Determine if the expression 3, r, to the power 5 , plus, 8, r, cubed3r 5 +8r 3 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The given expression can be written as 3r^5 + 8r^3.
A polynomial is an algebraic expression with variables and coefficients, where the exponents of the variables are non-negative integers.
In this case, 3r^5 and 8r^3 have non-negative integer exponents, which makes the expression a polynomial.
The type of the polynomial is a "monomial" because it consists of a single term.
The degree of the polynomial is determined by the highest exponent of the variable. In this case, the highest exponent is 5, so the degree of the polynomial is 5.
Perform the operation.
left bracket, minus, 7, x, squared, plus, 3, x, minus, 10, right bracket, plus, left bracket, minus, 6, x, squared, minus, 10, x, plus, 3, right bracket
(−7x
2
+3x−10)+(−6x
2
−10x+3)
To perform the given operation, we need to combine like terms.
(-7x^2 + 3x - 10) + (-6x^2 - 10x + 3)
Combining like terms, we add the coefficients of the terms with the same variable and exponent.
(-7x^2 - 6x^2) + (3x - 10x) + (-10 + 3)
-13x^2 - 7x - 7
Therefore, the simplified expression is -13x^2 - 7x - 7.
Find the sum of minus, 4, x, squared, minus, 8, x−4x
2
−8x and minus, x, squared, minus, 6, x, plus, 8−x
2
−6x+8.
To find the sum of the two given expressions, we need to combine like terms.
(-4x^2 - 8x) + (-x^2 - 6x + 8)
Combining like terms, we add the coefficients of the terms with the same variable and exponent.
(-4x^2 - x^2) + (-8x - 6x) + 8
-5x^2 - 14x + 8
Therefore, the simplified expression is -5x^2 - 14x + 8.
Perform the operation.
left bracket, 2, x, squared, minus, 4, right bracket, minus, left bracket, minus, x, squared, plus, 3, x, minus, 6, right bracket
(2x
2
−4)−(−x
2
+3x−6)
To perform the given operation, we need to distribute the negative sign to all terms inside the second set of parentheses.
(2x^2 - 4) - (-x^2 + 3x - 6)
Removing the parentheses:
2x^2 - 4 + x^2 - 3x + 6
Combining like terms, we add the coefficients of the terms with the same variable and exponent.
(2x^2 + x^2) + (-3x) + (-4 + 6)
3x^2 - 3x + 2
Therefore, the simplified expression is 3x^2 - 3x + 2.
Subtract x, minus, 4x−4 from minus, 8, x, squared, minus, 8−8x
2
−8.
To subtract the expression x - (4x - 4) from the expression -8x^2 - (8 - 8x):
First, let's simplify both expressions:
-8x^2 - (8 - 8x) = -8x^2 - 8 + 8x = -8x^2 + 8x - 8
x - (4x - 4) = x - 4x + 4 = -3x + 4
Now, we can subtract the second expression from the first:
-8x^2 + 8x - 8 - (-3x + 4) = -8x^2 + 8x - 8 + 3x - 4 = -8x^2 + 11x - 12
Therefore, the simplified expression is -8x^2 + 11x - 12.