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kbenitez90
11.10.2020 •
Mathematics
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.
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Ответ:
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
Dividend ⇒ the term before the division signDivisor ⇒ the term after the division signQuotient ⇒ the answerRemainder ⇒ 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
Ответ:
the correct answer is 12 hope this helps :D