Question

Dado os polinômios P(x)=3x³+2x²-4x , Q(x)= x²+3x-1 e T(x)= 4x-2, calcule:

a) 4P(x)

b) 2P(x)

c) 2P(x) - 5Q(x)

d) Q(x) . T(x)+ P(x)

e) [Q(x)]²

Answer 1

POLINÔMIOS

Operações com polinômios

Se $P(x)=3 x^{3}+2 x^{2} -4x$, $Q(x)= x^{2} +3x-1$ e $T(x)=4x-2$

temos que:

a) $4P(x)=4(3 x^{3}+2 x^{2} -4x)=12 x^{3}+8 x^{2} -16x$


b) $2P(x)=2(3 x^{3}+2 x^{2} -4x)=6 x^{3}+4 x^{2} -8x$


c) $2P(x)-5Q(x)=2(3 x^{3}+2 x^{2} -4x)-5( x^{2} +3x-1)$

$(6 x^{3}+4 x^{2} -8x )-(-5 x^{2}-15x+5)=6 x^{3}+9 x^{2}+7x+5$


d) $Q(x)*T(x)+P(x)=( x^{2} +3x-1)(3 x^{3}+2 x^{2} -4x)+(4x-2)$

$(3x^{5}+2 x^{4}-4 x^{3}+9 x^{4}+6 x^{3}-12 x^{2} -3 x^{3}-2 x^{2} +4x)+(4x-2)$

$3 x^{5}+11 x^{4}- x^{3}-14 x^{2} +8x-2$


e) $Q(x) ^{2}=( x^{2} +3x-1)( x^{2} +3x-1)$

$x^{4}+3 x^{3}- x^{2} +3 x^{3}+9 x^{2} -3x- x^{2} -3x+1$

$x^{4}+6 x^{3}+7 x^{2} -6x+1$