Question 1177973: Find the value of k if (x^3-x^2-5x-2)(x^4+x^3+kx^2-5x+2)=x^7-4x^5-14x^4-5x^3+19x^2-4. Found 2 solutions by MathLover1, greenestamps:Answer by MathLover1(20849) (Show Source):
The answer can be obtained with FAR less work than shown by the other tutor....
In the equation, k is the coefficient of the x^2 term. So look at ANY one coefficient in the product of a term which is x^2 or a higher power of x.
Example: The coefficient of the x^2 term in the product is 19. That coefficient comes from (1) the constant term in the first expression times the x^2 term in the second, (2) the product of the linear terms in the two expressions, and (3) the x^2 term in the first expression and the constant term in the second:
ANSWER: k=2
I could have used any other coefficient of the product of a term with degree 2 or higher.
Second example, using the coefficient of the x^4 term in the product:
