I need help in finding the remainder when you divide 5x2 + 4x -40 by x-4..
(5x2 = 5x(2)
I also need to know what is the completely factored form of 4x5 - 256x3
(4x5 = 4x(5) & 256x(3)
I also need the solutions of the equation 1.5x2 - 4.5x = -3
Thank You
To find the remainder when you divide 5x^2 + 4x - 40 by x - 4, you can use the polynomial long division method.
Step 1: Write down the dividend (5x^2 + 4x - 40) and the divisor (x - 4) side by side.
Step 2: Divide the first term of the dividend (5x^2) by the first term of the divisor (x) to get the quotient term (5x).
Step 3: Multiply the divisor (x - 4) by the quotient term (5x) and write it below the dividend.
5x * (x - 4) = 5x^2 - 20x
Step 4: Subtract the result from step 3 from the dividend.
(5x^2 + 4x - 40) - (5x^2 - 20x) = 24x - 40
Step 5: Bring down the next term from the dividend (-40).
Step 6: Divide the new dividend (24x - 40) by the divisor (x - 4) to get the next quotient term.
(24x) / (x) = 24
Step 7: Multiply the divisor (x - 4) by the new quotient term (24) and write it below the new dividend.
24 * (x - 4) = 24x - 96
Step 8: Subtract the result from step 7 from the new dividend.
(24x - 40) - (24x - 96) = 56
Step 9: Since the new dividend (56) is a constant term and there is no more variable term to divide by, the process is complete.
Therefore, when you divide 5x^2 + 4x - 40 by x - 4, the remainder is 56.
Now, for the completely factored form of 4x^5 - 256x^3, you can factor out a common factor of 4x^3.
Step 1: Write down the expression: 4x^5 - 256x^3
Step 2: Factor out the common factor, which is 4x^3.
4x^3 * (x^2 - 64)
Step 3: The expression can be further factored by using the difference of squares formula.
Step 4: Apply the formula, where a = x and b = 8.
(x - 8) * (x + 8)
Therefore, the completely factored form of 4x^5 - 256x^3 is 4x^3 * (x - 8) * (x + 8).
Lastly, to find the solutions of the equation 1.5x^2 - 4.5x = -3, you can start by setting the equation equal to zero.
Step 1: Write down the equation: 1.5x^2 - 4.5x + 3 = 0
Step 2: Simplify the equation by multiplying all terms by 2 to eliminate the decimal.
3x^2 - 9x + 6 = 0
Step 3: Use factoring or the quadratic formula to solve the equation.
Factoring:
(x - 1)(3x - 6) = 0
Setting each factor equal to zero and solving for x:
x - 1 = 0 --> x = 1
3x - 6 = 0 --> x = 2
Therefore, the solutions to the equation 1.5x^2 - 4.5x = -3 are x = 1 and x = 2.