What are the coefficients in the polynomial 4x² + 3x − 3?
A.) 4, -3, -3
B.) 4, 3
C.) 4, 3, 3
D.) -4, -3
The coefficients in a polynomial are the numbers in front of the variables (in this case, x) raised to various powers. So the coefficients in 4x² + 3x − 3 are 4, 3, and -3.
Answer: A) 4, -3, -3
Add or subtract.
(m2 – m + 3) + (m – 1)
First, we need to distribute the addition sign to every term in the second parentheses:
(m2 – m + 3) + (m – 1) =
m2 – m + 3 + m – 1
Now we can combine like terms (the -m and +m cancel out) and simplify:
m2 + 2
Answer: m2 + 2
Add or subtract.
(7x2 – x – 2) – (–6x3 + 3)
Remember that subtracting a negative is the same as adding a positive. So, we can rewrite this expression as:
7x2 - x - 2 + 6x3 - 3
Then, we can rearrange the terms and combine like terms:
6x3 + 7x2 - x - 5
Answer: 6x3 + 7x2 - x - 5
144^14 divided by 144^2
When dividing exponential expressions with the same base, we can subtract the exponents.
So in this case:
144^14 ÷ 144^2 = 144^(14-2) = 144^12
Therefore,
144^14 ÷ 144^2 = 144^12
x^16 divided by x^3
When dividing exponential expressions with the same base, we can subtract the exponents.
So in this case:
x^16 ÷ x^3 = x^(16-3) = x^13
Therefore,
x^16 ÷ x^3 = x^13
Which of the following expressions is true?
A. 43 • 44 = 412
B. 52 • 53 > 55
C. 32 • 35 < 38
D. 52 • 54 = 58
We can evaluate each of the expressions to determine which one is true.
A. 43 • 44 = 1892 (not equal to 412)
B. 52 • 53 = 2756, 55 = 3025 (true statement)
C. 32 • 35 = 1120, 38 = 1444 (true statement)
D. 52 • 54 = 2808, 58 = 14884 (not equal)
Therefore, the true statement is:
B. 52 • 53 > 55
Which of the following expressions is true?
A. 8^3 • 8^2 < 8^4
B. 4^4 • 4^4 = 4^16
C. 2^2 • 2^6 < 2^8
D. 3^3 • 3^3 > 3^5
We can evaluate each of the expressions to determine which one is true.
A. 8^3 • 8^2 = 8^5, 8^4 = 4096 (true statement)
B. 4^4 • 4^4 = 4^8, 4^16 = 4294967296 (not equal)
C. 2^2 • 2^6 = 2^8, 2^8 = 256 (not equal)
D. 3^3 • 3^3 = 3^6, 3^5 = 243 (not equal)
Therefore, the true statement is:
A. 8^3 • 8^2 < 8^4
Which of the following expressions is true?
A. 83 • 82 < 84
B. 44 • 44 = 416
C. 22 • 26 < 28
D. 33 • 33 > 35
We can evaluate each of the expressions to determine which one is true.
A. 83 • 82 = 5444, 84 = 4096 (not equal)
B. 44 • 44 = 1936, 416 = 16777216 (not equal)
C. 22 • 26 = 52, 28 = 256 (true statement)
D. 33 • 33 = 1089, 35 = 243 (not equal)
Therefore, the true statement is:
C. 22 • 26 < 28
Which of the following expressions is true?
A. 4^3 • 4^4 = 4^12
B. 5^2 • 5^3 > 5^5
C. 3^2 • 3^5 < 3^8
D. 5^2 • 5^4 = 5^8
We can evaluate each of the expressions to determine which one is true.
