Question

Please answer this quickly.

Answer 1

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!

Answer 2

Hey!!!
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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
$f(1) = 4 \times {1}^{3} + 3 \times {1}^{2} - 4 \times 1 + k \\ = 4 + 3 - 4 + k \\ = k + 3 \\ but \: f(1) = 0 \\ k + 3 = 0 \\ k = - 3$
2)●
${(5a - 7b)}^{3} + {(9c - 5a)}^{3} + {(7b - 9c)}^{3}$
This question's ans is in image
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Hope it helps!!! :)