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11 months ago

What is (-4x² + 3x + 3)(x² - 2x + 2) as a polynomial

Mathematics

1 answer:

gizmo_the_mogwai [7]11 months ago

5 0

The given expression is in the form of the polynomial as -4x⁴+11x³-5x²+6 and the degree of the polynomial is 4.

<h3>What is a polynomial?</h3>

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

$\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n$

It is given that the polynomial expression is, (-4x² + 3x + 3)(x² - 2x + 2)

We have to simplify the expression by multiplying the expression as,

=-4x²(x² - 2x + 2)+3x(x² - 2x + 2)+3(x² - 2x + 2)

=-4x⁴+8x³-8x²+3x³-6x²+6x+3x²-6x+6

= -4x⁴+11x³-5x²+6

Thus, the given expression is in the form of the polynomial as -4x⁴+11x³-5x²+6 and the degree of the polynomial is 4.

Learn more about Polynomial here:

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Which equation is exponential?

melamori03 [73]

The second because it's set at the power of 2, none of the other ones have a set exponent.

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2 years ago

Instructions:select all the correct locations on the tables. andrew wants to purchase a new television with a screen length that

DaniilM [7]

The <em>correct answers</em> are:

5x²+70x+245 ≥ 1050; and

Yes.

Explanation:

Let x be the width of the tablet. Since the width of the TV is 7 inches more than the tablet, the width of the TV would be x+7.

The length of the TV is 5 times the width; this makes the length 5(x+7) = 5x+35.

The area of the TV would be given by

(x+7)(5x+35).

Since Andrew wants the area to be at least 1050, we set the expression greater than or equal to 1050:

(x+7)(5x+35) ≥ 1050

Multiplying this, we have:

x*5x+x*35+7*5x+7*35 ≥ 1050

5x²+35x+35x+245 ≥ 1050

Combining like terms,

5x²+70x+245 ≥ 1050

To see if 8 is a reasonable width for the tablet, we substitute 8 for x:

5(8²)+70(8)+245 ≥ 1050

5(64)+560+245 ≥ 1050

320+560+245 ≥ 1050

1125 ≥ 1050

Since this inequality is true, 8 is a reasonable width.

5 0

2 years ago

Please help! I really need this

olga55 [171]

9514 1404 393

Answer:

see below

Step-by-step explanation:

You might do well to refer to the proof referenced here--the previous slide. We assume it more or less matches what we've done in the attachment.

6 0

2 years ago

Andre and Diego were each trying to solve 2x+6=3x-8 Describe the first step they each make to the equation

avanturin [10]

The first step was the combine the like terms; in this example he is subtracting the 3x on both sides of the =.

If you were to solve the equation it would look like this:

2x+6=3x-8
-3x -3x

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2 years ago

Using long division to find the quotient, what changes do you first

lora16 [44]

Answer:

$\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4$

Step-by-step explanation:

Given

$Dividend = 125x^3 - 8$

$Divisor = 5x - 2$

Required

Determine the quotient

See attachment for complete process.

First, divide 125x^3 by 5x

$\frac{125x^3}{5x} =25x^2$

Write $25x^2$ at the top

Multiply $5x - 2$ by $25x^2$

$= 125x^3 - 50x^2$

Subtract from 125x^3 - 8

i.e.

$125x^3 - 8 - (125x^3 - 50x^2) = 50x^2 - 8$

Step 2:

Divide 50x^2 by 5x

$\frac{50x^2}{5x} = 10x$

Write $10x$ at the top

Multiply $5x - 2$ by $10x$

$= 50x^2 - 20x$

Subtract from 50x^2 - 8

i.e.

$50x^2 - 8 - (50x^2 - 20x) = 20x - 8$

Step 3:

Divide 20x by 5x

$\frac{20x}{5x} = 4$

Write $4$ at the top

Multiply $5x - 2$ by $4$

$= 20x - 8$

Subtract from 20x - 8

i.e.

$20x - 8 - (20x - 8) = 0$

Hence:

$\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4$

8 0

2 years ago