Step 1 :
Trying to factor as a Difference of Squares:1.1 Factoring: x4-256 Theory : A difference of two perfect squares, A2-B2can be factored into (A+B)•(A-B)Proof:(A+B)•(A-B)= A2 - AB+BA-B2= A2 -AB+ AB - B2 = A2 - B2Note : AB = BA is the commutative property of multiplication. Note : -AB+ AB equals zero and is therefore eliminated from the expression.Check: 256 is the square of 16Check: x4 is the square of x2Factorization is :(x2 + 16)•(x2 - 16)Polynomial Roots Calculator :
1.2 Find roots (zeroes) of : F(x) = x2 + 16Polynomial Roots Calculator is a set of methods aimed at finding values ofxfor 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 integersThe Rational Root Theorem states that if a polynomial zeroes for a rational numberP/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 1 and the Trailing Constant is 16. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 ,2 ,4 ,8 ,16 Let us check ....
| -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 Roots Calculator found no rational roots
Trying to factor as a Difference of Squares:1.3 Factoring: x2 - 16 Check: 16 is the square of 4Check: x2 is the square of x1Factorization is :(x + 4)•(x - 4)