Match each polynomial expression to its factored form:
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x2+3x−4
4x2−4
4x2−4x
x2−16
Incorrect:
The correct matches are:
x^2 + 3x - 4 -> (x + 4)(x - 1)
4x^2 - 4 -> 4(x - 1)(x + 1)
4x^2 - 4x -> 4x(x - 1)
x^2 - 16 -> (x + 4)(x - 4)
To match each polynomial expression to its factored form, we can analyze the given expressions:
1. x^2 + 3x - 4:
To factor this expression, we need to find two numbers whose product is -4 and whose sum is 3. The numbers that satisfy this condition are 4 and -1. Therefore, the factored form of this expression is (x + 4)(x - 1).
2. 4x^2 - 4:
This expression is already in factored form because both terms share a common factor of 4. The factored form is 4(x^2 - 1).
3. 4x^2 - 4x:
Here, we need to factor out the greatest common factor (GCF), which is 4x. The factored form is 4x(x - 1).
4. x^2 - 16:
This expression is a difference of squares and can be factored as (x + 4)(x - 4).
So, the respective factored forms for each polynomial expression are:
1. (x + 4)(x - 1)
2. 4(x^2 - 1)
3. 4x(x - 1)
4. (x + 4)(x - 4)
To match each polynomial expression to its factored form, we need to factorize each polynomial expression.
1. x^2 + 3x − 4:
To factorize this expression, we need to find two numbers that multiply to give -4 and add up to 3. The numbers are 4 and -1. So, the factored form is (x + 4)(x - 1).
2. 4x^2 - 4:
This expression can be factored out by taking out a common factor. We can factor out 4 from both terms. The factored form is 4(x^2 - 1).
3. 4x^2 - 4x:
Again, we can factor out 4 from both terms. The factored form is 4x(x - 1).
4. x^2 - 16:
This expression is a difference of squares because 16 can be written as 4^2. The factored form is (x + 4)(x - 4).
Matching the expression to their factored forms:
1. x^2 + 3x − 4 = (x + 4)(x - 1)
2. 4x^2 - 4 = 4(x^2 - 1)
3. 4x^2 - 4x = 4x(x - 1)
4. x^2 - 16 = (x + 4)(x - 4)