Math, asked by angelaleena350, 6 months ago

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lat Dhu
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(2x - 3)(4x2 + 6x + 9) + (3 + 2x)(9 - 6x + 4x2)​

Answers

Answered by nirvan780512
0

Answer:

(8x³-12x²+27)

Step-by-step explanation:

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2". 

STEP1:Equation at the end of step 1 ((2x-3)•(((4•(x2))-6x)-9))+((2x+3)•((9-6x)+22x2)) STEP2:Trying to factor by splitting the middle term

 2.1     Factoring  4x2-6x+9 

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  +9 

Step-1 : Multiply the coefficient of the first term by the constant   4 • 9 = 36 

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   -6 .

     -36   +   -1   =   -37     -18   +   -2   =   -20     -12   +   -3   =   -15     -9   +   -4   =   -13     -6   +   -6   =   -12     -4   +   -9   =   -13

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step2: ((2x-3)•(((4•(x2))-6x)-9))+(2x+3)•(4x2-6x+9) STEP 3 :Equation at the end of step3: ((2x-3)•((22x2-6x)-9))+(2x+3)•(4x2-6x+9) STEP4:Trying to factor by splitting the middle term

 4.1     Factoring  4x2-6x-9 

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  -9 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -9 = -36 

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -6 .

     -36   +   1   =   -35     -18   +   2   =   -16     -12   +   3   =   -9     -9   +   4   =   -5     -6   +   6   =   0     -4   +   9   =   5     -3   +   12   =   9     -2   +   18   =   16     -1   +   36   =   35

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step4: (2x-3)•(4x2-6x-9)+(2x+3)•(4x2-6x+9) STEP5:STEP6:Pulling out like terms

 6.1     Pull out like factors :

   16x3 - 24x2 + 54  =   2 • (8x3 - 12x2 + 27) 

Polynomial Roots Calculator :

 6.2    Find roots (zeroes) of :       F(x) = 8x3 - 12x2 + 27

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  8  and the Trailing Constant is  27.

 The factor(s) are:

of the Leading Coefficient :  1,2 ,4 ,8

 of the Trailing Constant :  1 ,3 ,9 ,27

 Let us test ....  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      7.00        -1     2      -0.50      23.00        -1     4      -0.25      26.12        -1     8      -0.12      26.80        -3     1      -3.00      -297.00   

Note - For tidiness, printing of 27 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

2 • (8x3 - 12x2 + 27)

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