Answer:
A
Step-by-step explanation:
plug the domain values in, then order from least to greatest.
The remainder theorem says that dividing a polynomial by leaves a remainder of . Here, , then .
When you divide the given polynomial by x + 4, the remainder is 0. When you divide by x - 3, the remainder is 428.
To divide the polynomial p(x) = x^4 + 6x^3 + 7x^2 − 6x − 8 by x + 4 and x - 3 using the remainder theorem, first you substitute the roots of the divisor into the polynomial.
For x + 4, the root is -4. Substituting -4 into the polynomial yields p(-4) = (-4)^4 + 6*(-4)^3 + 7*(-4)^2 - 6*(-4) - 8 = 0. Thus, the remainder is 0 when dividing by x + 4.
For x - 3, the root is 3. Substituting 3 into the polynomial yields p(3) = (3)^4 + 6*(3)^3 + 7*(3)^2 - 6*(3) - 8 = 428 . Thus, the remainder is 428 when dividing by x - 3.
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Number 2 is the answer
The product of 1/2 multiplied by 1/2 is 1/4, which is less than 1/2. Therefore, when 1/2 is multiplied by 1/2, the result is not greater than 1/2.
When multiplying fractions, we multiply the numerators (the top numbers) to get the new numerator and the denominators (the bottom numbers) to get the new denominator. In this case, when we multiply 1/2 by 1/2, we multiply 1 (numerator) by 1 (numerator) to get 1 as the new numerator and 2 (denominator) by 2 (denominator) to get 4 as the new denominator. So, 1/2 times 1/2 equals 1/4.
When comparing 1/4 and 1/2, we can easily see that 1/4 is less than 1/2. Hence, the product of 1/2 times 1/2 is not greater than 1/2 - it is, in fact, less than 1/2. So, the answer is no.
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