Question

Find $k$ if $(x-k)(x+3 k)=x^{2}+4 x-12$.

   Find $k$ if $(x-k)(x+3 k)=x^{2}+4 x-12$.

College Algebra

College Algebra

Michael Sullivan 11th Edition

Chapter 0, Problem 102

Instant Answer

Solved by Expert Willis James

05/21/2021

Step 1

Now, we can compare the coefficients of the left side and the right side of the equation. We have: Show more…

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Find $k$ if $(x-k)(x+3 k)=x^{2}+4 x-12$.

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Key Concepts

Polynomial Expansion

This concept involves multiplying the factors in an expression to form a standard polynomial form. In the context of solving equations, expanding the product allows us to see and compare the coefficients of corresponding terms directly.

Comparing Coefficients

Once both sides of the equation are expressed as standard polynomials, comparing the coefficients of like powers of the variable is used to set up equations. This method helps identify the values of unknown parameters by equating corresponding coefficients on both sides.

Solving Equations

After setting up equations by comparing coefficients, this concept involves using algebraic methods to solve for the unknown variable. It is fundamental in determining the values that satisfy the equation, ensuring that the polynomial identity holds true.

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