Question

X^3+2X^2-X-2
BY FACTOR THEOREM​

Answer 1

Answer:

The correct answer is (x-1)(X+2)(x-2)

Step-by-step explanation:

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Answer 2

SOME POINTS FOR REMEMBRANCE:

IN QUESTIONS RELATED TO SOLVING FACTOR THEOREM

Step 1 : If f(-c)=0, ( x+ c) is a factor of the polynomial f(x).

Step 2 : If p(d/c)= 0, (cx-d) is a factor of the polynomial f(x).

Step 3 : If p(d/c)= 0, (cx-d) is a factor of the polynomial f(x).Step 3 : If p(-d/c)= 0, (cx+d) is a factor of the polynomial f(x).

Step 4 : If p(d/c)= 0, (cx-d) is a factor of the polynomial f(x).Step 3 : If p(-d/c)= 0, (cx+d) is a factor of the polynomial f(x).Step 4 : If p(c)=0 and p(d) =0, then (x-c) and (x-d) is a factor of the polynomial.

Step 5 : If p(d/c)= 0, (cx-d) is a factor of the polynomial f(x).Step 3 : If p(-d/c)= 0, (cx+d) is a factor of the polynomial f(x).Step 4 : If p(c)=0 and p(d) =0, then (x-c) and (x-d) is a factor of the polynomial.Rather than finding the factors by using polynomial long division method, the best way to find the factors are factor theorem and synthetic division method. This theorem is mainly used to remove the known zeros from polynomials leaving all unknown zeros unimpaired, thus by finding the zeros easily to produce the lower degree polynomial.

GIVEN:- X³ + 2X² - X - 2

TO FIND:- DIVIDE FOR QUOTIENT

METHOD USED:- FACTOR THEOREM

SOLUTION:-

》 let's check for the factors of the POLYNOMIAL by simply putting values

for x = 0

f(x) = 0 + 0 - 0 - 2

f(x) = -2 ........... so we will not take it as f(x) is not equal to 0

for x = 1

f(x) = 1 + 2 -1 - 2

f(x) = 0 .............. it SATISFIES

so factor is x - 1

for complete DIVISION see attachment,

NOW , SEE

f(x) = (x - 1)( x² - x - 2 )

NOW DEAR SPLIT THE TERM X² - X - 2 BY MIDDLE SPLITTING

=> X² - X - 2

=> x( x - 2 ) + 1( x - 2 )

=> (x + 1)(x - 2)

SO F(X) = (X + 1)(X - 2)(X - 1)

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