Factoring

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors, that when multiplied together give the original expression.

Front

What is a linear factor?

Back

A linear factor is a polynomial of degree one, typically in the form of (ax + b), where a and b are constants.

Front

Factor the expression: 5v² - 30v + 40

Back

5(v - 4)(v - 2)

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression is typically expressed as (ax + b)(cx + d), where a, b, c, and d are constants.

Front

Factor the expression: 3v² - 4v - 7

Back

(3v - 7)(v + 1)

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials helps simplify expressions, solve equations, and find roots of functions.

Front

Factor the expression: 2x² - 12x - 14

Back

2(x + 1)(x - 7)

Front

What is the difference between a prime polynomial and a composite polynomial?

Back

A prime polynomial cannot be factored into simpler polynomials over the integers, while a composite polynomial can be factored into two or more non-trivial factors.

Front

Factor the expression: x² - 6x + 8

Back

(x - 2)(x - 4)

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function and influences the shape of its graph.