In English please solve In an understand

If the discount is 15%, then Kina paid $100\% - 15\% = 85\%$ of the normal price.

Let $P$ be the normal price. We have $0.85 \times P = 357\,000$.

The normal price of the TV set is 420,000 fcfa.

Question 2:
Given that $(x-1)$ is one of the factors of $f(x) = 2x^3 + x^2 - 2x - 1$.

a) Show that $(x-1)$ is a factor of $f(x)$.

According to the Factor Theorem, $(x-1)$ is a factor of $f(x)$ if and only if $f(1) = 0$.

Since $f(1) = 0$, we have shown that $(x-1)$ is a factor of $f(x)$.

b) Find the other two factors of $f(x)$.

Since $(x-1)$ is a factor, we can divide $f(x)$ by $(x-1)$ to find the quotient. Using synthetic division with the root $x=1$:

1 | 2   1   -2   -1
  |     2    3    1
  -----------------
    2   3    1    0

The quotient is $2x^2 + 3x + 1$.

We need to factor the quadratic polynomial $2x^2 + 3x + 1$.
We look for two numbers whose product is $2 \times 1 = 2$ and whose sum is 3. These numbers are 1 and 2.

The other two factors of $f(x)$ are $(2x+1)$ and $(x+1)$.

Question 3:

a) Find the value of $x$, given that $2^{x+1} = \frac{1}{4^3}$.

We know that $4 = 2^2$.

Since the bases are equal, the exponents must be equal.

The value of $x$ is -7.

b) Simplify $\frac{5-x}{5} - \frac{2-x}{10}$.

The common denominator for 5 and 10 is 10.
Rewrite the first fraction with the denominator 10:

The simplified expression is $\frac{8-x}{10}$.

Question 4:
The function $f$ is defined on $\mathbb{R}$ as $f(x) = 2-8x^2$.

a) Evaluate $f(2)$.

The value of $f(2)$ is -30.

b) Factorize $f(x)$ completely.

Here, $1 = 1^2$ and $4x^2 = (2x)^2$.

The factored form of $f(x)$ is $2(1-2x)(1+2x)$.

c) Solve the equation $f(x) = 0$.

For the product to be zero, at least one of the factors must be zero.

The solutions to the equation $f(x)=0$ are $x = \frac{1}{2}$ and $x = -\frac{1}{2}$.

Question 5:
Copy and complete the table accompanying this question.

The truth table needs to be completed for ~p (negation of p) and q ^ ~p (q AND not p).

Here is the completed table: