Question

what is the product?
$(x - 3)(2x^2 - 5x + 1)$
$2x^3 - 11x^2 + 16x - 3$
$2x^3 - x^2 + 16x - 3$
$2x^3 - 11x^2 + 16x + 3$
$2x^3 - x^2 + 16x + 3$

Explanation:

Step1: Distribute $x$ to the trinomial

$x \cdot 2x^2 + x \cdot (-5x) + x \cdot 1 = 2x^3 - 5x^2 + x$

Step2: Distribute $-3$ to the trinomial

$-3 \cdot 2x^2 + (-3) \cdot (-5x) + (-3) \cdot 1 = -6x^2 + 15x - 3$

Step3: Combine the two results

$2x^3 - 5x^2 + x - 6x^2 + 15x - 3$

Step4: Combine like terms

$2x^3 + (-5x^2 -6x^2) + (x + 15x) - 3 = 2x^3 -11x^2 +16x -3$

Answer:

$2x^3 - 11x^2 + 16x - 3$