19x2+6-(3(x2-7)+9) Final result : 2 • (8x2 + 9)
Step by step solution :Step 1 :Trying to factor as a Difference of Squares :
1.1 Factoring: x2-7
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 : 7 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step 1 : ((19•(x2))+6)-(3•(x2-7)+9)
Step 2 :Equation at the end of step 2 : (19x2 + 6) - (3x2 - 12)
Step 3 :Step 4 :Pulling out like terms :
4.1 Pull out like factors :
16x2 + 18 = 2 • (8x2 + 9)
Polynomial Roots Calculator :
4.2 Find roots (zeroes) of : F(x) = 8x2 + 9
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 8 and the Trailing Constant is 9.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4 ,8
of the Trailing Constant : 1 ,3 ,9
Let us test
P Q P/Q F(P/Q) Divisor -1 1 -1.00 17.00 -1 2 -0.50 11.00 -1 4 -0.25 9.50 -1 8 -0.13 9.13 -3 1 -3.00 81.00
Note - For tidiness, printing of 19 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Final result : 2 • (8x2 + 9)
