Question

q3.
a) multiply and combine like terms to determine the product of these polynomials.
(2x²−1) (x + 3)
(i) 2x² + 6x − 3
(ii) 2x³ + 6x² − x − 3
(iii) 2x + 3

b) multiply and combine like terms to determine the product of these polynomials.
(3x³ + 4) (x + 1)
(i) 3x⁴ + 3x³ + 4x + 1
(ii) 2x² + 6x − 3
(iii) 3x⁴ − 3x³ − 4x − 1

Explanation:

Step1: Apply distributive property

$(2x^2 - 1)(x + 3) = 2x^2(x) + 2x^2(3) - 1(x) - 1(3)$

Step2: Calculate each term

$= 2x^3 + 6x^2 - x - 3$

Step3: Match with options

Result matches option (ii)

Step4: Apply distributive property

$(3x^3 + 4)(x + 1) = 3x^3(x) + 3x^3(1) + 4(x) + 4(1)$

Step5: Calculate each term

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

Step6: Check options (typo note)

Assuming option (i) has a typo (last term 4 instead of 1), it is the closest match.

Answer:

a) (ii) $2x^3 + 6x^2 - x - 3$
b) (i) $3x^4 + 3x^3 + 4x + 1$ (assuming typo in last term)