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Given f(x) = 4x^3 + 3x^2 - 4x + k.
Given g(x) = x - 1.
By factor theorem, we get
x - 1 = 0
x = 1.
Now,
Plug x = 1 in f(x), we get
f(1) = 4(1)^3 + 3(1)^2 - 4(1) + k = 0
= 4 + 3 - 4 + k = 0
= k + 3 = 0
= k = -3.
(9)
Given (5a - 7b)^3 + (9c - 5a)^3 + (7b - 9c)^3
We know that (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
= > (5a)^3 - 3(5a)^2 * (7b) + 3(5a)(7b)^2 - (7b)^3 + (9c)^3 - 3(9c)^2 * 5a + 3(9c)(5a)^2 - (5a)^2 + (5a)^3 + (7b)^3 - 3(7b)^2 * 9c + 3(7b)(9c)^2 - (9c)^3
= > 125a^3 - 525a^2b + 735ab^2 - 343b^3 + 729c^3 - 1215ac^2 + 674a^2c - 125a^3 + 343b^3 - 1323b^2c + 1701bc^2 - 729c^3
= > -525a^2b + 675a^2c + 735ab^2 - 1215ac^2 - 1323b^2c + 1701bc^2.
Hope this helps!
Given g(x) = x - 1.
By factor theorem, we get
x - 1 = 0
x = 1.
Now,
Plug x = 1 in f(x), we get
f(1) = 4(1)^3 + 3(1)^2 - 4(1) + k = 0
= 4 + 3 - 4 + k = 0
= k + 3 = 0
= k = -3.
(9)
Given (5a - 7b)^3 + (9c - 5a)^3 + (7b - 9c)^3
We know that (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
= > (5a)^3 - 3(5a)^2 * (7b) + 3(5a)(7b)^2 - (7b)^3 + (9c)^3 - 3(9c)^2 * 5a + 3(9c)(5a)^2 - (5a)^2 + (5a)^3 + (7b)^3 - 3(7b)^2 * 9c + 3(7b)(9c)^2 - (9c)^3
= > 125a^3 - 525a^2b + 735ab^2 - 343b^3 + 729c^3 - 1215ac^2 + 674a^2c - 125a^3 + 343b^3 - 1323b^2c + 1701bc^2 - 729c^3
= > -525a^2b + 675a^2c + 735ab^2 - 1215ac^2 - 1323b^2c + 1701bc^2.
Hope this helps!
siddhartharao77:
:-)
Answered by
0
Hey!!!
________________________________
1)●Let f(x)= 4x^3 + 3x^2 - 4x + k
Since,(x-1) is the factor of f (x)
So, x-1=0
x=1
Now,By factor theorum

2)●

This question's ans is in image
________________________________
Hope it helps!!! :)
________________________________
1)●Let f(x)= 4x^3 + 3x^2 - 4x + k
Since,(x-1) is the factor of f (x)
So, x-1=0
x=1
Now,By factor theorum
2)●
This question's ans is in image
________________________________
Hope it helps!!! :)
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