1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lozanna [386]
2 years ago
5

Factor the polynomial, x2 + 5x + 6

Mathematics
1 answer:
patriot [66]2 years ago
4 0

Answer:

Choice b.

x^{2} + 5\, x + 6 = (x + 3)\, (x + 2).

Step-by-step explanation:

The highest power of the variable x in this polynomial is 2. In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to 0.)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to 0. The discriminant of this polynomial is (5^{2} - 4 \times 1 \times 6) = 1.

\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}.

Similarly:

\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}.

By the Factor Theorem, if x = x_{0} is a root of a polynomial, then (x - x_0) would be a factor of that polynomial. Note the minus sign between x and x_{0}.

  • The root x = -2 corresponds to the factor (x - (-2)), which simplifies to (x + 2).
  • The root x = -3 corresponds to the factor (x - (-3)), which simplifies to (x + 3).

Verify that (x + 2)\, (x + 3) indeed expands to the original polynomial:

\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}.

You might be interested in
Three taps can fill a tank in 1.5 hours how many tab can feel it in 45 minutes ​
kap26 [50]

Answer:

30 Tabs?

Step-by-step explanation:

Not so sure on this, I just divided 45/1.5.

5 0
3 years ago
A meter is 3.37 inches more than a yard swimmer a swims 100 meters and swimmer b swims 100 yeards how many more feet did swimmer
olga_2 [115]
Swimmer a swims 100 meters, which is 100 1-meters, which is 100
(1 yards +3.37 inches) = 100 yards + 337 inches.

1 yard is 3 feet, so 100 yards are 300 feet.

100 in is 8.33 feet so
337 in is (337*8.33)/100=28.07 feet


Swimmer b swims 100 yards, which is 300 feet

Swimmer a swam 28.07 feet.


4 0
3 years ago
Please help. I'm stuck.
Bezzdna [24]
The root \sqrt{10} can be converted into the power 10^{ \frac{1}{2} }. Therefore we can rewrite the problem as (10^{ \frac{1}{2} } )^ {\frac{3}{4} x} and then follow the exponent rules about a power to a power, multiplying 1/2 and 3/4 together.

Thus the problem becomes 10^{\frac{3}{8}x}, which then can be turned into \sqrt[8]{10} ^{3x}, making the last option our answer.

4 0
3 years ago
Simplify expression x8y-26/x14y-5 × x-39y-21
koban [17]

The simplified form of the expression is x^{-45} y^{-42}

<h3>Simplifying an expression</h3>

From the question, we are to simplify the given expression

The given expression is

\frac{x^{8}y^{-26}  }{x^{14}y^{-5}  } \times x^{-39} y^{-21}

The expression can be simplified as shown below

\frac{x^{8}y^{-26}  }{x^{14}y^{-5}  } \times x^{-39} y^{-21}

\frac{x^{8} \times x^{-39} \times  y^{-26} \times  y^{-21}  }{x^{14} \times y^{-5}  }

\frac{x^{8+-39} \times  y^{-26+-21}  }{x^{14} \times y^{-5}  }

\frac{x^{8-39} \times  y^{-26-21}  }{x^{14} \times y^{-5}  }

\frac{x^{-31} \times  y^{-47}  }{x^{14} \times y^{-5}  }

Then,

\frac{x^{-31} }{x^{14} } \times \frac{ y^{-47} }{ y^{-5} }

x^{-31-14} \times y^{-47--5}

x^{-31-14} \times y^{-47+5}

x^{-45} \times y^{-42}

x^{-45} y^{-42}

Hence, the simplified form of the expression is x^{-45} y^{-42}

Learn more on Simplifying an expression here: brainly.com/question/2320607

#SPJ1

3 0
2 years ago
a soccar team spent $55 dollars on supplies for a car wash then earned $275 whats their total after paying for supplies
IrinaK [193]
To find what profit they made, subtract what they earned from what they spent money on. 275-55=220. They made a total of $220 after paying for supplies. I hope this helps! :)
8 0
3 years ago
Other questions:
  • Help with math please.
    5·2 answers
  • What is the r value of the following geometric sequence?<br> 2, 6, 18, 54,...
    12·1 answer
  • Melanie works at the local animal shelter after school. The table below shows how much money she earned and the number of hours
    8·2 answers
  • When we prove a theorem using a proof, we start with a list of the ___ information.
    10·1 answer
  • 10+20+15<br> /2<br> will give branliest
    10·2 answers
  • In the first quadrant, you start at (10,7)
    10·2 answers
  • What value of k will make the expressions equivalent?<br> A. -42<br> B. -34<br> C. 16<br> D. 114
    13·1 answer
  • PLZ HELP ASAP WILL GIVE BRAINLIEST
    6·1 answer
  • Y is less than or equal to
    8·1 answer
  • Use the picture attached.
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!