MATHEMATICS HIGH SCHOOL

Use long division to find the quotient below.
(4x² - 7x-2) + (x-2)

Answers

Answer 1

Answer:

Answer:

4x+1

Step-by-step explanation:

$(4x^2-7x-2)/(x-2)= \n\n(x-2)(4x+1)/(x-2)= \n\n4x+1$

Hope this helps!

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One number is 1 more than 2 times another. Their product is 10. Find the numbers.

Answers

whenever a problem says "one number" and "another number" we can substitute x and y. for this we have x=2y+1 and xy=1. since we know the value of x (2y+1) we can substitute it for the other equation to get (2y+1)y=10. simplify to get 2y^2+y=10. from here you can do a few methods to solve this, but the simplest in my opinion is by factoring.

In order to factor it must be equal to 0, so we have 2y^2+y-10=0. We factor this and get y=5 (we also get y=-4 but it is an extraneous root). now we can plug that into either equation and find that x=2.

this means our two numbers are 5 and 2

What is the circumference of this circle?2 cm
about 3 centimeters
about 13 centimeters
about 22 centimeters
about 35 centimeters

Answers

About 13 cm

circumference = 2 * pi * radius

Answer:

Option B

Step-by-step explanation:

C = 2πr where r is radius as given.

Let us take pi as 3.14

C = 2* 3.14* 2 = 12.56 cm

About 13 cm

Which is the equation of a line with the slope of -2 that passes through the point (-2,0)

Answers

y = -2x - 4

-2x is the slope and -4 is the y intercept.

The equation of a line is y = mx + b (m is the slope; b is the y-intercept)

We are given the slope of -2 so...

y = -2x + b

We must determine b. Since they give us a point, we can sub in the x and y coords (-2,0)

0 = -2(-2) + b
0 = 2 + b
[Subtract 2 from both sides]
0-2=2-2+b
-2=b

Now, go back to the original equation (before adding coordinates in) and input b.

y = -2x-2

Eli plans to repaint some classroom bookcases. He has 12 galnt. All of the bookcases are the same size and each requires 3/2 gallon of paint. How many bookcases will he be able to paint?

Answers

Answer:

8 bookcases

Step-by-step explanation:

12 / (3/2) = (12*2)/3 = 8

Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? x(x2 + 4) + 5(x2 + 4) x2(x + 4) + 5(x + 4) x2(x + 5) + 4(x + 5) x(x2 + 5) + 4x(x2 + 5)

Answers

x²(x + 4) + 5(x + 4)

Further explanation

Factoring (also called factorization) is the reserve operation of multiplication. When we factor (or factorize) a polynomial, we write it as a product of its factors.

Grouping is one of the factoring methods. Other methods such as isolating common factors and identities.

Steps for grouping:

We group the terms with a common factor.
We can isolate a common factor and put it outside the parentheses.

Let’s start.

$\boxed{ \ x^3 + 4x^2 + 5x + 20 = \ ? \ }$

$\boxed{ \ = (x^3 + 4x^2) + (5x + 20) \ }$

$\boxed{\boxed{ \ = x^2(x + 4) + 5(x + 4) \ }}$

We can also group the terms as follows.

$\boxed{ \ x^3 + 4x^2 + 5x + 20 = \ ? \ }$

$\boxed{ \ = (x^3 + 5x) + (4x^2 + 20) \ }$

$\boxed{\boxed{ \ = x(x^2 + 5) + 4(x^2 + 5) \ }}$

We will get the same results from the two ways above. Let's see.

First group, $\boxed{ \ x^2(x + 4) + 5(x + 4) \ } \rightarrow \boxed{ \ (x + 4) (x^2 + 5) \ }$
Second group, $\boxed{ \ x(x^2 + 5) + 4(x^2 + 5) \ } \rightarrow \boxed{ \ (x^2 + 5) (x + 4) \ }$

Thus the part which shows one way to determine the factors of x³ + 4x² + 5x + 20 by grouping is $\boxed{\boxed{ \ x^2(x + 4) + 5(x + 4) \ }}$

Learn more

Which expression is equivalent to the product of a binomial and a trinomial after it has been fully simplified brainly.com/question/1394854
The y-intercept of the quadratic function f(x) = (x – 6)(x – 2) brainly.com/question/1332667
Which is the graph of f(x) = (x - 1)(x + 4) brainly.com/question/2334270

Keywords: which shows, one way, to determine, the factors of x³ + 4x² + 5x + 20, by grouping, common factor, polynomial, identities

The correct option is $\fbox{\text{Option B}}$ that is ${x^2}\left( {x + 4} \right) + 5\left( {x + 4} \right)$ that shows one way to determine the factors of ${x^3} + 4{x^2} + 5x + 20$ .

Further explanation:

Factors are the numbers if we multiply them we get the original number.

Factorization is finding the numbers if we multiply them we get the original number.

Prime factorization is finding the numbers if we multiply them we get the original number.

Given:

The polynomial is ${x^3} + 4{x^2} + 5x + 20$ .

The options are,

A. $x\left( {{x^2} + 4} \right) + 5\left( {{x^2} + 4} \right)$ .

B. ${x^2}\left( {x + 4} \right) + 5\left( {x + 4} \right)$ .

C. ${x^2}\left( {x + 5} \right) + 5\left( {x + 5} \right)$ .

D. $x\left( {{x^2} + 5} \right) + 4x\left( {{x^2} + 5} \right)$

Explanation:

Consider the polynomial ${x^3} + 4{x^2} + 5x + 20$ as $P\left( x \right)$ .

Steps involve in finding the factors of ${x^3} + 4{x^2} + 5x + 20$ are as follows,

First we have to make the groups of the terms as,

$P\left( x \right) = \left( {{x^3} + 4{x^2}} \right) + \left( {5x + 20} \right)$

Now factorize the above 2 groups.

$\begin{gathered}P\left( x \right) = {x^2}\left( {x + 4} \right)+5\left( {{x^2}+4} \right)\n= \left( {{x^2}+5} \right)\left( {x+4} \right) \n\end{gathered}$

The factors of ${x^3} + 4{x^2} + 5x + 20\text{ } \text{are} \left( {{x^2} + 5} \right) \text{and} \left( {x + 4} \right)$ .

Option A is not correct as the first common factor is $x$ from group one but it not the highest common factor.

$\fbox{\text{Option B}}$ is correct as the factors are same as the factors of the polynomial.

Option C is not correct as the factors are not same as the factors of the polynomial.

Option D is not correct as the factors are not same as the factors of the polynomial.

Learn more:

1. Learn more about the polynomial brainly.com/question/12996944

2. Learn more about logarithm model brainly.com/question/13005829

3. Learn more about the product of binomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Polynomials

Keywords: factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.

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