(i) Will the value of $2 x^{2} + 12 x + 3$ for x = - 4 be greater than or less than 15?

(ii) If $x^{2}$ is added to $2 x^{2} + 12 x + 3$ and 15 is subtracted from it then evaluate its value at x = -4? [3 MARKS]

Q. Read the information given below and answer the questions that follows:
If f(x) = 2x + 3 and g(x) =

\frac{x - 3}{2}

, then

For what value of x; f(x) = g(x – 3)

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If (x+2)n(x−2)=(x+2)(x2−4) for all values of x, what is the value of n?

The correct option is B 2Given, (x+2)n(x−2)=(x+2)(x2−4)We know that x2−4=(x−2)×(x+2). So the right side expression will become (x+2)2×(x−2).Now by comparing on both sides, we can say that the value of n is 2.

If ${(x + 2)}^{n} (x - 2) = (x + 2) (x^{2} - 4)$ for all values of $x$ , what is the value of $n$ ?

The correct option is B $2$
Given, $(x + 2)^{n} (x - 2) = (x + 2) (x^{2} - 4)$
We know that $x^{2} - 4 = (x - 2) \times (x + 2)$ .
So the right side expression will become ${(x + 2)}^{2} \times (x - 2)$ .
Now by comparing on both sides, we can say that the value of $n$ is $2$ .