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2 years ago

Dividing the polynomial P(x) by x + 3 yields a quotient Q(x) and a remainder of 7. If Q(3)=1, find P (3) and P(-3).

Social Studies

1 answer:

kondor19780726 [428]2 years ago

8 0

1. The value of the polynomial P(3) obtained is 16

2. The value of the polynomial P(–3) obtained is 7

<h3>Remainder theorem</h3>

If F(x) is a polynomial and it is divided by C

to give Q and a remainder of D

Then,

Polynomial = (Quotient × divisor) + remainder

F(x) = (Q × C ) + D

Where

F(x) is the polynomial

Q is the quotient

C is the divisor

D is the remainder

<h3>1. How to determine the value of P(3)</h3>

Divisor = x + 3
x = 3
Quotient [Q(x)] = 1
Remainder = 7
Polynomial [P(3)] =?

Polynomial = (Quotient × divisor) + remainder

P(x) = [Q(x) × (x + 3)] + 7

P(3)= [Q(3) × (x + 3)] + 7

P(3) = [1 × (3 × 3)] + 7

P(3) = 9 + 7

P(3) = 16

<h3>2. How to determine the value of P(–3)</h3>

Divisor = x + 3
x = –3
Remainder = 7
Polynomial [P(–3)] =?

Polynomial = (Quotient × divisor) + remainder

P(x) = [Q(x) × (x + 3)] + 7

P(–3)= [Q(–3) × (–3 + 3)] + 7

P(–3) = [Q(–3) × 0] + 7

P(–3) = 0 + 7

P(–3) = 7

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