Question

factorise the following polynomials

Answer 1

Hey Mate!

Here is your answer dear you were searching for :-
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1)g(x) = x+9 = 0
x= -9

$p(x) = x {}^{3} + 13x {}^{2} + 31x - 45 \\ p( - 9) = ( - 9) {}^{3} + 13( - 9) {}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: + 31( - 9) \: - 45 \\ = - 729 + 1053 - 279 - 45 \\ = 1053 - 1053 \\ = 0$


2) g(x) = 2x+3=0 ➡ x= -3/2

$p(x) = 4x {}^{3} + 20x {}^{2} + 33x + 18 \\ p( \frac{ - 3}{2} ) = 4( \frac{ - 3}{2} ) {}^{3} + 20(\frac{ - 3}{2}) {}^{2} \\ 33 \times \frac{ - 3}{2} + 18 \\ \\ 4 \times \frac{ - 27}{8} + 20 \times \frac{9}{4} + 33 \times \frac{ - 3}{2} \\ + 18 \\ \\ \frac{ - 27}{2} + 45 + \frac{ - 99}{2} + 18 \\ \\ \frac{ - 27 + 90 - 99 + 36}{2} \\ \\ \frac{126 - 126}{2} \\ \\ = 0$



Hope it helps!

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