Match the expression to the type of quadratic and reasoning.
NOTE: Type of quadratic goes in column 2, reasoning goes in column 3. Reasoning statements start with "This expression…"
Expression
1. x^2 + 2x + 3 Type of Quadratic: blank
2. x^2 + 11x + 10 Type of Quadratic: blank
3. 14x^2 - 4x + 16 Type of Quadratic: blank
4. 4x^2 - 20x + 25 Type of Quadratic: blank
5. x^2 - 36 Type of Quadratic: blank
6. 10x^2 + 19x + 6 Type of Quadratic: blank
Answer choices:
A. Difference of Two Squares
B. a > 1, Grouping
C. a = 1
D. Prime
E. Greatest Common Factor ONLY
F. Perfect Square Trinomial
G. This expression cannot be factored as it is.
H. This expression can only have a factor taken out of each term and the remaining trinomial cannot be factored further
I. This expression contains two perfect squares and has a subtraction sign in the middle.
J. This expression starts and ends with a perfect square. If you take the square root of the first and last term and multiply those together and then multiply by 2, you get the middle term
K. This expression requires us to multiply a to c and then find the two numbers that give us a product that is that number and a sum that is the middle term. Then we replace the middle term with those two numbers and continue to factor by taking out the greatest common factor from the first pair terms and then the second pair of terms. We factor once more, taking out the greatest common factor again to get our final answer
L. This expression is not a special case and does not have a greatest common factor. We find two numbers that give us a product of c (last term) and a sum of b (middle term)
1. x^2 + 2x + 3 Type of Quadratic: L; Reasoning: This expression is not a special case and does not have a greatest common factor. We find two numbers that give us a product of c (last term) and a sum of b (middle term)
2. x^2 + 11x + 10 Type of Quadratic: K; Reasoning: This expression requires us to multiply a to c and then find the two numbers that give us a product that is that number and a sum that is the middle term. Then we replace the middle term with those two numbers and continue to factor by taking out the greatest common factor from the first pair terms and then the second pair of terms. We factor once more, taking out the greatest common factor again to get our final answer
3. 14x^2 - 4x + 16 Type of Quadratic: C; Reasoning: a = 1
4. 4x^2 - 20x + 25 Type of Quadratic: F; Reasoning: This expression starts and ends with a perfect square. If you take the square root of the first and last term and multiply those together and then multiply by 2, you get the middle term
5. x^2 - 36 Type of Quadratic: A; Reasoning: This expression contains two perfect squares and has a subtraction sign in the middle.
6. 10x^2 + 19x + 6 Type of Quadratic: G; Reasoning: This expression cannot be factored as it is.