In this site we will try to explain coefficients as well as help those of you who may be a bit lost in the Math Maze. Question 12a was about factoring quadratics. In the famous words of that great mathematician -
When factoring a quadratic where the coefficient of the squared variable is 1, find two integers that multiply together to give you the third term and add together to give you the coefficient of the middle term.
Oh wait, I said that. Sure, sure, someone else probably said it first, but let them get there own website. Notice the word coefficient in the description. What the heck does that mean? For that matter, what do integers, terms, and quadratic mean? I'm glad you asked.
Integers are whole numbers along with negative numbers. Whole numbers being 0, 1, 2, 3, ... No fractions. But, whole numbers don't include the negative numbers while integers do include the negatives.
A term, in mathematics, is a group of numbers multiplied or divided together. Expressions and equations are composed of terms that are either added or subtracted from each other. Sometimes a term is a number and a variable multiplied times each other like 7x would be 7 times x where x is the variable and 7 is the coefficient. Those two combine to make a term.
Did you miss it? I just defined it in the paragraph about terms. I can be so clever at times.
Quadratics is an expression or equation where the highest exponent is 2.
In the above image, the red numbers are coefficients. Note that the exponent of x in the term 3x is 1, the default exponent. You could think of the term -7 as being negative seven times x to the zero power, since anything to the zero power is 1.
Remember, the question wants us to find the term that cannot be factored using integers.
Answer a) is x^2 + 4x + 4 2x2 = 4 and 2 + 2 = 4 so this one can be factored.
Answer b) x^2 + x - 20 well (5)(-4) = -20 and 5 - 4 = 1 so this one also works.
Answer c) x^2 + 4x - 5 works with 5(-1) = -5 and 5 - 1 = 4
So the answer is d) x^2 + 4x + 5 there are no two integers with a product of 5 and a sum of 4.
The pressure is on, keep your cool - I know you can do this!!
Which one of these trinomials can not be factored using integers?
A) x2 + 3x + 4
B) x2 + 3x - 4
C) x2 + 3x - 28
D) x2 + 3x + 2
Which of the above could not be factored using integers?
There are a lot of places that use the word, A free resource for definitions is Dictionary.com. You could give it a try.