Factoring quadratics is an important skill in algebra that allows us to solve equations and understand the behavior of quadratic functions. By factoring quadratics, we can find the roots of the equation, determine the vertex of a parabola, and graph the function. This worksheet will provide you with practice problems to help you master the process of factoring quadratics.
Factoring quadratics involves breaking down a quadratic equation into two binomial factors. This can be done using various methods such as the AC method, grouping, and the difference of squares. By practicing these techniques, you will become more comfortable with factoring quadratics and be able to solve more complex equations.
Worksheet Problems
1. Factor the following quadratic equations:
– x^2 + 5x + 6
– 2x^2 – 11x + 12
– 3x^2 + 10x – 8
2. Solve the following quadratic equations by factoring:
– x^2 – 4x – 5 = 0
– 2x^2 + 7x – 15 = 0
– 4x^2 – 12x + 9 = 0
3. Factor the following quadratic expressions:
– 4x^2 + 8x + 4
– x^2 – 9
– 6x^2 – 13x + 6
4. Apply the zero-product property to solve the following equations:
– (x – 3)(x + 2) = 0
– (2x – 5)(x + 4) = 0
– (3x + 1)(x – 2) = 0
5. Complete the square for the following quadratic functions:
– f(x) = x^2 + 6x + 9
– g(x) = x^2 – 4x + 4
– h(x) = x^2 + 10x + 25
By completing this worksheet on factoring quadratics, you will improve your skills in solving quadratic equations and understanding the properties of quadratic functions. Remember to practice regularly to reinforce your knowledge and become more confident in factoring quadratics. Good luck!