3/4x/\2+4x+5 factorise mark as brainliest and 50 pts awarded
Answers
Answer:
Explanation:
x3-4x2-4x-5
Final result :
(x2 + x + 1) • (x - 5)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(((x3) - 22x2) - 4x) - 5
Step 2 :
Checking for a perfect cube :
2.1 x3-4x2-4x-5 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3-4x2-4x-5
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x3-5
Group 2: -4x2-4x
Pull out from each group separately :
Group 1: (x3-5) • (1)
Group 2: (x+1) • (-4x)
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 :
2.3 Find roots (zeroes) of : F(x) = x3-4x2-4x-5
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 1 and the Trailing Constant is -5.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,5
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -6.00
-5 1 -5.00 -210.00
1 1 1.00 -12.00
5 1 5.00 0.00 x-5
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that
x3-4x2-4x-5
can be divided with x-5
Polynomial Long Division :
2.4 Polynomial Long Division
Dividing : x3-4x2-4x-5
("Dividend")
By : x-5 ("Divisor")
dividend x3 - 4x2 - 4x - 5
- divisor * x2 x3 - 5x2
remainder x2 - 4x - 5
- divisor * x1 x2 - 5x
remainder x - 5
- divisor * x0 x - 5
remainder 0
Quotient : x2+x+1 Remainder: 0
Trying to factor by splitting the middle term
2.5 Factoring x2+x+1
The first term is, x2 its coefficient is 1 .
The middle term is, +x its coefficient is 1 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1
Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is 1 .
-1 + -1 = -2
1 + 1 = 2
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
(x2 + x + 1) • (x - 5)
SOME WHAT CORRECT ACCORDING TO MY CLARITY
Answer:
yeah
Pls mark this as the Brainliest answer!!!