Step 1 :
Trying to element as a difference of Squares:1.1 Factoring: x4-256 theory : A distinction of two perfect squares, A2-B2can be factored right into (A+B)•(A-B)Proof:(A+B)•(A-B)= A2 - AB+BA-B2= A2 -AB+ ab - B2 = A2 - B2Note : abdominal muscle = BA is the commutative building of multiplication. Keep in mind : -AB+ abdominal amounts to zero and also is therefore eliminated native the expression.Check: 256 is the square that 16Check: x4 is the square of x2Factorization is :(x2 + 16)•(x2 - 16)Polynomial root Calculator :
1.2 find roots (zeroes) the : F(x) = x2 + 16Polynomial root Calculator is a set of techniques aimed in ~ finding worths ofxfor which F(x)=0 Rational roots Test is among the above mentioned tools. It would certainly only discover Rational Roots that is numbers x which deserve to be expressed together the quotient of two integersThe Rational root Theorem claims that if a polynomial zeroes for a reasonable numberP/Q then ns is a factor of the Trailing continuous and Q is a variable of the leading CoefficientIn this case, the leading Coefficient is 1 and also the Trailing consistent is 16. The factor(s) are: the the top Coefficient : 1of the Trailing continuous : 1 ,2 ,4 ,8 ,16 Let us test ....
| -1 | 1 | -1.00 | 17.00 | ||||||
| -2 | 1 | -2.00 | 20.00 | ||||||
| -4 | 1 | -4.00 | 32.00 | ||||||
| -8 | 1 | -8.00 | 80.00 | ||||||
| -16 | 1 | -16.00 | 272.00 | ||||||
| 1 | 1 | 1.00 | 17.00 | ||||||
| 2 | 1 | 2.00 | 20.00 | ||||||
| 4 | 1 | 4.00 | 32.00 | ||||||
| 8 | 1 | 8.00 | 80.00 | ||||||
| 16 | 1 | 16.00 | 272.00 |
Polynomial root Calculator discovered no rational root
Trying to factor as a distinction of Squares:1.3 Factoring: x2 - 16 Check: 16 is the square that 4Check: x2 is the square of x1Factorization is :(x + 4)•(x - 4)