Question

What is the remainder when (x3 − 7x2 − 18x + 42) is divided by (x + 3)?

Answer 1

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 2

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

Explanation:

`\text{Given the polynomial }x^3-7x^2-18x+42`

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

`P(x)=x^3-7x^2-18x+42`

By remainder theorem,

`P(3)=(-3)^3-7(-3)^2-18(-3)+42`

`P(3)=-27-63+54+42`

`P(x)=6`

Hence, the remainder is 6