Question

por favor me pueden ayudar con esto

Answer 1

Respuesta:

Explicación paso a paso:

$P(x)=-7x^{4} +6x^{2} +6x+5$

$Q(x)=-2x^{2} +2+3x^{5}$

$R(x)=x^{3} +x^{5}+3x^{2}$

a)  $P(x)+Q(x)$

    ($-7x^{4} +6x^{2} +6x+5$) + ($-2x^{2} +2+3x^{5}$)

    $-7x^{4} +6x^{2} +6x+5-2x^{2} +2+3x^{5}$

    $3x^{5}-7x^{4} +(6-2)x^{2} +6x+(5+2)$

    $3x^{5}-7x^{4} +4x^{2} +6x+7$

b)  $P(x)-Q(x)$

    $(-7x^{4} +6x^{2} +6x+5)-(-2x^{2} +2+3x^{5})$

    $-7x^{4} +6x^{2} +6x+5+2x^{2} -2-3x^{5}$

    $-3x^{5}-7x^{4} +(6+2)x^{2} +6x+(5-2)$

    $-3x^{5}-7x^{4} +8x^{2} +6x+3$

c)  $P(x)+Q(x)+R(x)$

    $(-7x^{4} +6x^{2} +6x+5)+(-2x^{2} +2+3x^{5})+(x^{3} +x^{5}+3x^{2})$

    $-7x^{4} +6x^{2} +6x+5-2x^{2} +2+3x^{5}+x^{3} +x^{5}+3x^{2}$

    $(3+1)x^{5}-7x^{4}+x^{3}+(6-2+3)x^{2} +6x+(5+2)$

    $4x^{5}-7x^{4}+x^{3}+7x^{2} +6x+7$

d)  $P(x)-Q(x)-R(x)$

    $(-7x^{4} +6x^{2} +6x+5)-(-2x^{2} +2+3x^{5})-(x^{3} +x^{5}+3x^{2})$

    $-7x^{4} +6x^{2} +6x+5+2x^{2} -2-3x^{5}-x^{3} -x^{5}-3x^{2}$

    $(-3-1)x^{5}-7x^{4}-x^{3}+(6+2-3)x^{2} +6x+(5-2)$

    $-4x^{5}-7x^{4}-x^{3}+5x^{2} +6x+3$

e)   $R(x)+P(x)-Q(x)$

    $(x^{3} +x^{5}+3x^{2})+(-7x^{4} +6x^{2} +6x+5)-(-2x^{2} +2+3x^{5})$

    $x^{3}+x^{5}+3x^{2}-7x^{4} +6x^{2} +6x+5+2x^{2} -2-3x^{5}$

    $(1-3)x^{5}-7x^{4}+x^{3}+(3+6+2)x^{2} +6x+(5-2)$

    $-2x^{5}-7x^{4}+x^{3}+11x^{2} +6x+3$

f)   $P(x)-R(x)+Q(x)$

    $(-7x^{4} +6x^{2} +6x+5)-(x^{3} +x^{5}+3x^{2})+(-2x^{2} +2+3x^{5})$

    $-7x^{4} +6x^{2} +6x-x^{3} -x^{5}-3x^{2}+5-2x^{2} +2+3x^{5}$

    $(-1+3)x^{5}-7x^{4}-x^{3}+(6-3-2)x^{2} +6x+(5+2)$

    $2x^{5}-7x^{4}-x^{3}+x^{2} +6x+7$