The expression for D in factored form - 3x^3 - x^2 - 12x + 14 .You would use the method of polynomial factorization.
Factor out the known factors: Since (x-2) and (x-1) are factors of D(x), we can write:
D(x) = (x-2)(x-1) * Q(x)
where Q(x) is a polynomial of degree 1.
Expand the product:
D(x) = x^2 - 3x + 2 * Q(x)
Substitute the remaining polynomial:
3x^3 - 2x^2 - 15x + 14 = x^2 - 3x + 2 * Q(x)
Solve for Q(x):
3x^3 - x^2 - 12x + 14 = Q(x)
This remaining polynomial can be factored further using various methods, depending on its coefficient structure.
However, the key point is that we have successfully used the known factors to simplify the original expression significantly.
Diagram:
Pros: Diagrams can provide a visual representation of the factored form, especially for quadratic expressions.
Cons: For higher-degree polynomials, diagrams become complex and impractical.
Additionally, diagrams don't offer step-by-step reasoning or guarantee the correctness of the factorization.
Therefore, using a diagram is not suitable for factoring D(x).