Factorise:4x³-21x-10
Answers
Q 4x^3-21x-10
Step-by-step explanation:
(22x3 - 21x) - 10
Find roots (zeroes) of : F(x) = 4x3-21x-10
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 4 and the Trailing Constant is -10.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4
of the Trailing Constant : 1 ,2 ,5 ,10
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
4x3-21x-10
can be divided by 3 different polynomials,including by 2x-5
Polynomial Long Division :
2.2 Polynomial Long Division
Dividing : 4x3-21x-10 ("Dividend")
By 2x-5 ("Divisor")
dividend 4x3 - 21x - 10
- divisor * 2x2 4x3 - 10x2
remainder 10x2 -21x - 10
- divisor * 5x1 10x2 - 25x
remainder 4x - 10
- divisor * 2x0 4x - 10
remainder 0
Quotient : 2x2+5x+2 Remainder: 0
Trying to factor by splitting the middle term
2.3 Factoring 2x2+5x+2
The first term is, 2x2 its coefficient is 2 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is +2
Step-1 : Multiply the coefficient of the first term by the constant 2 • 2 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is 5 .
-4 + -1 = -5
-2 + -2 = -4
-1 + -4 = -5
1 + 4 = 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 4
2x2 + 1x + 4x + 2
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x+1)
Add up the last 2 terms, pulling out common factors :
2 • (2x+1)
Step-5 : Add up the four terms of step 4 :
(x+2) • (2x+1)
Which is the desired factorization