a4 - 5a2 - 36 factorise
Answers
Answer:
4-5-38.......:.....:
Answer:
Step-by-step explanation:
a4-5a2-36
Final result :
(a2 + 4) • (a + 3) • (a - 3)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "a2" was replaced by "a^2". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((a4) - 5a2) - 36
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring a4-5a2-36
The first term is, a4 its coefficient is 1 .
The middle term is, -5a2 its coefficient is -5 .
The last term, "the constant", is -36
Step-1 : Multiply the coefficient of the first term by the constant 1 • -36 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -5 .
-36 + 1 = -35
-18 + 2 = -16
-12 + 3 = -9
-9 + 4 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4
a4 - 9a2 + 4a2 - 36
Step-4 : Add up the first 2 terms, pulling out like factors :
a2 • (a2-9)
Add up the last 2 terms, pulling out common factors :
4 • (a2-9)
Step-5 : Add up the four terms of step 4 :
(a2+4) • (a2-9)
Which is the desired factorization
Polynomial Roots Calculator :
2.2 Find roots (zeroes) of : F(a) = a2+4
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a 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 4.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 5.00
-2 1 -2.00 8.00
-4 1 -4.00 20.00
1 1 1.00 5.00
2 1 2.00 8.00
4 1 4.00 20.00
Polynomial Roots Calculator found no rational roots
Trying to factor as a Difference of Squares :
2.3 Factoring: a2-9
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 : a2 is the square of a1
Factorization is : (a + 3) • (a - 3)
Final result :
(a2 + 4) • (a + 3) • (a - 3)
Processing ends successfully.