Solve Quadratics by Factoring Practice

Solve by factoring: x² - 9x + 20 = 0

• x = 3 and x = 7

• x = 4 and x = 5

• x = 2 and x = 10

• x = 1 and x = 20

What is the zero-product property?

• If ab = 0, then either a = 0 or b = 0.

• If a + b = 0, then a = -b.

• If a = 0, then ab = 0 for any b.

• If ab ≠ 0, then both a and b are non-zero.

What are the roots of a quadratic equation?

• The values of x that make the equation equal to zero.

• The coefficients of the equation.

• The maximum or minimum points of the graph.

• The points where the graph intersects the y-axis.

What is a binomial?

• A polynomial with three terms.

• A polynomial with two terms.

• A polynomial with one term.

• A polynomial with four terms.

What is completing the square?

• A method used to solve linear equations by factoring.

• A method used to solve quadratic equations by rewriting it in vertex form.

• A technique for simplifying polynomial expressions.

• A strategy for finding the roots of cubic equations.

Solve by factoring: x² = 18x - 81

• x = 0 and x = 18

• x = 9 and x = 9

• x = -9 and x = -9

• x = 18 and x = -9

What is the vertex form of a quadratic equation?

• y = a(x - h)² + k, where (h, k) is the vertex.

• y = ax² + bx + c, where a, b, and c are constants.

• y = a(x + h)² + k, where (h, k) is the vertex.

• y = a(x - h)² - k, where (h, k) is the vertex.

What is the relationship between the coefficients and the roots of a quadratic equation?

• The sum of the roots is -b/a and the product is c/a.

• The sum of the roots is a/b and the product is b/c.

• The sum of the roots is c/a and the product is -b/a.

• The sum of the roots is b/a and the product is a/c.

What is the quadratic formula?

• x = (-b ± √(b² - 4ac)) / (2a)

• x = (b ± √(b² + 4ac)) / (2a)

• x = (-b ± √(b² + 4ac)) / (2a)

• x = (b ± √(b² - 4ac)) / (2a)

How do you check if your factored solution is correct?

• Substitute the roots back into the original equation to see if it equals zero.

• Multiply the factors together to see if they match the original equation.

• Graph the factors and check if they intersect the x-axis.

• Use synthetic division to verify the factors.