Factor by Grouping

Factor the expression: @@x^3 - 4x^2 - 4x + 16@@

• (x - 4)(x^2 - 4)

• (x + 4)(x^2 - 4)

• (x - 2)(x^2 + 2)

• (x - 4)(x^2 + 4)

What is the purpose of Factor by Grouping?

• To simplify polynomials and make them easier to solve or analyze.

• To find the roots of a polynomial equation.

• To convert a polynomial into a standard form.

• To determine the degree of a polynomial.

• (2x^2 - 1)(x - 4)

• (2x^2 + 1)(x + 4)

• (x - 2)(2x^2 + 2)

• (x + 4)(2x^2 - 1)

Factor the expression: @@7r^3 - 8r^2 + 42r - 48@@

• (r^2 + 6)(7r - 8)

• (r - 6)(7r + 8)

• (r + 6)(7r - 8)

• (r^2 - 6)(7r + 8)

How do you identify common factors in Factor by Grouping?

• Look for common terms in each group of the polynomial. Factor out the greatest common factor (GCF) from each group.

• Identify the highest degree term in the polynomial and factor it out.

• Group all terms together and factor out the smallest coefficient.

• Use synthetic division to find the common factors.

What is the first step in Factor by Grouping?

• To find the greatest common factor of the polynomial.

• To rearrange the polynomial into two groups that can be factored separately.

• To apply the quadratic formula to the polynomial.

• To combine like terms in the polynomial.

What is the significance of the signs in a polynomial when factoring?

• They determine the degree of the polynomial.

• They indicate how terms combine and affect the grouping and factoring process.

• They are irrelevant to the factoring process.

• They only affect the final result of the polynomial.

What is a trinomial?

• A polynomial with exactly two terms.

• A polynomial with exactly three terms.

• A polynomial with exactly four terms.

• A polynomial with no terms.

What is a polynomial?

• A mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

• A type of equation that has only one variable.

• A mathematical expression that can only include positive integers.

• A formula used to calculate the area of geometric shapes.

Factor the expression: @@x^3 - 5x^2 + 5x - 25@@

• (x^2 + 5)(x - 5)

• (x - 5)(x^2 - 5)

• (x + 5)(x^2 - 5)

• (x - 5)(x^2 + 5)