factorise the following ( difference between two squares) : x⁴+9
please answer this question....
Answers
Step-by-step explanation:
1.1 Factoring: x4-9
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 9 is the square of 3
Check : x4 is the square of x2
Factorization is : (x2 + 3) • (x2 - 3)
Polynomial Roots Calculator :
1.2 Find roots (zeroes) of : F(x) = x2 + 3
Polynomial Roots Calculator is a set of methods aimed at finding values of x for 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 integers
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 1 and the Trailing Constant is 3.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 4.00
-3 1 -3.00 12.00
1 1 1.00 4.00
3 1 3.00 12.00
Polynomial Roots Calculator found no rational roots
Trying to factor as a Difference of Squares:
1.3 Factoring: x2 - 3
Check : 3 is not a square !!
Answer:
= (x^2)^2 + 3^2
= (x^2 - 3^2)^2 + 2*x^2*3
That should be the answer
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Step-by-step explanation: