Factoring

Front

What is factoring in algebra?

Back

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

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression ax² + bx + c is typically expressed as (px + q)(rx + s), where p, q, r, and s are constants.

Front

How do you factor the expression x² + 11x + 24?

Back

To factor x² + 11x + 24, look for two numbers that multiply to 24 and add to 11. The factors are (x + 8)(x + 3).

Front

What is the significance of the roots in factoring?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero. Factoring helps to find these roots by expressing the polynomial as a product of its factors.

Front

What is the difference between a factor and a multiple?

Back

A factor is a number that divides another number without leaving a remainder, while a multiple is the result of multiplying a number by an integer.

Front

How do you factor the expression 3a² + 4a + 1?

Back

To factor 3a² + 4a + 1, find two numbers that multiply to (3*1) = 3 and add to 4. The factors are (3a + 1)(a + 1).

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions evenly.

Front

How do you determine if x - 5 is a factor of x² - 9x + 20?

Back

To determine if x - 5 is a factor, use polynomial long division or synthetic division. If the remainder is zero, then x - 5 is a factor.

Front

What is the factored form of x² + 4x + 3?

Back

The factored form of x² + 4x + 3 is (x + 1)(x + 3).

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group.