Question

plz solve tgis question ​

Answer 1

Answer:

The Remainder Theorem states that when you divide a polynomial p(x) by any factor (x-a); which is not necessarily a factor of the polynomial; you will obtain a new smaller polynomial and a remainder, and this remainder is the value of p(x) at x = a, that is p(a).

Let p(x) = 2x³ + ax² + 3x - 5 and q(x) = x³ + x² - 4x - a and the factor given is g(x) = x - 1, therefore, by remainder theorem, the remainders are p(1) and q(1) respectively and thus,

p(1) = (2 × 1³) + (a × 1²) + (3 × 1) - 5 = (2x 1) + (ax 1) + 3 − 5 = 2+a

2 = a

q(1) = 1³ + 1² − (4 × 1) − a = 1 + 1 – 4- a=-2 - a

Now since it is given that both the polynomials p(x) = 2x³ + ax² + 3x - 5 and q(x) = x³ + x² - 4x - a leave the same remainder when divided by (x - 1), therefore p(1) = q (1) that is:a = -a-2

⇒a+a= -2

⇒ 2a = -2

2 2 ⇒a==

⇒a=-1

Hence, a = -1.