Factoring the Quadratic Expression x2-x-2
What is the factored form of x2-x-2 Quizlet?
The factored form of a quadratic expression is an expression that can be written in the form (ax + b) (cx + d), where a, b, c, and d are constants and a and c are not equal to zero. The factored form of a quadratic expression can be obtained by factoring out the greatest common factor (GCF) from the expression.
The Quadratic Expression
The given quadratic expression is x2 – x – 2. To factor this expression, we need to find the GCF of the two terms. In this case, the GCF of x2 and x is x.
Finding the Greatest Common Factor (GCF)
The GCF of x2 and x is x, since x is the largest number that divides both x2 and x without leaving a remainder.
Factoring Out the GCF
Now that we have found the GCF, we can factor out x from both terms:
x2 – x – 2 = x(x) – x(1)
Factoring by Difference of Squares
Notice that the expression x(x) – x(1) is in the form of x(x – 1). This is a classic example of the difference of squares identity:
x(x – 1) = x^2 – x
So, we can write the original expression x2 – x – 2 as:
x2 – x – 2 = x^2 – x – 2
The Factored Form
Therefore, the factored form of the quadratic expression x2 – x – 2 is x^2 – x – 2.
Factoring Using Grouping
Alternatively, we can factor the quadratic expression x2 – x – 2 using grouping:
x2 – x – 2 = (x^2 – x) – 2
= x(x – 1) – 2
However, this does not result in the same factored form as the previous one.
The Difference of Two Squares
Another way to factor the quadratic expression x2 – x – 2 is to use the difference of two squares identity:
x2 – x – 2 = (x + 1)(x – 2)
This identity states that a^2 – b^2 = (a + b)(a – b).
So, we can rewrite the original expression x2 – x – 2 as:
x2 – x – 2 = (x + 1)(x – 2)
What is the Factored Form of x2-x-2 Quizlet?
Now that we have explained the concept of factoring a quadratic expression and shown how to factor the given expression x2 – x – 2, let’s take a quiz to test our understanding.
Quizlet Exercise:
- Factor the expression x2 – x – 2
- Write the factored form of x2 – x – 2
Answer Key
- x2 – x – 2 = x(x – 1) – 2
- x2 – x – 2 = (x + 1)(x – 2)
Conclusion
In this article, we learned how to factor a quadratic expression by finding the greatest common factor (GCF), factoring out the GCF, and using the difference of squares identity. We also showed how to factor the given expression x2 – x – 2 using different methods. By practicing these methods, you can become proficient in factoring quadratic expressions and solve a wide range of problems.