The factor theorem of algebra states that if a polynomial, P (x), is divided by x-a, then the remainder is P (a). Verify the remainder theorem by showing that when x^2-2x-16

is divided by x+3 the remainder is the same as P (-3).

Remainder for (x^2-2x-16) / (x+3) ?

P (-3) ?

Question

Mathematics

Jacob Cantu

31 October, 08:58

The factor theorem of algebra states that if a polynomial, P (x), is divided by x-a, then the remainder is P (a). Verify the remainder theorem by showing that when x^2-2x-16

is divided by x+3 the remainder is the same as P (-3).

Remainder for (x^2-2x-16) / (x+3) ?

P (-3) ?

+1

Answers (1)

Know the Answer?

Meredith Villegas · Answer 1

Okay ... by using long division method first

we have

x²-2x-16 : x+3

quotient = x-5, remainder = - 1

using factor Theorem

we have

f (-3) = (-3) ² - 2 (-3) - 16 = 9+6-16 = - 1 (remainder)

so the remainder theorem is valid

The factor theorem of algebra states that if a polynomial, P (x), is divided by x-a, then the remainder is P (a). Verify the remainder theorem by showing that when x^2-2x-16is divided by x+3 the remainder is the same as P (-3).Remainder for (x^2-2x-16) / (x+3) ?P (-3) ?

The factor theorem of algebra states that if a polynomial, P (x), is divided by x-a, then the remainder is P (a). Verify the remainder theorem by showing that when x^2-2x-16

is divided by x+3 the remainder is the same as P (-3).

Remainder for (x^2-2x-16) / (x+3) ?

P (-3) ?