review #3 - Polynomial Addition and Multiplication Simplify the expression to a polynomial in standard form: (4x³ - 5x² - 3x + 7)(2x - 5). Distribute: 4x³(2x) + 4x³(-5) - 5x²(2x) - 5x²(-5) - 3x(2x) - 3x(-5) + 7(2x) + 7(-5) Multiply: 8x⁴ - 20x³ - 10x³ + 25x² - 6x² + 15x + 14x - 35 Combine like terms: 8x⁴ - 30x³ + 19x² + 29x - 35 Simplify the expression to a polynomial in standard form: 3(2x - 5)(x² - 4x + 2). Multiply the first two expressions: 3(2x - 5) = 6x - 15 Multiply that answer by the third expression: (6x - 15)(x² - 4x + 2) Distribute: 6x(x²) + 6x(-4x) + 6x(2) - 15(x²) - 15(-4x) - 15(2) Multiply: 6x³ - 24x² + 12x - 15x² + 60x - 30 Combine like terms: 6x³ - 39x² + 72x - 30 Simplify the expression to a polynomial in standard form: (3x - 1)(-2x² + 4x - 7). Distribute: 3x(-2x²) + 3x(4x) + 3x(-1) - 1(-2x²) - 1(4x) - 1(-7) Multiply: -6x³ + 12x² - 21x + 2x² - 4x + 7 Combine like terms: -6x³ + 14x² - 25x + 7

Polynomial Addition and Multiplication

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