Question

4x^3 -12x^2+ax+b has x-3 as a factor but when it is divided by x+2 has remainder is -75 find a and b​

Answer 1

Answer:

let f(x)=4x^3+ax^2-bx+3 f(x) divided by x-2 leaves remainder 2 f(2)=2 ... How do you find the remainder when it is divided by x + 2? ... p( x) = 4 * (-3)^3 + a * (-3)^2 - b * (-3) + 3 = 3. 4 * (- 27)

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

(4x^3+ax^2 - bx+3) ÷(x - 2)=

By synthetic division method.

( You can also do it by long division method. The synthetic division method is short cut where as long division method is completedly messy)

x - 2=0

=> x=2

2 | (4 )———( a )——- ( -b )——— (3) |

—— (4 )——— (8)———-(16a) ———(32a - 2b+3)

According to the question (32a - 2b +3)=2 —(i)

Similarly when the expression is divided by x+3

-3 | (4)————(a) ———(-b)————-(3)

——(4) ————(-12)———(36–3a) ——(-108+9a+3b+3)=(-105+9a+3b)

According to the question,

(- 105+9a+3b)=3 ———————-(ii)

Solving (i) & (ii) we get

a= - 1 & b= - 30.

Rewrite the equation replacing a & b by -1 & -30 respectively, the equation becomes

(4x^3-x^2+30x+3)÷(x+2) by Synthetic method.

-2 | (4)———-(-1)———(30)——(3)

——-(4) ———(-8)——-(18)——-(-96)

3+(-96)= - 93 is the required REMAINDER □Ans.

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