Question

(6x²+3x+10) by (2x+3)​

Answer 1

Answer:

This is an algebraic test. I will introduce you to the remainder theorem which states that, when a polynomial function, f(x) is divided by a factor x-c, the remainder is f(c). Now let try which factor will give us a remainder of zero(0).

For (x-1): f(1)=1^3 - 6*1^2 + 3*1 +10 =8

for (x+1):f(-1)=(-1)^3–6*(-1)^2+3*(-1)+10=0

Therefore (x+1) is one of the factors.

(x^3–6x^2+3x+10)/(x+1)=x^2–7x+10

An easy way to solve the second quadratic factor is:

look for factors with a product of 10 and a sum of -7. in this case it will be (-5) and (-2)

x^2–2x-5x+10=0

x(x-2)-5(x-2)=0

(x-5)(x-2)=0

Therefore we know have all the factors:

(x+1)(x-5)(x-2)=x^3–6x^2+3x+10

thank you guys!

Answer 2

Answer:

3x -3

and remainder is 19