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(2x - 3)(4x2 + 6x + 9) + (3 + 2x)(9 - 6x + 4x2)
Answers
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)