solve these problems urgent please
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ridhima46:
you know the answer of the first question?Is it given in answer sheet .My answer is (x-3)(x^2+7x+21)
If yes than tell I'll send how i have done it
otherwise no problem
right now I'm sending you some examples which are given in my book
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1 Ans:- p(x) = x - 3x - 9x - 5
Factors of 5 = 1,5,-1,-5
p(1) = 1 - 3 x (1) - 9 x (1) - 5
= 1 -3 - 9 - 5
= 1 - 17 = - 16 ≠ 0
p(-1) = (-1) x 3 x (-1) - 9 x (-1) -5
= -1 - 3 + 9 - 5 = -9 + 9 = 0
p(-1) =0
∴ (x+1) is a factor of p(x)
p(x) ÷ (x+1)
x - 3x - 9x - 5 ÷ x + 1
= x - 4x - 5
x - 4x - 5
x - 5x + 1x - 5
= x ( x - 5) + 1 ( x - 5)
= ( x - 5) ( x + 1 )
2Ans:- Ans) p(x) = x - 3x - 9x - 5
Factors of 5 = 1,5,-1,-5
p(1) = 1 - 3 x (1) - 9 x (1) - 5
= 1 -3 - 9 - 5
= 1 - 17 = - 16 ≠ 0
p(-1) = (-1) x 3 x (-1) - 9 x (-1) -5
= -1 - 3 + 9 - 5 = -9 + 9 = 0
p(-1) =0
∴ (x+1) is a factor of p(x)
p(x) ÷ (x+1)
x - 3x - 9x - 5 ÷ x + 1
= x - 4x - 5
x - 4x - 5
x - 5x + 1x - 5
= x ( x - 5) + 1 ( x - 5)
= ( x - 5) ( x + 1 )
3Ans:-. Let p(y) = 2y +y -2y-1
Constant term = 1
So, factors of 1=1, -1
We will put the value of its factors in p(x)
Substituting 1 in place of y in p(y)
we get,
2(1) + 1 - 2(1) -1
= 2 + 1-2 -1
= 0
which means y-1 is a factor of p(y)
Now divide p(y) by y-1
Then we get 2y + 3y+1
Now factorise this by splitting the middle term,
we get,
2y +3y +1
= 2y +2y +1y +1
=2y (y+1) + 1(y+1)
=(2y + 1) (y+1)
Factors of p(y) = (y-1) (2y+1) (y+1)
Factors of 5 = 1,5,-1,-5
p(1) = 1 - 3 x (1) - 9 x (1) - 5
= 1 -3 - 9 - 5
= 1 - 17 = - 16 ≠ 0
p(-1) = (-1) x 3 x (-1) - 9 x (-1) -5
= -1 - 3 + 9 - 5 = -9 + 9 = 0
p(-1) =0
∴ (x+1) is a factor of p(x)
p(x) ÷ (x+1)
x - 3x - 9x - 5 ÷ x + 1
= x - 4x - 5
x - 4x - 5
x - 5x + 1x - 5
= x ( x - 5) + 1 ( x - 5)
= ( x - 5) ( x + 1 )
2Ans:- Ans) p(x) = x - 3x - 9x - 5
Factors of 5 = 1,5,-1,-5
p(1) = 1 - 3 x (1) - 9 x (1) - 5
= 1 -3 - 9 - 5
= 1 - 17 = - 16 ≠ 0
p(-1) = (-1) x 3 x (-1) - 9 x (-1) -5
= -1 - 3 + 9 - 5 = -9 + 9 = 0
p(-1) =0
∴ (x+1) is a factor of p(x)
p(x) ÷ (x+1)
x - 3x - 9x - 5 ÷ x + 1
= x - 4x - 5
x - 4x - 5
x - 5x + 1x - 5
= x ( x - 5) + 1 ( x - 5)
= ( x - 5) ( x + 1 )
3Ans:-. Let p(y) = 2y +y -2y-1
Constant term = 1
So, factors of 1=1, -1
We will put the value of its factors in p(x)
Substituting 1 in place of y in p(y)
we get,
2(1) + 1 - 2(1) -1
= 2 + 1-2 -1
= 0
which means y-1 is a factor of p(y)
Now divide p(y) by y-1
Then we get 2y + 3y+1
Now factorise this by splitting the middle term,
we get,
2y +3y +1
= 2y +2y +1y +1
=2y (y+1) + 1(y+1)
=(2y + 1) (y+1)
Factors of p(y) = (y-1) (2y+1) (y+1)
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