Determine the truth value of each statement based on the expression. 6x 2 - 2x - 14y + 3x 1. before simplifying, there are 4 terms in the expression. true or false 2. 6x 3 and 3x are like terms. true or false 3. the coefficient on y is 14. true or false 4. simplified, the expression is 6x 2 + 5x - 14y. true or false 5. the commutative property allows the expression to be written as 6x 2 - 14y + 3x - 2x. true or false

1. True. The four terms are {6x², -2x, -14y, 3x}

2. False. x³ ≠ x, so the constellation of variables is different, making the terms unlike.

3. False. The coefficient of y is -14. (Definitions vary, so I believe this could be argued both ways. Refer to your text or reference material for a definitive answer.)

4. False. The simplified expression is 6x² +x -14y. The coefficient of x is (-2+3)=1.

5. True. The commutative property of addition lets you interchange the addends in parentheses:

... 6x² + (-2x) + (-14y +3x) ⇒ 6x² + (-14y +3x) + (-2x)

Regarding the coefficient of y: some definitions of polynomial say that operations between terms can include addition or subraction. This allows you to consider the -14y in the expression to be either of "subtracting 14y" or "adding -14y". Your viewpoint determines whether you consider the coefficient to be 14 or -14. (Personally, I like to keep signs with numbers, which is why I listed -14y as one of the terms in question 1, and why I answered question 3 as False.) If it were -14², the order of operations requires you to consider 14² to be subtracted. If y had the value -1, you would be adding the term 14. Many people would evaluate the term as -14(-1) = 14, rather than -(-14).

True

False

False

False

True

(these are the answers I got a 100)