All categories

3 years ago

Factor completely 3x^2+9x-33(x^2+3)3(x^2+3-1)3x(x^2+3x-1)prime

Mathematics

1 answer:

Firdavs [7]3 years ago

4 0

Answer:

Answer from the answer data to choose from

Factor completely

$3\left(x+\dfrac{3-\sqrt{13}}{2}\right)\left(x+\dfrac{3+\sqrt{13}}{2}\right)$

Step-by-step explanation:

$3x^2+9x-3=(3)(x^2)+(3)(3x)-(3)(1)\\\\=(3)(x^2+3x-1)\\\\\text{For}\ x^2+3x-1\ \text{use the quadratic formula}\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x^2+3x-1\to a=1,\ b=3,\ c=-1\\\\x=\dfrac{-3\pm\sqrt{3^2-4(1)(-1)}}{2(1)}=\dfrac{-3\pm\sqrt{9+4}}{2}=\dfrac{-3\pm\sqrt{13}}{2}=-\dfrac{3\pm\sqrt{13}}{2}\\\\3x^2+9x-3=3\left(x+\dfrac{3-\sqrt{13}}{2}\right)\left(x+\dfrac{3+\sqrt{13}}{2}\right)$

You might be interested in

Factorize x^2/16+xy+4y^2

lisov135 [29]

Answer:

$\frac{x^2}{16} +xy+4y^2$ can be factored out as: $(\frac{x}{4} +2\,y)^2$

Step-by-step explanation:

Recall the formula for the perfect square of a binomial :

$(a+b)^2=a^2+2ab+b^2$

Now, let's try to identify the values of $a$ and $b$ in the given trinomial.

Notice that the first term and the last term are perfect squares:

$\frac{x^2}{16} = (\frac{x}{4} )^2\\4y^2=(2y)^2$

so, we can investigate what the middle term would be considering our $a=\frac{x}{4}$ , and $b=2y$ :

$2\,a\,b=2\,(\frac{x}{4}) \,(2\,y)=x\,y$

Therefore, the calculated middle term agrees with the given middle term, so we can conclude that this trinomial is the perfect square of the binomial:

$(\frac{x}{4} +2\,y)^2$

4 0

3 years ago

Each year for 3 years, the time it takes you to run a mile decreases by 10 seconds. Find the total change time

hichkok12 [17]

Answer: 109.5

Step-by-step explanation: EACH year for three years would be 1095 if you multiply 365 (each year) by 3 (the amount of years) and then divide that by 10. Im not entirely sure but I hope I helped

7 0

3 years ago

Divide x to the 1 half power divided by x to the 2 sevenths power.

juin [17]

$\frac{x^\frac{1}{2} }{x^\frac{2}{7}}$

According to the rule of exponents $\frac{a^m}{a^n} = a^{(m-n)}$ , i.e. when two terms are in division with same base , we subtract the exponents

$\frac{x^\frac{1}{2} }{x^\frac{2}{7}} = x^{(\frac{1}{2}) - (\frac{2}{7})}$

$=x^\frac{3}{14}$

x to the 3 fourteenths power

5 0

3 years ago

What is a unit fraction

amid [387]

A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n. Examples are 1/1, 1/2, 1/3, 1/4 ,1/5, etc.

3 0

3 years ago

Read 2 more answers

How do you show the work ? help

vaieri [72.5K]

Its super easy all u have to do is go on tiger math and the first link will take you to it and u put in the question and it will give you a step by step how to do it and it will give you the answer

5 0

3 years ago

Factor completely 3x^2+9x-33(x^2+3)3(x^2+3-1)3x(x^2+3x-1)prime​

Factor completely 3x^2+9x-33(x^2+3)3(x^2+3-1)3x(x^2+3x-1)prime