Answer: (4x2 + 4x - 5) • (x - 1)
Step-by-step explanation: 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 5.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4
of the Trailing Constant : 1 ,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
4x3-9x+5
can be divided with x-1
2.2 Polynomial Long Division
Dividing : 4x3-9x+5
("Dividend")
By : x-1 ("Divisor")
dividend 4x3 - 9x + 5
- divisor * 4x2 4x3 - 4x2
remainder 4x2 - 9x + 5
- divisor * 4x1 4x2 - 4x
remainder - 5x + 5
- divisor * -5x0 - 5x + 5
remainder 0
Quotient : 4x2+4x-5 Remainder: 0
2.3 Factoring 4x2+4x-5
The first term is, 4x2 its coefficient is 4 .
The middle term is, +4x its coefficient is 4 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 4 • -5 = -20
Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is 4 .
-20 + 1 = -19
-10 + 2 = -8
-5 + 4 = -1
-4 + 5 = 1
-2 + 10 = 8
-1 + 20 = 19
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
