Factoring Polynomials

Front

What is factoring in mathematics?

Back

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

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the Master Product method in factoring?

Back

The Master Product method involves finding two numbers that multiply to give the product of the leading coefficient and the constant term, and add to give the middle coefficient.

Front

How do you factor a polynomial of the form ax^2 + bx + c?

Back

To factor a polynomial of this form, look for two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the polynomial using these numbers to factor by grouping.

Front

What is the factored form of a difference of squares?

Back

The factored form of a difference of squares, a^2 - b^2, is (a + b)(a - b).

Front

How do you factor out the greatest common factor (GCF) from a polynomial?

Back

To factor out the GCF, identify the largest factor that is common to all terms in the polynomial, then divide each term by this factor and write it outside the parentheses.

Front

What is the factored form of x^2 - 36?

Back

The factored form of x^2 - 36 is (x + 6)(x - 6), which is a difference of squares.

Front

What is the significance of the coefficients in a polynomial?

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Coefficients are the numerical factors that multiply the variables in a polynomial, determining the polynomial's shape and position on a graph.

Front

How do you factor the polynomial 5n³ - 10n² + 3n - 6?

Back

To factor 5n³ - 10n² + 3n - 6, group the terms: (5n² + 3)(n - 2).

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.