Question

Add.

(−5x^4 + 6x^3 − 43) + (6x^5 − x^2 + 12x + 12)

Express the answer in standard form.

Enter your answer in the box.

________________

Answer 1

@Vocaloid

Answer 2

first step is to distribute that + sign across the parentheses (since it's a + sign none of the other signs change)

so:

(−5x^4 + 6x^3 − 43) + (6x^5 − x^2 + 12x + 12)
=
-5x^4 + 6x^3 - 43 + 6x^5 - x^2 + 12x + 12

[not done yet]

Answer 3

if you notice, all the exponents on x terms are different, so none of x-terms are like terms

the only like terms are: -43 and 12

-43 + 12 = -31

Answer 4

now,

-5x^4 + 6x^3 + 6x^5 - x^2 + 12x - 31

to arrange this into "standard form" we just arrange the terms so that the exponents are decreasing - can you try this? none of the original signs or numbers will change, just the order

let me know if you get stuck

Answer 5

yo, if you're having a little trouble -

which term has the highest exponent?

Answer 6

standard form: 54x² + (-85)

Answer 7

not quite, let's try to use what's in the problem ^_^

Answer 8

quick review:

a term is a smaller expression separated from the rest of the expression using + or - signs

Answer 9

let's underline each individual term, shall we

Answer 10

Combine like terms

Answer 11

remember what we said earlier ^^ all the exponents are different so these cannot be combined

Answer 12

now, there are 6 underlined terms - which of these terms has the highest exponent?

Answer 13

12x and 6x^5

Answer 14

which one has the higher exponent? 12x or 6x^5?

Answer 15

remember that x = x^1

Answer 16

6x^5

Answer 17

awesome, so 6x^5 comes first in our answer

what about the next highest exponent?

Answer 18

6x^3

Answer 19

5x^4

Answer 20

good, -5x^4 [there's a negative sign and we can't forget that]

6x^3 comes after that

what's the next highest exponent term after 6x^3?

Answer 21

x^2

Answer 22

good (don't forget that negative sign though)

what about after that?

Answer 23

12x

Answer 24

good, and then the last one is -31

so let's put everything in order:

6x^5 - 5x^4 + 6x^3 - x^2 + 12x - 31 = your final answer in standard form

Answer 25

Which polynomial is a quintic binomial?

A. 5x^2 − 2x + 1

B. x^4 + 2x^3 − x^2 + 7x + 11

C. x^2 + 4x

D. 3x^5 + 2

Answer 26

the answer is D correct ?

Answer 27

good, D, well done

Answer 28

Let ​ f(x) = x^2 + 15x + 56 .



What are the zeros of the function?

Enter your answers in the boxes.


______ and _________