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Mathematics

Grade10

Easy

Question

Let $straight p space left parenthesis straight x right parenthesis space equals straight x space minus space 2 space comma space straight q space left parenthesis straight x right parenthesis space equals space straight x squared space minus space 3 straight x space plus space 1$ . Identify the rule for the function p.q

$x^{3} - 5 x^{2} + 7 x + 2$
$x^{3} - 5 x^{2} + 7 x - 2$
$x^{3} - 5 x^{2} + 6 x - 2$
$x^{3} + 5 x^{2} + 7 x - 2$

hint Hint:

(p.q) (x) = p (x) .q (x)

The correct answer is: $straight x cubed minus 5 straight x squared plus 7 straight x minus 2$

Given $straight p left parenthesis straight x right parenthesis equals straight x minus 2 comma straight q left parenthesis straight x right parenthesis equals straight x squared minus 3 straight x plus 1$
(p.q) (x) = p (x) .q (x) = (x - 2) . (x²- 3x + 1)
= x (x²- 3x + 1) -2 (x²- 3x + 1) = x³- 3x²+ x - 2x²+ 6x - 2
= x³- 5x²+ 7x - 2.

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