Question

pls help meeee very urgent​

Answer 1

Qᴜᴇsᴛɪᴏɴ :-

find the value of a , if the division of ax³ + 9x² + 4x - 10 is divided by (x + 3), Leaves Remainder 5 .

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

The remainder theorem : If you divide a polynomial f(x) by (x - h), then the remainder is f(h). The theorem states that our remainder equals f(h). we just need to evaluate the polynomial when x = h to find the remainder.

Sᴏʟᴜᴛɪᴏɴ :-

→ f(x) = ax³ + 9x² + 4x - 10

→ (x + 3) = 0

→ x = (-3)

→ Remainder = 5

So,

→ f(-3) = ax³ + 9x² + 4x - 10 = 5

→ a(-3)³ + 9(-3)² + 4(-3) - 10 = 5

→ (-27a) + 9*9 - 4*3 - 10 = 5

→ (-27a) + 81 - 22 = 5

→ (-27a) = 5 - 59

→ (-27a) = (-54)

→ a = (-54)/(-27)

→ a = 2 (Ans.)

Hence, Value of a will be 2.

Answer 2

Given:

F(x)= ax³+9x²+4x-10

g(x) = x+3

Then,

→x+3=0

→x = -3

by dividing f(x) by x+ 3 it leaves a remainder 5

f(x)=f(-3)= ax³+9x²+4x-10 = 5

→a(-3)³+9(-3)²+4(-3)-10=5

→-27a+9(9)-12-10=5

→-27a+81-12-10=5

→-27a+59 = 5

→-27a = 5- 59

→-27a = -54

→a = -54/-27

→a= 2

Hence the Value of a= 2