For questions 1-3, simplify the polynomial.
1. 14x^2 + 4 + 3x - 12x^2 - 3 + 11x
2. 3x^2 + 6 - 2x + 5x - 4x^2 + 9
3. 2x^2 + 6x - 7x + 8 - 3x^2 + 1
4. In the expression -7x - 3x^2 + 5, what is the coefficient of x?
Add or subtract.
5. (m^2 - m + 3) + (m - 1)
6. (4x^2 - 2x - 1) - (-3x^3 + 2)
7. Suppose you earned 8t - 3 dollars on Monday and 6t + 5 dollars on Tuesday. What were your total earnings? Simplify your answer.
8. f^2 * f^3
9.100^12/100^8
10. x^16/x^3
11. 4^4 * 4^10
12. 4^4 * 4^44
Write the value of the expression.
13. 2^3/2^3
14. 4^7/4^9
Multiply. Write the result in scientific notation.
15. (8*10^3)(7*10^5)
16. (2.2*10^-3)(4*10^-2)
Simplify the expression.
17. 6t^3 * 6t^3
18. -3(4x + 5)
19. 4k^2(-3k^2 - 4k + 5)
20. (-4x) * 9x^2
21. (6y^2 - 4y) + (7y^2 - 7y)
Sorry, I'm just really having trouble understanding polynomials. I've watched several videos and by now, the concept normally would've clicked, but it's really just not getting through my thick skull.
Number 13 is either a typo or a trick :) Too easy. What is anything divided by itself?
I neeed help I need thee answers
1. Well, first let's organize those terms. We have 14x^2 - 12x^2 + 3x + 11x + 4 - 3. Now let's combine similar terms. So we end up with 2x^2 + 14x + 1.
2. Let's gather those terms again. We have 3x^2 - 4x^2 - 2x + 5x + 6 + 9. Now, let's combine like terms. We get -1x^2 + 3x + 15.
3. Let's gather those terms once more. We have 2x^2 - 3x^2 + 6x - 7x + 8 + 1. Now, let's combine like terms. We end up with -x^2 - x + 9.
4. Ah, the coefficient of x in the expression -7x - 3x^2 + 5 is simply -7. And that's no joke!
5. We have (m^2 - m + 3) + (m - 1). Let's combine the like terms in each set of parentheses first. We get m^2 - m + m - 1 + 3. Now, combining like terms, we have m^2 + 2.
6. Here we have (4x^2 - 2x - 1) - (-3x^3 + 2). Remember, when you subtract a negative, it's the same as adding. So this simplifies to 4x^2 - 2x - 1 + 3x^3 - 2. Now let's combine like terms. We end up with 3x^3 + 4x^2 - 2x - 3.
7. Alright, let's calculate your total earnings! You earned 8t - 3 dollars on Monday and 6t + 5 dollars on Tuesday. To find the total, we simply add these expressions together. So, your total earnings are 8t - 3 + 6t + 5. Combining like terms, we get 14t + 2.
8. So, f^2 * f^3 is the same as f^(2 + 3) which is f^5.
9. Well, 100^12 divided by 100^8 is 100^(12 - 8) which is 100^4. So the answer is 10,000.
10. When you divide x^16 by x^3, you subtract the exponents, so it becomes x^(16 - 3) which simplifies to x^13.
11. Oh, this one is easy! It's just 4^(4 + 10), which gives us 4^14.
12. Now we're reaching some big numbers! It's 4^(4 + 44), which gives us 4^48. That's a rather large number!
13. Here we have 2^3 divided by 2^3. Well, since both the numerator and denominator have the same base of 2, we can simply subtract the exponents. So 2^(3 - 3) gives us 2^0. And let me tell you a secret, any number to the power of 0 is 1!
14. Similarly, we have 4^7 divided by 4^9. Since both have the same base of 4, we subtract the exponents again. So we get 4^(7 - 9) which simplifies to 4^(-2).
15. In scientific notation, we express numbers as a product of a number between 1 and 10 and a power of 10. So, when we multiply (8 * 10^3) by (7 * 10^5), we get 56 * 10^(3 + 5), which is equal to 56 * 10^8.
16. To multiply (2.2 * 10^-3) by (4 * 10^-2), we multiply the numbers and add the exponents. So we get (2.2 * 4) * 10^(-3 + -2), which simplifies to 8.8 * 10^-5.
17. We have 6t^3 multiplied by 6t^3. When we multiply like bases, we add the exponents. So we end up with 6^(3 + 3) * t^(3 + 3), which gives us 6^6 * t^6.
18. We are multiplying -3 by 4x and -3 by 5. So, the expression simplifies to -12x - 15.
19. We have 4k^2 multiplied by -3k^2 and 4k^2 multiplied by 5. So, the expression simplifies to -12k^4 - 16k^3 + 20k^2.
20. Here we have (-4x) multiplied by 9x^2. When we multiply like bases, we add the exponents. So, we are left with -36x^3.
21. Perfect, we have (6y^2 - 4y) + (7y^2 - 7y). Let's combine the like terms within each set of parentheses first. We get 6y^2 - 4y + 7y^2 - 7y. Now, combining like terms, we have 13y^2 - 11y.
Hope that brought a smile to your face!