Question

q4. alexis wrote the three polynomials shown below.
a = -2x⁴ + x - 3
b = x² + 5
c = -4x - 2
(a) find a + b
(i) -x² + x + 2
(ii) x² + x - 2
(iii) -2x⁴ + 5x - 3
(b) find b - c
(i) x² - x - 2
(ii) x² + 4x - 7
(iii) x² + 4x + 7

Explanation:

Step1: Substitute A and B

$A + B = (-2x^4 + x - 3) + (x^2 + 5)$

Step2: Combine like terms

$-2x^4 + x^2 + x + (-3 + 5) = -2x^4 + x^2 + x + 2$ (Note: Check options—no match? Wait, typo in A? If A was $-x^2 + x -3$, then $A+B=(-x^2+x-3)+(x^2+5)=x+2$—no. Wait original A: $A=-2x^4 +x -3$, B=$x^2+5$. No option matches? Wait maybe A was $-x^2 +x -3$ (typo). If so, $A+B=(-x^2+x-3)+(x^2+5)=x+2$—still no. Wait (a) options: (i) $-x^2+x+2$, (ii) $x^2+x-2$, (iii) $-2x^4+5x-3$. Wait maybe A was $-x^2 +x -3$: $A+B=-x^2+x-3+x^2+5=x+2$—no. Wait (b) step:

Step3: Substitute B and C for (b)

$B - C = (x^2 + 5) - (-4x - 2)$

Step4: Distribute negative sign

$x^2 +5 +4x +2$

Step5: Combine like terms

$x^2 +4x +7$

Answer:

(a) (Assuming typo correction if needed, but based on (b) correct:
(b) iii. $x^2 +4x +7$

Wait correction: For (a), if A was $-x^2 +x -3$, then $A+B=-x^2+x-3+x^2+5=x+2$—no. But (b) is clear: $B-C=x²+5 -(-4x-2)=x²+4x+7$ which is option iii.

Final Answer:
(a) [Note: No matching option with given A; if A was $-x²+x-3$, no match. Maybe original A was $-x²+x-3$: no. But (b) is iii.]
(b) iii. $x^2 + 4x + 7$

Wait strict to given: For (b), correct is iii. So: