Solving Quadratics by factoring
Flashcard
•
Mathematics
•
9th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a quadratic equation?
Back
A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
2.
FLASHCARD QUESTION
Front
What does it mean to factor a polynomial?
Back
Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.
3.
FLASHCARD QUESTION
Front
What is the first step in solving a quadratic equation by factoring?
Back
The first step is to set the equation to zero and check if there is a greatest common factor (GCF) that can be factored out.
Tags
CCSS.HSA-REI.B.4B
4.
FLASHCARD QUESTION
Front
How do you find the roots of a quadratic equation after factoring?
Back
Set each factor equal to zero and solve for the variable.
Tags
CCSS.HSA-REI.B.4B
5.
FLASHCARD QUESTION
Front
What is the relationship between the coefficients and the roots of a quadratic equation?
Back
For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.
Tags
CCSS.HSA-REI.B.4B
6.
FLASHCARD QUESTION
Front
What is the significance of the discriminant in a quadratic equation?
Back
The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.
Tags
CCSS.HSA-REI.B.4B
7.
FLASHCARD QUESTION
Front
What are the steps to factor the quadratic x² + 2x - 24?
Back
1. Identify two numbers that multiply to -24 (the constant term) and add to 2 (the coefficient of x). 2. The numbers are 6 and -4. 3. Factor as (x + 6)(x - 4) = 0.
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