Factoring - All Types

What is the difference of squares formula?

• a² - b² = (a + b)(a - b)

• a² + b² = (a + b)(a - b)

• a² - b² = (a - b)(a - b)

• a² - b² = (a + b)(a + b)

Factor the expression x² - 25 using the difference of squares formula.

• (x + 5)(x - 5)

• (x + 25)(x - 25)

• (x - 5)(x - 5)

• (x + 5)(x + 5)

What is factoring in mathematics?

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

• Factoring is the method of adding two or more expressions to create a new expression.

• Factoring involves finding the square root of an expression to simplify it.

• Factoring is the technique of rearranging an expression to make it easier to solve.

What is the factored form of 18a² - 15a?

• 3a(6a - 5)

• 3a(6a + 5)

• 6a(3a - 5)

• 9a(2a - 5)

What is the role of coefficients in polynomials?

• Coefficients are the numerical factors that multiply the variables in a polynomial, determining the polynomial's value.

• Coefficients are the variables that represent the degree of the polynomial.

• Coefficients are the constants that are added to the polynomial's terms.

• Coefficients are the exponents that indicate the power of the variables.

What is the factored form of x² + 5x + 6?

• (x + 1)(x + 6)

• (x + 2)(x + 3)

• (x + 3)(x + 2)

• (x + 4)(x + 1)

What is the relationship between factoring and solving quadratic equations?

• Factoring a quadratic equation allows us to set each factor equal to zero to find the solutions.

• Factoring is only used to simplify expressions, not to solve equations.

• Factoring and solving quadratic equations are unrelated processes.

• Factoring can only be used for linear equations, not quadratic equations.

What is the greatest common factor (GCF)?

• The smallest number that divides all terms in a polynomial.

• The largest expression that divides all terms in a polynomial without leaving a remainder.

• The sum of all coefficients in a polynomial.

• The product of all terms in a polynomial.

Factor -10xy⁹z + 8y³z⁵ by finding the GCF.

• 2y³z(-5xy⁶ + 4z⁴)

• -2y³z(5xy⁶ - 4z⁴)

• 2y³z(5xy⁶ + 4z⁴)

• -2y³z(-5xy⁶ - 4z⁴)

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 constant value that does not change.

• A geometric shape defined by points in a plane.