Respuesta :

caylus
Hello,

P(x)=x^3-7x^2-18x+42
P(-3)=(-3)^3-7*(-3)²-18*(-3)+42=-27-63+54+42=6

If we do the division:

x^3-7x^2-18x+52=(x+3)(x²-10x+12) +6

Remainder=6

Answer:

[tex]\text{The remainder is 6 when }x^3-7x^2-18x+42\text{ is divided by (x + 3)}[/tex]

Step-by-step explanation:

[tex]\text{Given the polynomial }x^3-7x^2-18x+42[/tex]

we have to find the remainder when above polynomial is divided by (x+3)

[tex]P(x)=x^3-7x^2-18x+42[/tex]

By remainder theorem,

[tex]P(3)=(-3)^3-7(-3)^2-18(-3)+42[/tex]

[tex]P(3)=-27-63+54+42[/tex]

[tex]P(x)=6[/tex]

Hence, the remainder is 6

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