Factoring Quadratics

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 numbers to get a sum.

• Factoring involves finding the square root of a number to simplify it.

• Factoring is the process of dividing an expression into its components.

What is a quadratic expression?

• A polynomial of degree 1, typically in the form ax + b, where a and b are constants.

• A polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

• A polynomial of degree 3, typically in the form ax³ + bx² + cx + d, where a, b, c, and d are constants.

• A constant value that does not change.

What is the role of the discriminant in a quadratic equation?

• It determines the coefficients of the equation.

• It indicates the number of solutions based on the value of b.

• It determines the nature of the roots of the quadratic equation: if positive, two real roots; if zero, one real root; if negative, no real roots.

• It provides the vertex of the parabola represented by the equation.

What does it mean for an expression to be prime?

• An expression is prime if it cannot be factored into simpler expressions with integer coefficients.

• An expression is prime if it can be expressed as a product of two or more integers.

• An expression is prime if it has exactly two distinct integer factors.

• An expression is prime if it is a polynomial of degree one.

What are the factors of the expression 4x² - 49?

• (2x - 7)(2x + 7)

• (4x - 7)(x + 7)

• (2x - 14)(2x + 14)

• (4x + 7)(x - 7)

What is the difference between factoring and expanding an expression?

• Factoring is breaking down an expression into products, while expanding is multiplying out the factors to get the original expression.

• Factoring involves adding terms together, while expanding involves subtracting terms.

• Factoring is used to simplify an expression, while expanding is used to complicate it.

• Factoring and expanding are the same processes used interchangeably.

How can you check if your factors are correct?

• By adding them together to see if you obtain the original expression.

• By multiplying them back together to see if you obtain the original expression.

• By dividing the original expression by one of the factors.

• By substituting the factors into the original expression.

What is the significance of the quadratic formula?

• It provides the solutions to a quadratic equation ax² + bx + c = 0.

• It is used to calculate the area of a triangle.

• It determines the roots of a linear equation.

• It helps in finding the maximum value of a function.

What is the other factor of the expression x² - x - 20 if one factor is (x - 5)?

• (x + 4)

• (x - 4)

• (x + 5)

• (x - 5)

What is the method of completing the square?

• Completing the square is a method used to convert a quadratic expression into a perfect square trinomial, which can then be factored easily.

• Completing the square involves finding the roots of a quadratic equation using the quadratic formula.

• Completing the square is a technique for solving linear equations by isolating the variable.

• Completing the square is a method for graphing linear functions by identifying their slope.