Question

20 points! I would really like some help! :) (Question attached below)

Answer 1

Answer:

See below.

Step-by-step explanation:

(a)

To multiply two polynomials, multiply every term of the first polynomial by every term of the second polynomial. Then combine like terms.

$(\dfrac{1}{2}x - \dfrac{1}{4})(5x^2 - 2x + 6) =$

$= \dfrac{1}{2}x \times 5x^2 - \dfrac{1}{2}x \times 2x + \dfrac{1}{2}x \times 6 - \dfrac{1}{4} \times 5x^2 + \dfrac{1}{4} \times 2x - \dfrac{1}{4} \times 6$

$= \dfrac{5}{2}x^3 - x^2 + 3x - \dfrac{5}{4}x^2 + \dfrac{1}{2}x - \dfrac{3}{2}$

$= \dfrac{5}{2}x^3 - \dfrac{9}{4}x^2 + \dfrac{7}{2}x - \dfrac{3}{2}$

(b)

No. Since the binomials are different, the product of two different binomials and the same trinomial will give different results.