Question

Pls help me with this, thank you

Nonsense will be reported​

Answer 1

$\large\underline{\sf{Solution-1}}$

Given polynomial is

$\rm \: - {10x}^{3} + 5x + k$

Let assume that

$\rm \: f(x) \: = \: - {10x}^{3} + 5x + k$

We know

Remainder Theorem states that if a polynomial p(x) of degree more than one is divided by x - a, then remainder is p(a).

So, here when f(x) is divided by x + 1, the remainder is 4

$\rm \: f( - 1) = 4$

$\rm \: - 10 {( - 1)}^{3} + 5( - 1) + k = 4$

$\rm \: 10 - 5 + k = 4$

$\rm \: 5+ k = 4$

$\rm\implies \: \: k \: = \: - \: 1$

Hence, Option (B) is correct.

$\red{\large\underline{\sf{Solution-2}}}$

$\rm \: Number\:of\:days\: = 5x - 3$

$\rm \: Earning \: = \: {15x}^{2} + 16x - 15$

Let we reduce this to factorize form with the help of splitting of middle terms

$\rm \: Earning \: = \: {15x}^{2} + 25x - 9x - 15$

$\rm \: Earning \: = \: 5x(3x + 5) - 3(3x +5)$

$\rm \: Earning \: = \: (3x + 5)(5x - 3)$

So,

$\rm \: Earning \: per \: day \: = \: \dfrac{Earning}{Number\:of\:days\:}$

$\rm \: Earning \: per \: day \: = \: \dfrac{(3x + 5)(5x - 3)}{5x - 3\:}$

$\bf\implies \:\rm \: Earning \: per \: day \: = \: 3x + 5$

So, Option D is correct.

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ADDITIONAL INFORMATION

Factor theorem states that if a polynomial f(x) of degree more than one is divided by x - a, then remainder is 0.

OR

If x - a is a factor of polynomial f(x) of degree more than one, then f(a) = 0

Answer 2

$\sf\purple{Solution:-}$

$\rm\longmapsto\boxed{ \rm{Answer \: in \: the \: above \: attachment}}$

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@Shivam

#BeBrainly