Factorise (2x-3)^3+125
Answers
Answer:(2x-3)3=125
Three solutions were found :
x = 4
x =(2-√-300)/8=(1-5i√ 3 )/4= 0.2500-2.1651i
x =(2+√-300)/8=(1+5i√ 3 )/4= 0.2500+2.1651i
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(2*x-3)^3-(125)=0
Step by step solution :
Step 1 :
1.1 Evaluate : (2x-3)3 = 8x3-36x2+54x-27
Step 2 :
Pulling out like terms :
2.1 Pull out like factors :
8x3 - 36x2 + 54x - 152 =
2 • (4x3 - 18x2 + 27x - 76)
Checking for a perfect cube :
2.2 4x3 - 18x2 + 27x - 76 is not a perfect cube
Trying to factor by pulling out :
2.3 Factoring: 4x3 - 18x2 + 27x - 76
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 27x - 76
Group 2: -18x2 + 4x3
Pull out from each group separately :
Group 1: (27x - 76) • (1)
Group 2: (2x - 9) • (2x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
2.4 Find roots (zeroes) of : F(x) = 4x3 - 18x2 + 27x - 76
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 4 and the Trailing Constant is -76.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4
of the Trailing Constant : 1 ,2 ,4 ,19 ,38 ,76
Step-by-step explanation:
Answer
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