1.
(-x^{3} + 3x^{2} + 3) + (3x^{2} + x + 4)
A. -x^{3} + 6x^{2} + x + 7
B. -x^{3} + 9x^{2} + x + 7
C. 2x^{6} + x + 7 D. 2x^{5} - x + 7
Correct Answer
A. A
Explanation
The given expression is a sum of two polynomials. By combining like terms, we can simplify the expression to -x^3 + 6x^2 + x + 7. This matches option A.
2.
(2x^{7} + 5x + 4) + (5x^{9} + 8x)
A. 5x^{9} + 2x^{7} + 13x + 4
B. 5x^{9} + 7x^{7} + 13x + 4
C. 7x^{9} + 13x + 4 D. 7x^{16} + 13x + 4
Correct Answer
A. A
Explanation
The given expression is (2x7 + 5x + 4) + (5x9 + 8x). By simplifying the expression, we can combine like terms to get 5x9 + 2x7 + 13x + 4. Therefore, the correct answer is A.
3.
(3x^{6} + 4x + 3) + (3x^{8} + 6x)
A. 6x^{14} + 4x + 3
B. 3x^{8} + 10x^{7} + 13x + 4
C. 3x^{8} + 3x^{6} + 10x + 3 D. 3x^{8} + x^{6} + 4x + 3
Correct Answer
C. C
Explanation
The given expression is a sum of two polynomials. To simplify it, we combine like terms by adding the coefficients of the same degree variables. In the first polynomial, we have 3x^6 and in the second polynomial, we have 3x^8. So the sum of these two terms is 3x^8 + 3x^6. Similarly, we add the coefficients of x terms, which gives us 10x. Finally, we add the constant terms, which gives us 3. Therefore, the simplified expression is 3x^8 + 3x^6 + 10x + 3, which matches option C.
4.
(10x^{2} + 3x + 5) + (2x^{3} + 6x + 5)
A. 12x^{5} + 3x + 10
B. 10x^{3} + 2x^{2} + 10
C. 2x^{3} + 10x^{2} + 9x + 10 D. 2x^{3} + 12x^{2} + 9x + 10
Correct Answer
C. C
Explanation
The given expression is a sum of two polynomials. To simplify the expression, we need to combine like terms. By adding the coefficients of the same degree terms, we get the resulting polynomial. In this case, by adding the coefficients of the x^3 terms, we get 2x^3. By adding the coefficients of the x^2 terms, we get 10x^2. By adding the coefficients of the x terms, we get 9x. Finally, by adding the constant terms, we get 10. Therefore, the correct answer is C.
5.
(8x^{8} + 8x^{7} + 9) - (3x^{7} + 2x + 5)
A. 8x^{8} + 11x^{7} - 2x + 4
B. 8x^{8} + 5x^{7} - 2x + 4
C. 11x^{15} + 5x^{8} - 2x + 4 D. 5x^{8} + 6x^{7} - 14
Correct Answer
B. B
Explanation
The given expression can be simplified by combining like terms. The terms 8x8 and 8x7 cannot be simplified further, so they remain the same. The terms 9, 3x7, 2x, and 5 can be combined to get -3x7 + 2x + 4. Therefore, the simplified expression is 8x8 + 8x7 + 9 - (3x7 + 2x + 5) = 8x8 + 8x7 + 9 - 3x7 - 2x - 5 = 8x8 + 5x7 - 2x + 4. Hence, the correct answer is B.
6.
(9x^{8} + 8x^{7} + 9) - (6x^{7} + 2x + 2)
A. 9x^{15} + 3x^{7} + 7
B. 3x^{8} + 2x^{7}- 2x + 7
C. 9x^{8} + 2x^{7} - 2x + 7 D. 11x^{8} + 10x^{7} + 7
Correct Answer
C. C
Explanation
The given expression can be simplified as follows: (9x8 + 8x7 + 9) - (6x7 + 2x + 2).
Simplifying the expression within the brackets first, we get: 72x + 56x + 9 - 42x - 2x - 2.
Combining like terms, we get: 86x + 7.
Therefore, the correct answer is C: 9x8 + 2x7 - 2x + 7.
7.
(2x^{7} + 7x^{4} + 6) - (2x^{4} - x)
A. 2x^{7} + 9x^{4} - x + 6
B. 4x^{11} + 6x^{3} +6
C. 2x^{7} + 5x^{4} + x + 6 D. 6x^{3} + 6
Correct Answer
C. C
Explanation
The given expression involves multiplication and subtraction. To simplify it, we need to apply the order of operations, which states that multiplication should be done before subtraction. First, we evaluate the multiplication terms: 2x7 = 14, 7x4 = 28, 2x4 = 8. Then, we substitute these values back into the expression: (14 + 28 + 6) - (8 - x). Simplifying further, we have 48 + 6 - 8 + x. Combining like terms, we get 54 - 8 + x. Finally, we simplify the expression to 46 + x. The correct answer, option C, matches this simplified expression.
8.
(3x^{7} + 8x^{4} + 7) - (x^{4} - 2x)
A. 7x^{4} - x + 7x
B. 3x^{11} + 7x^{3} + 5x
C. 3x^{7} + 7x^{4} + 2x + 7 D. 2x^{7} + 6x^{3} + 6
Correct Answer
C. C
Explanation
The given expression is (3x7 + 8x4 + 7) - (x4 - 2x). Simplifying this expression, we get 21x + 32x + 7 - x4 + 2x. Rearranging the terms, we get -x4 + 55x + 7. Comparing this with the options, we can see that option C, 3x7 + 7x4 + 2x + 7, matches the simplified expression. Therefore, the correct answer is C.
9.
10x^{8} + 11x^{6} - 2x + 5 - (8x^{8} + 6x^{7} - 5)
A. 2x^{0} + 5x^{1} - 2x
B. 2x^{8} - 6x^{7} + 11x^{6} - 2x + 10
C. 18x^{8} -17x^{7} + x^{6} - 2x + 10 D. 2x^{8} - 6x^{7} + 9x^{6} - x + 10
Correct Answer
B. B
Explanation
The given expression is simplified by subtracting the terms inside the parentheses from the terms outside the parentheses. This results in the following expression: 10x8 + 11x6 - 2x + 5 - 8x8 - 6x7 + 5. Simplifying further, we combine like terms to get: 2x8 - 6x7 + 11x6 - 2x + 10. Therefore, the correct answer is option B.
10.
(-2x^{3} + 4x^{2} + 6) + (2x^{2} + 6x + 3) A. -2x^{5} + 10x^{2} + 6x + 9 B. -x^{6} + 6x^{2} + 12x + 9 C. -2x^{3} + 6x^{2} + 6x + 9 D. -2x^{3} + 6x + 9
Correct Answer
C. C
Explanation
The given expression is a sum of two polynomials. When we combine like terms, we get -2x^3 + 6x^2 + 6x + 9. Therefore, the correct answer is C.