Answer: olynomial Long Division
Dividing : x3 + x2 - 20x + 24
("Dividend")
By : x - 3 ("Divisor")
dividend x3 + x2 - 20x + 24
- divisor * x2 x3 - 3x2
remainder 4x2 - 20x + 24
- divisor * 4x1 4x2 - 12x
remainder - 8x + 24
- divisor * -8x0 - 8x + 24
remainder 0
Quotient : x2+4x-8 Remainder: 0
Factoring x2+4x-8
The first term is, x2 its coefficient is 1 .
The middle term is, +4x its coefficient is 4 .
The last term, "the constant", is -8
Step-1 : Multiply the coefficient of the first term by the constant 1 • -8 = -8
Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is 4 .
-8 + 1 = -7
-4 + 2 = -2
-2 + 4 = 2
-1 + 8 = 7
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Find roots (zeroes) of : F(x) = x3 + x2 - 23x + 24
See theory in step 1.3
In this case, the Leading Coefficient is 1 and the Trailing Constant is 24.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,3 ,4 ,6 ,8 ,12 ,24
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 47.00
-2 1 -2.00 66.00
-3 1 -3.00 75.00
-4 1 -4.00 68.00
-6 1 -6.00 -18.00
-8 1 -8.00 -240.00
-12 1 -12.00 -1284.00
-24 1 -24.00 -12672.00
1 1 1.00 3.00
2 1 2.00 -10.00
3 1 3.00 -9.00
4 1 4.00 12.00
6 1 6.00 138.00
8 1 8.00 416.00
12 1 12.00 1620.00
24 1 24.00 13872.00
Polynomial Roots Calculator found no rational roots
Answer: x3 + x2 - 23x + 24
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x
Explanation: