Question

Use the remainder Theorem to find the remainder for (x2- 2)/(x - 1) and state whether or not the binomial is a factor of
the polynomial.

Answer 1

Answer:

The remainder is -1

The binomial is not a factor of the polynomial

Step-by-step explanation:

In the algebraic division, there are 4 terms

1. Dividend ⇒ the term before the division sign
2. Divisor ⇒ the term after the division sign
3. Quotient ⇒ the answer
4. Remainder ⇒ appear when the dividend not divisible by the divisor (the divisor is not a factor of the dividend)

The remainder theorem:

• If you divide a polynomial f(x) by (x - h), then the remainder is f(h).

• You do not need to use the long division to find the remainder, just evaluate the polynomial when x = h to find the remainder.
• If h(h) = 0, then (x - h) is a factor of f(x)

Let us use it to solve the question

∵ The dividend is x² - 2

∴ f(x) = x² - 2

∵ The divisor is x - 1

∴ (x - h) = (x - 1)

∴ h = 1

Let us find f(1)

∵ f(1) = (1)² - 2 = 1 - 2 = -1

∴ f(1) = -1

∴ The remainder is -1

∵ f(1) ≠ 0

∴ x - 1 is not a factor of x² - 2

∴ The binomial is not a factor of the polynomial