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
MA_775_DIABLO [31]
3 years ago
6

Factor the expression 12x^2 +7x+1

Mathematics
1 answer:
Leona [35]3 years ago
7 0

Answer:

\boxed{\textsf{ The factorised form is \textbf{(4x+1)(3x+1)}.}}

Step-by-step explanation:

A quadratic polynomial is given to us and we need to find its factorised form . The given quadratic polynomial is ,

\sf\implies p(x)= 12x^2+7x+1

And this equation is similar to the equation in ax² + bx + c form . So in order to factorise it .

Step 1: <u>Multiply </u><u>the </u><u>coefficient </u><u>of </u><u>x²</u><u> </u><u>with </u><u>the </u><u>constant</u><u> </u><u>term </u><u>.</u>

Here the coefficient of x² is 12 and the constant term is 1 . So on multiplying them we get 12*1= 12 .

Step 2: <u>Look </u><u>out</u><u> </u><u>for </u><u>the </u><u>possible</u><u> </u><u>factors </u><u>of </u><u>the </u><u>number</u><u> </u><u>.</u>

Here the obtained number is 12 . So the possible factors of 12 is

  • 1 *12
  • -1*-12
  • 2*6
  • -2*-6
  • 4*3
  • -4*-3

Step3: <u>Choose </u><u>the </u><u>factor </u><u>whose </u><u>sum </u><u>is </u><u>equal </u><u>to </u><u>the </u><u>coefficient</u><u> </u><u>of </u><u>the </u><u>middle</u><u> </u><u>term </u><u>.</u>

Here we can see that the middle term is 7 . And the sum of 4 and 3 is equal to 7 . Hence here we will break 7x as 4x + 3x .

Step 4: <u>After </u><u>proper</u><u> </u><u>arrangements</u><u> </u><u>take </u><u>out</u><u> the</u><u> </u><u>common</u><u> </u><u>term </u><u>and </u><u>then </u><u>factorise</u><u>.</u>

After suitable rearrangment we get ,

\sf\implies p(x)= 12x^2+4x+3x+1 \\\\\sf\implies p(x)= 4x(3x+1)+1(3x+1) \\\\\implies\boxed{\red{\sf p(x)= (4x+1)(3x+1)}}

You might be interested in
Solve for x in a triangle. Round your answer to the nearest hundredth
Molodets [167]
16cos(28). Type that in like last time.
8 0
3 years ago
Completează tabelul de mai jos:
KiRa [710]
I’ll what is this language
4 0
3 years ago
Pls, it’s for a test , ;&lt; . I Wanna actually Get a good grade. PLS HELP you will get 20 points
kow [346]
Answer: B. y=9
Explanation: divide both sides of the equation by three
y3/3 = y
27/3=9
y=9
hope this helps:)
7 0
2 years ago
Read 2 more answers
Explain how to multiply the following whole numbers 21 x 14
Lesechka [4]

Answer:

\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}

________

\frac{\begin{matrix}\space\space&\textbf{0}&8&4\\ +&\textbf{2}&1&0\end{matrix}}{\begin{matrix}\space\space&\textbf{2}&9&4\end{matrix}}

Step-by-step explanation:

Given

21\:\times \:14

Line up the numbers

\begin{matrix}\space\space&2&1\\ \times \:&1&4\end{matrix}

Multiply the top number by the bottom number one digit at a time starting with the ones digit left(from right to left right)

Multiply the top number by the bolded digit of the bottom number

\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}

Multiply the bold numbers:    1×4=4

\frac{\begin{matrix}\space\space&2&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&4\end{matrix}}

Multiply the bold numbers:    2×4=8

\frac{\begin{matrix}\space\space&\textbf{2}&1\\ \times \:&1&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&8&4\end{matrix}}

Multiply the top number by the bolded digit of the bottom number

\frac{\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&8&4\end{matrix}}

Multiply the bold numbers:    1×1=1

\frac{\begin{matrix}\space\space&\space\space&2&\textbf{1}\\ \space\space&\times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&\space\space&8&4\\ \space\space&\space\space&1&\space\space\end{matrix}}

Multiply the bold numbers:    2×1=2

\frac{\begin{matrix}\space\space&\space\space&\textbf{2}&1\\ \space\space&\times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&\space\space&8&4\\ \space\space&2&1&\space\space\end{matrix}}

Add the rows to get the answer. For simplicity, fill in trailing zeros.

\frac{\begin{matrix}\space\space&\space\space&2&1\\ \space\space&\times \:&1&4\end{matrix}}{\begin{matrix}\space\space&0&8&4\\ \space\space&2&1&0\end{matrix}}

adding portion

\begin{matrix}\space\space&0&8&4\\ +&2&1&0\end{matrix}

Add the digits of the right-most column: 4+0=4

\frac{\begin{matrix}\space\space&0&8&\textbf{4}\\ +&2&1&\textbf{0}\end{matrix}}{\begin{matrix}\space\space&\space\space&\space\space&\textbf{4}\end{matrix}}

Add the digits of the right-most column: 8+1=9

\frac{\begin{matrix}\space\space&0&\textbf{8}&4\\ +&2&\textbf{1}&0\end{matrix}}{\begin{matrix}\space\space&\space\space&\textbf{9}&4\end{matrix}}

Add the digits of the right-most column: 0+2=2

\frac{\begin{matrix}\space\space&\textbf{0}&8&4\\ +&\textbf{2}&1&0\end{matrix}}{\begin{matrix}\space\space&\textbf{2}&9&4\end{matrix}}

Therefore,

\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}

________

\frac{\begin{matrix}\space\space&\textbf{0}&8&4\\ +&\textbf{2}&1&0\end{matrix}}{\begin{matrix}\space\space&\textbf{2}&9&4\end{matrix}}

6 0
3 years ago
Solve 7x − 2y = −3<br> 14x + y = 14
Sauron [17]
7x - 2y = -3

14x + y = 14
14x -14x + y = 14-14x
Y = 14 - 14x

7x -2y = -3
7x - 2(14 - 14x) = -3
7x -28 + 28x = -3
7x + 28x - 28 = -3
35x - 28 = -3
35x - 28 + 28 = -3 + 28
35x = 25
35x/35 = 25/35
X = 25/35 = 5/7.

Y = 14 - 14x
Y = 14 - 14(5/7)
Y = 14 - 10
Y = 4.

The solution P(5/7,4).
8 0
3 years ago
Read 2 more answers
Other questions:
  • erica can run 1/6 of a kilometer in a minute her school is 3/4 of a kilometer away from her home at this speed how long would it
    9·2 answers
  • Maeve survey a large number of students at the bowling alley about their favorite weekend activity
    14·1 answer
  • IS IT 4.5?
    13·1 answer
  • If u(x)=x^5-x^4+x^2 and v(x)=-x^2, which expression is equivalent to (u/v)(x)?
    9·2 answers
  • Helpppppppp meeeee!!!!!​
    7·1 answer
  • Mr. Garza's family is attending the local soccer game. He has 30 to spend on food and drinks . The cost of chips is $2 and the c
    5·1 answer
  • What is madeline mistake
    7·1 answer
  • 9. plsss help, will give brianlist
    9·1 answer
  • HELPPP ME PLEASEE
    12·1 answer
  • The sum of two integers is 250.If one of them is -87,find the others integers​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!