Question

Create a unique example of dividing a polynomial by a monomial and provide the simplified form. Explain, in complete sentences, the two ways used to simplify this expression and how you would check your quotient for accuracy.

Answer 1

@ganeshie8 @phi @jdoe0001 @whpalmer4

Answer 2

can you help

Answer 3

can you write down a monomial ?

Answer 4

x

Answer 5

can you write down a polynomial ?

Answer 6

5x2+2x3?

Answer 7

ok, but you should use ^ to show exponents.
5x^2 + 2x^3

normally we write the terms in order of biggest exponent to smallest, so this way
\[ 2x^3 + 5x^2\]

I was going to suggest multiplying the monomial by the polynomial, but your polynomial can be divided by \(x^2\)

so try
\[ \frac{ 2x^3 + 5x^2}{x^2} \]

Answer 8

2x^5+5x^4? @phi

Answer 9

you multiplied
\[ x^2(2x^3 +5x^2)\]
that can be "distributed" by multiplying each term inside the parens
\[ x^2 \cdot 2x^3+ x^2 \cdot 5x^2\]
when you multiply, you can change the order (for example, with numbers 2*3 is the same as 3*2... it works the same for letters)
\[ 2\cdot x^2 \cdot x^3+ 5 \cdot x^2 \cdot x^2\]

x^2 is short for x*x
x^3 is short for x*x*x
x^2 * x^2 is short for x*x * x*x*x
or, using the short way, x^5

but you do not want to multiply you want to divide.

Answer 10

**typo**
x^2 is short for x*x
x^3 is short for x*x*x
x^2 * x^3 is short for x*x * x*x*x
or, using the short way, x^5

Answer 11

dividing is almost the same as multiplying
\[ \frac{ 2x^3 + 5x^2}{x^2} \]
divide x^2 into each term

\[ \frac{2x^3}{x^2} + \frac{5x^2}{x^2} \]

Answer 12

if you write x^3 the long way, as x*x*x and x^2 as x*x, the problem is
\[ \frac{2 \cdot x \cdot x \cdot x }{ x \cdot x } + \frac{5 \cdot x \cdot x }{ x \cdot x }\]

Answer 13

when you divide anything by itself you get 1

in other words, every time you can pair up an x in the top with an x in the bottom, they divide into themselves and give you 1

Answer 14

not clear ?