Question

(x-4) (2x^4-3x^2-18x+a)​

Answer 1

Answer:

(x-4) (2x^4-3x^2-18x+a)​

if we multiply this equtions then

2x^5-3x^3-18x^2+ax-8x^4+12x^2+72-4a

-6x^2+2x^5-3x^3+ax-8x^4+72-4a

Answer 2

Answer:

a = -392

Note:

★ Remainder theorem : If a polynomial p(x) is divided by (x - a) , then the remainder is given as , R = p(a).

★ Factor theorem : i) If (x - a) is a factor of the polynomial p(x) , then the remainder obtained on dividing p(x) by (x - a) is zero , ie ; R = p(a) = 0.

ii) If the remainder obtained on dividing the polynomial p(x) by (x - a) is zero , ie ; if p(a) = 0 , then (x - a) is a factor of p(x).

Solution:

Let the given polynomial be p(x) .

Thus,

p(x) = 2x² - 3x² - 18x + a

Also,

It is given that , (x - 4) is a factor of the given polynomial p(x).

Thus,

According to the factor theorem , the remainder obtained on dividing p(x) by (x - 4) must be zero .

Thus,

=> R = 0

=> p(4) = 0

=> 2•(4)⁴ - 3•(4)² - 18•4 + a = 0

=> 512 - 48 - 72 + a = 0

=> 392 + a = 0

=> a = -392

Hence,

Required value of a is (-392) .