Question

Factorise 2x4-7x3-13x2+63x-45

Answer 1

2x4-7x3-13x2+63x-45

can be divided by 4 different

polynomials,including by 2x-5

Polynomial Long Division :

4.2 Polynomial Long Division

Dividing : 2x 4 -7x 3 -13x 2 +63x-45

("Dividend")

By : 2x-5 ("Divisor")

dividend 2x 4 - 7x 3 - 13x 2 + 63x - 45

- divisor * x 3 2x 4 - 5x 3

remainder - 2x 3 - 13x 2 + 63x - 45

- divisor * -x 2 - 2x 3 + 5x 2

remainder - 18x 2 + 63x - 45

- divisor * -9x 1 - 18x 2 + 45x

remainder 18x - 45

- divisor * 9x 0 18x - 45

remainder 0
Quotient : x 3 -x 2 -9x+9 Remainder: 0
Polynomial Roots Calculator :
4.3 Find roots (zeroes) of : F(x) = x 3 -x 2 -9x+9
See theory in step 4.1
In this case, the Leading Coefficient is 1 and the Trailing Constant is 9.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,9
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 16.00
-3 1 -3.00 0.00 x+3
-9 1 -9.00 -720.00
1 1 1.00 0.00 x-1
3 1 3.00 0.00 x-3
9 1 9.00 576.00

Answer 2

(x-1)(x-3)(x+3)(2x-5)