Question

b) Show that (x+3) is a factor of 2x2-x-21. Hence factorise 2x2-x-21.
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Answer 1

$i) Let \:p(x) = 2x^{2} - x - 21$

$p(-3) = 2(-3)^{2} - (-3) - 21$

$= 18 + 3 - 21$

$= 21 - 21$

$= 0$

Therefore.,

$\green { (x+3)\: is \: a \: factor \: of \: p(x) }$

$\underline { Factorisation : }$

$Given \: 2x^{2} - x - 21$

/* Splitting the middle term,we get */

$= 2x^{2} -6x + 7x - 21$

$= 2x(x-3) + 7(x-3)$

$= (x-3)(2x+7)$

Therefore.,

$\red{ Factors \:of \: 2x^{2} - x - 21 }$

$\green { = (x-3)(2x+7) }$

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