Question

1. find the result of subtracting (-3x^{2}+5x - 7) from (x^{2}-2x + 1).

a. (4x^{2}+3x - 6)
b. (-4x^{2}+7x - 8)
c. (4x^{2}-7x + 8)
d. (4x^{2}-7x - 8)

Explanation:

Step1: Write the subtraction expression

$(x^2 - 2x + 1) - (-3x^2 + 5x - 7)$

Step2: Distribute the negative sign

$x^2 - 2x + 1 + 3x^2 - 5x + 7$

Step3: Combine like terms for $x^2$

$x^2 + 3x^2 = 4x^2$

Step4: Combine like terms for $x$

$-2x - 5x = -7x$

Step5: Combine constant terms

$1 + 7 = 8$

Step6: Assemble the final polynomial

$4x^2 - 7x + 8$

Answer:

c. $4x^2 - 7x + 8$