A. 4^3 • 4^4 = 4^7, 4^12 = 16777216 (not equal)
B. 5^2 • 5^3 = 125^2, 5^5 = 3125 (true statement)
C. 3^2 • 3^5 = 3^7, 3^8 = 6561 (true statement)
D. 5^2 • 5^4 = 5^6, 5^8 = 390625 (not equal)
Therefore, the true statements are:
B. 5^2 • 5^3 > 5^5
C. 3^2 • 3^5 < 3^8
3^4 divided by 3^4
When dividing exponential expressions with the same base, we can subtract the exponents. So in this case:
3^4 ÷ 3^4 = 3^(4-4) = 3^0
But any non-zero number raised to the power 0 equals 1, so:
3^4 ÷ 3^4 = 1
4^7 divided by 4^9
When dividing exponential expressions with the same base, we can subtract the exponents. So in this case:
4^7 ÷ 4^9 = 4^(7-9) = 4^(-2)
But any non-zero number raised to a negative exponent is equal to the reciprocal of that number raised to the positive exponent. So:
4^(-2) = 1/4^2 = 1/16
Therefore:
4^7 ÷ 4^9 = 1/16
Multiply. Write the result in scientific notation.
(1.4 • 101)(8 • 104)
When multiplying numbers in scientific notation, we can multiply their coefficients and add their exponents.
(1.4 • 10^1)(8 • 10^4) = (1.4 * 8) * 10^(1+4) = 11.2 * 10^5
Since 11.2 is between 1 and 10, we can write the final answer in scientific notation by shifting the decimal point to get a coefficient between 1 and 10.
11.2 * 10^5 = 1.12 * 10^6
Therefore,
(1.4 • 10^1)(8 • 10^4) = 1.12 • 10^6
(1.4 • 101)(8 • 104)
To multiply these two numbers, we can first multiply their coefficients to get:
1.4 * 8 = 11.2
Then we can multiply their powers of 10:
10^1 * 10^4 = 10^(1+4) = 10^5
Putting it all together, we get:
(1.4 • 10^1) * (8 • 10^4) = 11.2 • 10^5
We can also write this in scientific notation by shifting the decimal point to get a coefficient between 1 and 10:
(1.4 • 10^1) * (8 • 10^4) = 1.12 • 10^6
Therefore, the multiplication of (1.4 • 10^1) and (8 • 10^4) is equal to 1.12 • 10^6.
(1.7 ∙ 10–4)(5 ∙ 10–5)
When multiplying numbers in scientific notation, we can multiply their coefficients and add their exponents.
(1.7 ∙ 10–4)(5 ∙ 10–5) = (1.7 * 5) * 10^(-4-5) = 8.5 * 10^(-9)
Therefore,
(1.7 ∙ 10–4)(5 ∙ 10–5) = 8.5 * 10^(-9)
Simplify the expression.
7t4 ∙ 7t4
When multiplying two terms with the same base, we can add their exponents.
So in this case:
7t^4 ∙ 7t^4 = 7^1 ∙ t^(4+4) = 49t^8
Therefore,
7t^4 ∙ 7t^4 = 49t^8
Simplify the expression.
–x(7x – 8)
We can use the distributive property of multiplication over addition or subtraction to simplify this expression:
-x(7x – 8) = -x * 7x + (-x) * (-8)
= -7x^2 + 8x
Therefore,
-x(7x – 8) = -7x^2 + 8x
Simplify the expression.
3k2(–2k2 – 4k + 7)
Again, using the distributive property of multiplication, we can simplify this expression:
3k^2(–2k^2 – 4k + 7) = -6k^4 - 12k^3 + 21k^2
Therefore,
3k^2(–2k^2 – 4k + 7) = -6k^4 - 12k^3 + 21k^2
Simplify the expression.
(2k + 3)(k – 1)
We can use the distributive property of multiplication to simplify this expression:
(2k + 3)(k – 1) = 2k^2 - 2k + 3k - 3
= 2k^2 + k - 3
Therefore,
(2k + 3)(k – 1) = 2k^2 + k - 3
Simplify the expression.
(–y + 4)(2y – 1)
We can use the distributive property of multiplication to simplify this expression:
(–y + 4)(2y – 1) = -2y^2 + y + 8y - 4
= -2y^2 + 9y - 4
Therefore,
(–y + 4)(2y – 1) = -2y^2 + 9y - 4