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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)}}

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