Question

divide using polynomial long division or synthetic division.\\((4x^{3}-8x^{2}+5x - 10)div(x - 2)=square\\)

Explanation:

Step1: Split polynomial terms

Group terms to factor:
$(4x^3 - 8x^2) + (5x - 10)$

Step2: Factor each group

Factor out common terms:
$4x^2(x - 2) + 5(x - 2)$

Step3: Factor out $(x-2)$

Combine factored groups:
$(x - 2)(4x^2 + 5)$

Step4: Cancel common factor

Divide by $(x-2)$:
$\frac{(x - 2)(4x^2 + 5)}{x - 2} = 4x^2 + 5$

Answer:

$4x^2 + 5$