sslc maths Factorisation - காரணிப்படுத்தல்

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Factorisation

2. FACTOR THEOREM ¸¡Ã½¢ò§¾üÈõ
P(x) be a polynomial with degree ‘n’ (n>1) and ‘a’
bea real number .
(i) If P(a) = 0 then (x-a) is a factor of p(x).
(ii) If (x-a) is a factor ofp(x) then p(a) = 0 ¬Ìõ

3. Factorize the Polynomial(Ex3.5Q-vi-pg86)
x3 + 13x2 + 32x + 20

4. Factorize x3 + 13x2 + 32x + 20
x3 x2
1 +13 x+32 +20
1 +32
33 33
13 +20
+ = +66
Sum of the Co-efficients are not 0 so (x-1) is not a
factor.
Sum of even and oddpowers are equalso (x+1) is a
factor

5. Factorize. x3 +13x2 +32x + 20
(x+1) is a factor
1 13 32 20
(x+1) is a factor then x +1 = - 1- 1
0
11
1 x -1
-1
12
12 x -1
-12
20
20 x -1
-20
0
Remainder0 so (x+1) is a factor

6. 0
11
-1
12
-12
20
-20
0
1 13 32 20-1 Find the square roots of
quadratic equation
x2 +12x +201 +20+12
x =20
+ =? ?
x
10 2
Find Factors of 20 which sums are 12 multiplesare 20.

7. Sum of two numbers are12 and its multiples are 20 that
numbers are10 and 2
0
11
-1
12
-12
20
-20
0
1 13 32 20-1 Find the square roots of
quadratic equation
x2 +12x +201
12
x = 20
+ =
x
10 2

8. 2
Factors of x3 + 13x2 + 32x + 20
are (x+1), (x+2), (x+10)
0
11
-1
12
-12
20
-20
0
1 13 32 20-1 Find the square roots of
quadratic equation
x2 +12x +201
12
x = 20
+ =
x
10