Answer:
a = 1
k = -3
n = -4
l = 12
Step-by-step explanation:
To find the values of A, k, n and l, so that (x² - 4)(x - 3) = ax³ + kx² + nx + l, we can expand the factored expression and compare the coefficients of the corresponding terms on each side of the equation.
Expand the factored expression:
[tex]\begin{aligned}(x^2-4)(x-3)&=x^2(x-3)-4(x-3)\\&=x^3-3x^2-4x+12\end{aligned}[/tex]
Now, we can compare this with the given polynomial ax³ + kx² + nx + l:
[tex]ax^3+kx^2+nx+l=x^3-3x^2-4x+12[/tex]
By comparing the coefficients, we can identify the values:
[tex]a = 1[/tex]
[tex]k = -3[/tex]
[tex]n = -4[/tex]
[tex]l = 12[/tex]
Therefore, the values are a = 1, k = -3, n = -4 and l = 12.
