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3 years ago

Multiply (x4 + 1) (3x2 + 9x + 2)

2 answers:

4 0

Hello there!

(x^4 + 1)(3x^2 + 9x + 2)

We need to use the distributive property

=(x^4)(3x^2) + (x^4)(9x) + (x^4)(2) + (1)(9x) + (1)(2)

= 3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2

Let me know if you have any misunderstanding. As always, it is my pleasure to help students like you.

SVEN [57.7K]3 years ago

4 0

Answer: The required multiplied expression is $3x^6+9x^5+2x^4+3x^2+9x+2.$

Step-by-step explanation: We are given to multiply the following :

$E=(x^4+1)(3x^2+9x+2)~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following property to execute the multiplication :

$(a+b)\times c=a\times c+b\times c.$

From (i), we have

$E\\\\=(x^4+1)(3x^2+9x+2)\\\\=x^4(3x^2+9x+2)+1(3x^2+9x+2)\\\\=3x^6+9x^5+2x^4+3x^2+9x+2.$

Thus, the required multiplied expression is $3x^6+9x^5+2x^4+3x^2+9x+2.$

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3 years ago

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kaheart [24]

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3 years ago

A train leaves boston at 2:00 pm. a second train leaves the same city in the same direction at 6:00 pm. the second train travels

AURORKA [14]

$\boxed {\boxed { \text {Distance = Speed x Time}}}$

First Train:
Time taken = 9 hours (2pm to 11pm)
Let the speed be x
Distance = Time x Speed = 9x

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Speed = x + 48
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3 0

4 years ago

NEED HELP

Zina [86]

Answer:

$\displaystyle \frac{1}{2}(x^3-2x^2-5x+6)$

Step-by-step explanation:

Polynomials

The polynomial whose graph is shown is of third degree because it has three real roots. The roots of a polynomial are the values of x that make the expression equal to zero. We can see it happens three times in the graph provided. The roots or zeros are

x=-2, x=1, x=3

The factored form of a polynomial whose roots $x_1, x_2, x_3$ are known is

$a(x-x_1)(x-x_2)(x-x_3)$

We know the value of the roots, thus the polynomial is written as

$a(x+2)(x-1)(x-3)$

We need to find the value of a. We do that by replacing the value of x=0 and finding a that makes f(0)=3 (as seen in the graph). Thus

$a(0+2)(0-1)(0-3)=3$

$a(2)(-1)(-3)=3$

$a(6)=3$

$\displaystyle a=\frac{3}{6}$

$\displaystyle a=\frac{1}{2}$

Thus the factored form of the polynomial is

$\displaystyle \frac{1}{2}(x+2)(x-1)(x-3)$

Let's multiply all the factors

$\displaystyle \frac{1}{2}(x+2)(x-1)(x-3)$

$\displaystyle \frac{1}{2}(x^2+2x-x-2)(x-3)$

$\displaystyle \frac{1}{2}(x^2+x-2)(x-3)$

$\displaystyle \frac{1}{2}(x^3-3x^2+x^2-3x-2x+6)$

$\boxed{ \displaystyle \frac{1}{2}(x^3-2x^2-5x+6)}$

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4 years ago

How do you write an equation of a line in standard form if you have two points?

ziro4ka [17]

First find the slope using the slope formula M= (y2-y1) divided by (x2-x1) and then take the slope and and the 1st set of points (x1, y1) and plug it into the slope intercept formula which is y-y1=m(x-x1), then you need to add or subtract variables to correlate with the standard form formula which is ax + by = c.
Hope that helps!

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4 years ago