Question

Select the correct answer from each drop-down menu.
Simplify the following polynomial expression.

(3x^2 - x - 7) - (5x^2 - 4x - 2) + (x + 3)(x + 2)
The polynomial simplifies to an expression that is a _________ ____________ with a degree of _____

first blank:
Constant
Linear
Quadratic

Second blank:
Binomial
Trinomial
Monomial

Third blank:
0
1
2

Answer 1

let's first multiply the two terms

what is
(x+3)(x+2)

do you know how to multiply it out?

Answer 2

x^2 + 2x + 3x + 6

Answer 3

good, can you simplify it too?

add the like terms :)

Answer 4

x^2 + 5x + 6

Answer 5

good so now we have

(3x^2 - x - 7) - (5x^2 - 4x - 2) + x^2 + 5x + 6

can you distribute the - sign into the parenthesis?

- (5x^2 - 4x - 2)

= ??

Answer 6

The sign?
-5x^2 +4x +2?

Answer 7

yeah, perfect!

so now we have

3x^2 - x - 7 - 5x^2 + 4x + 2 + x^2 + 5x + 6

can you add / subtract all the like terms?

Answer 8

-1x^2 + 8x - 1
I did that in my head not on paper so it might be wrong

Answer 9

let me check, one sec

Answer 10

okay

Answer 11

you were almost correct but take a look at the numbers

-7 + 2 + 6

= + 1

so your final answer should be

-x^2 + 8x + 1

Answer 12

read the question again
thats not what it's asking for

Answer 13

I know, so let's take a look at the final expression

what is x^2 tell us?

Is it linear? Quadratic? or a constant?

Answer 14

Do you know the difference between them?

A constant is just a number like 5
A linear equation would be something like y = 4x + 3
A quadratic equation is something like 3x^2 + 5x + 6

that should tell you the answer lol

but linear equations have just 'x'
quadratic equations have x^2

Answer 15

quadratic
trinomial
2

Answer 16

You got them all, good job!

Answer 17

Thank you!

Answer 18

No problem!