Use the remainder theorem to find P(c) P(x)=6x^3-x^2+4x+3,a=3.

Jaycee Cox

Jaycee Cox

Answered question

2023-02-14

Use the remainder theorem to find P(c) P ( x ) = 6 x 3 - x 2 + 4 x + 3 , a=3.

Answer & Explanation

Marcel Yoder

Marcel Yoder

Beginner2023-02-15Added 4 answers

When we divide a polynomial P(x) (here P ( x ) = 6 x 3 - x 2 + 4 x + 3 ) by a binomial of degree one say (x-a), (here (x-3) as we wish P(a) with a=3), it is said that the remainder theorem applies. The balance is P. (a).
Normally, one would replace x with a to obtain P(a), but since the remainder theorem is required, we should divide P(x) by (x-a), with the remainder being P. (a). Let's divide 6 x 3 - x 2 + 4 x + 3 using synthetic division to get this (x-3).
3 X 6 X - 1 X X X 4 3
1 X X × 18 X X X 51 X X 165
x X 6 X × x 17 X X X 55 X X 168
i.e. while quotient is 6 x 2 + 17 x + 55 , remainder is 168.

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