- #1
camilus
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if the polynomial [tex]x^3+3x^2+9x+3[/tex] is a factor of [tex]x^4+4x^3+6Px^2+4Qx + R[/tex], what is [tex]R(P+Q)[/tex]?
I didn't do that to solve the problem. But if you want to know if I double-checked the answer, then yes, it works out.camilus said:Did you divide the first polynomial into the second?
then you could get the separate results and set them equal to zero, or you could multiply back and create equations.
camilus said:Thats what I mean. Using long division of polynomials, the coefficients of each can be set equal to zero and resolved. Other than that, you can't multiply back the the (x+1) to the first polynomial and set the coefficients equal to the the coefficients of the second polynomial, and like earlier, just solve for P, Q, and R.
A simple polynomial problem is an algebraic expression that involves only addition, subtraction, and multiplication of constants and variables raised to a non-negative integer power. These problems can be solved by applying the rules of algebra.
To solve a simple polynomial problem, you must first simplify the expression by combining like terms. Then, use the distributive property to remove parentheses. Finally, solve for the variable by isolating it on one side of the equation.
Yes, a simple polynomial problem can have multiple solutions. This is because there can be different values for the variable that satisfy the equation. These solutions can be found by using algebraic techniques such as factoring or the quadratic formula.
The degree of a simple polynomial problem is the highest exponent of the variable in the expression. For example, in the expression 3x^2 + 5x + 2, the degree is 2. The degree is important because it determines the number of solutions a polynomial problem can have.
Simple polynomial problems have many real-life applications, including calculating perimeter and area, determining profit and loss in business, and predicting the growth of populations or investments. They are also used in physics and engineering to model and solve problems involving motion and forces.