(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]

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Solution

Each part: 1.5 Marks

(i) Value of the expression for $x = - 4$

$2 x^{2} + 12 x + 3$

$2 (- 4)^{2} + 12 (- 4) + 3$

$2 (16) - 48 + 3$

$32 - 48 + 3 = - 15$

Hence, the value of expression $2 x^{2} + 12 x + 3$ at $x = - 4$ is lesser than 15.

(ii) As per question

$x^{2}$ is added to $2 x^{2} + 12 x + 3$ and 15 is subtracted from it

So, the final expression is:

$2 x^{2} + 12 x + 3 + x^{2} - 15$

$3 x^{2} + 12 x - 12$

On putting x = -4 in the above equation we get:

$3 \times (- 4)^{2} + 12 \times (- 4) - 12$

$= 48 - 48 - 12$

$= - 12$

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