factorise.
(m^2 - 3m) (m^2 - 3m - 26) - 56
Answers
Step-by-step explanation:
The first term is, m2 its coefficient is 1 .
The middle term is, -3m its coefficient is -3 .
The last term, "the constant", is -26
Step-1 : Multiply the coefficient of the first term by the constant 1 • -26 = -26
Step-2 : Find two factors of -26 whose sum equals the coefficient of the middle term, which is -3 .
-26 + 1 = -25
-13 + 2 = -11
-2 + 13 = 11
-1 + 26 = 25
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
2
:
m • (m - 3) • (m2 - 3m - 26) - 56
STEP
3
:
Polynomial Roots Calculator :
3.1 Find roots (zeroes) of : F(m) = m4-6m3-17m2+78m-56
Polynomial Roots Calculator is a set of methods aimed at finding values of m for which F(m)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers m 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 -56.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,7 ,8 ,14 ,28 ,56
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -144.00
-2 1 -2.00 -216.00
-4 1 -4.00 0.00 m+4
-7 1 -7.00 3024.00
-8 1 -8.00 5400.00
-14 1 -14.00 50400.00
-28 1 -28.00 730800.00
-56 1 -56.00 10830456.00
1 1 1.00 0.00 m-1
2 1 2.00 0.00 m-2
4 1 4.00 -144.00
7 1 7.00 0.00 m-7
8 1 8.00 504.00
14 1 14.00 19656.00
28 1 28.00 471744.00
56 1 56.00 8731800.00
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that
m4-6m3-17m2+78m-56
can be divided by 4 different polynomials,including by m-7