Question

what do you get when you subtract $-2x^3 + 3x^2 - x + 4$ from $x^3 - 4x^2 + 5x - 1$?
a. $3x^3 - 7x^2 + 6x - 5$
b. $-3x^3 + 7x^2 - 4x + 5$
c. $-x^3 - x^2 + 4x - 3$
d. $x^3 + x^2 + 6x + 3$

Explanation:

Step1: Write the subtraction expression

$(x^3 -4x^2 +5x -1) - (-2x^3 +3x^2 -x +4)$

Step2: Distribute the negative sign

$x^3 -4x^2 +5x -1 +2x^3 -3x^2 +x -4$

Step3: Combine like terms for $x^3$

$x^3 +2x^3 = 3x^3$

Step4: Combine like terms for $x^2$

$-4x^2 -3x^2 = -7x^2$

Step5: Combine like terms for $x$

$5x +x = 6x$

Step6: Combine constant terms

$-1 -4 = -5$

Step7: Assemble the final polynomial

$3x^3 -7x^2 +6x -5$

Answer:

a. $3x^3 -7x^2 +6x -5$