Factorise
x³+x²-16x+20
Answers
x³ + x² - 16x + 20
= x³ - 2x² + 3x² - 6x - 10x + 20
= x²(x - 2) + 3x(x - 2) - 10(x - 2)
= (x² + 3x - 10)(x - 2)
= (x² - 2x + 5x - 10)(x - 2)
= [x(x - 2)+5(x - 2)](x - 2)
= [(x - 2)(x+5)](x - 2)
= (x - 2)(x + 5)(x - 2).
Answer:
is the solution for the given equation
Step-by-step explanation:
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x3+x2
Group 2: -16x+20
Pull out from each group separately :
Group 1: (x+1) • (x2)
Group 2: (4x-5) • (-4)
Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
Find roots (zeroes) of : F(x) = x3+x2-16x+20
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 20.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,5 ,10 ,20
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 36.00
-2 1 -2.00 48.00
-4 1 -4.00 36.00
-5 1 -5.00 0.00 x+5
-10 1 -10.00 -720.00
-20 1 -20.00 -7260.00
1 1 1.00 6.00
2 1 2.00 0.00 x-2
4 1 4.00 36.00
5 1 5.00 90.00
10 1 10.00 960.00
20 1 20.00 8100.00
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
x3+x2-16x+20
can be divided by 2 different polynomials, including by x-2
Polynomial Long Division
Dividing : x3+x2-16x+20
("Dividend")
By : x-2 ("Divisor")
dividend x3 + x2 - 16x + 20
- divisor * x2 x3 - 2x2
remainder 3x2 - 16x + 20
- divisor * 3x1 3x2 - 6x
remainder - 10x + 20
- divisor * -10x0 - 10x + 20
remainder 0
Quotient : x2+3x-10 Remainder: 0
Trying to factor by splitting the middle term
Factoring x2+3x-10
The first term is, x2 its coefficient is 1 .
The middle term is, +3x its coefficient is 3 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 1 • -10 = -10
Step-2 : Find two factors of -10 whose sum equals the coefficient of the middle term, which is 3 .
-10 + 1 = -9
-5 + 2 = -3
-2 + 5 = 3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 5
x2 - 2x + 5x - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-2)
Add up the last 2 terms, pulling out common factors :
5 • (x-2)
Step-5 : Add up the four terms of step 4 :
(x+5) • (x-2)
Which is the desired factorization
Reference Link
- https://brainly.in/question/9512497