Question

1. subtract ( 3x^2 - 2x + 7 ) from ( 5x^2 - x + 1 ).

a. ( 8x^2 - 3x + 8 )
b. ( 2x^2 + x - 6 )
c. ( 2x^2 + x + 6 )
d. ( 2x^2 - 3x - 6 )

Explanation:

Step1: Set up subtraction expression

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

Step2: Distribute the negative sign

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

Step3: Combine like terms for $x^2$

$$(5x^2 - 3x^2) = 2x^2$$

Step4: Combine like terms for $x$

$$(-x + 2x) = x$$

Step5: Combine constant terms

$$(1 - 7) = -6$$

Step6: Combine all results

$$2x^2 + x - 6$$

Answer:

b. $2x^{2}+x-6$