Question

(iii) 6x2 + x - 15 is divided by 3x + 5.
In each case, verify your answer.​

Answer 1

SOLUTION

TO DETERMINE

$\displaystyle \sf{ \frac{6 {x}^{2} + x - 15 }{3x + 5} \: }$

and to verify the answer

EVALUATION

First we simplify the numerator

$\sf{6 {x}^{2} + x - 15 \: }$

$= \sf{6 {x}^{2} +(10 - 9) x - 15 \: }$

$= \sf{6 {x}^{2} +10 x - 9x - 15 \: }$

$= \sf{2x(3x + 5) - 3(3x + 5) \: }$

$= \sf{(3x + 5)(2x - 3)\: }$

Hence

$\displaystyle \sf{ \frac{6 {x}^{2} + x - 15 }{3x + 5} \: }$

$= \displaystyle \sf{ \frac{(3x + 5)(2x - 3) }{3x + 5} \: }$

$\displaystyle \sf{ = 2x - 3\: }$

VERIFICATION

Here

$\sf{(3x + 5)(2x - 3) \: }$

$= \sf{3x (2x - 3) + 5(2x - 3) \: }$

$\sf{ = 6 {x}^{2} - 9x + 10x - 15\: }$

$= \sf{6 {x}^{2} + x - 15 \: }$

Hence verified

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