All categories

3 years ago

Which is the completely factored form of 12x4 + 39x3 + 9x2?

Mathematics

2 answers:

mote1985 [20]3 years ago

5 0

Answer: The completely factored form will be

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

Step-by-step explanation:

Since we have given that

$12x^4 + 39x^3 + 9x^2$

We need to find the factored form,

So, here we go:

1) Taking out the common factor i.e. 3x² :

$12x^4 + 39x^3 + 9x^2\\\\3x^2(4x^2+13x+3)$

2) We get a quadratic equation , we will split the middle term:

$(4x^2+13x+3)\\\\4x^2+12x+x+3=0\\\\4x(x+3)+1(x+3)=0\\\\(4x+1)(x+3)=0$

3) Now, combine the all of the factors:

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

Hence, the completely factored form will be

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

Advocard [28]3 years ago

3 0

Hello,

12x^4+39x^3+9x²=x²(12x²+39x+9)=x²(12x²+36x+3x+9)=x²(4x(3x+9)+(3x+9))
=x²(3x+9)(4x+1)
=3x²(x+3)(4x+1)

You might be interested in

PLEASE HELP! A juice company gives prizes to anyone finding specially marked caps on its juice bottles. You and your friends buy

laiz [17]

The odds in favor of winning a prize in the contest of the juice company which gives prizes to anyone finding specially marked caps is 3.2.

<h3>What is odds against?</h3>

In probability, the term odds against is the ratio of probability of non occurring a favorable event to the probability of occurring a favorable event. It can be given as,

$\text{odd against}=\dfrac{P(\overline A)}{P(A)}$

Here, $P(\overline A)$ is the probability of not occurring a favorable event, and P(A) is the probability of occurring a favorable event.

A juice company gives the prizes to anyone finding specially marked caps on its juice bottles. The 4 bottles have winning cap in 20 bottles. Thus, the probability of winning is,

$P(A)=\dfrac{4}{20}\\P(A)=\dfrac{1}{5}$

The probability of not winning is,

$P(\overline A)=1-\dfrac{1}{5}\\P=\dfrac{4}{5}$

Thus, the odd against the winning is,

$\text{odd against}=\dfrac{\dfrac{4}{5}}{\dfrac{1}{4}}\\\text{odd against}=\dfrac{16}{5}\\\text{odd against}=3.2$

Thus, the odds in favor of winning a prize in the contest of the juice company which gives prizes to anyone finding specially marked caps is 3.2.

Learn more about the odds against here;

brainly.com/question/1870238

#SPJ1

7 0

2 years ago

Give the equation of the horizontal asymptote shown below.

Oxana [17]

Polynomial division yields

$\dfrac{7x^2}{x^2+5}=7-\dfrac{35}{x^2+5}$

As $x\to\pm\infty$ , you have the remainder term approaching $0$ , so the horizontal asymptote is the line $y=7$ .