Find the value by substituting the given value of x into the polynomial and simplifying.

Question

P(x) = 5x³ + 2x² + x − 1; P(−2)

P(−2) =

Then find the value by performing long division and finding the remainder.

Answer 1

Answer 2

P(x) = 5x³ + 2x² + x − 1

P(−2) = 5(-2)³ + 2 (2)² + (-2) -1

=-8*5 + 2(4) -2-1

= -40 +8 -3

= -35

Long division

Since p(-2) , we use X+2

5x³ + 2x² + x − 1

x+2

X+2 √5x³ + 2x² + x − 1

5x³ + 10x² ←multiply (x+2) by 5x²

-8x² +x ←subtracted

-8x -16x ←multiply (x+2) by -8x

17x -1 ←subtracted

17x + 34 ←multiply (x+2) by 17

-35 ←subtracted

We get the same answer of -35

Answer 3

5x^3+2x^2 +x -1

f(-2) = 5(-2)^3 +2(-2)^2-2 -1= --40+8-3=-35

with long divsion (5x^3 +2x^+x-1)/(x+2)= 5x^2 -8x +17 with remainder=-35

but that means, replacing x by -2, as (5(-2)^3+2(-2)^2 -2+1)/(-1+2)=-27/0= undefined

but you can't divide by zero

Answer 4

P(x) = 5x³ + 2x² + x - 1

P(-2) = -40 + 8 - 2 - 1 = -35

By the Remaider Theorem, if P(x) is divided by x - (-2), then the remainder will be the same as P(-2).