SOLUTION: hi i am a tenth grade student needing help in algebra 2. my directions say Use synthetic division and the remainder theorem to find P(a) the problem is {{{ P(x)= x^3+7x^2+4x}}

Question 230380: hi i am a tenth grade student needing help in algebra 2. my directions say Use synthetic division and the remainder theorem to find P(a)

the problem is ;a=-2
Found 2 solutions by user_dude2008, jsmallt9:
Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!

-2 | 1 7 4 0 | ---------------------

-2 | 1 7 4 0 | --------------------- 1

-2 | 1 7 4 0 | -2 --------------------- 1 5

-2 | 1 7 4 0 | -2 -10 12 --------------------- 1 5 -6 12

Answer: P(a)=12
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
for P(a) we will divide P(x) by x-a using synthetic division. For a = 2:

2 | 1 7 4 0 --- 2 18 44 --------------- 1 9 22 44

Since our remainder is 44, P(2) = 44.

To understand why this works, let's think about division in general.
Let P(x) = any polynomial function
Let (x-a) = the divisor
Let Q(x) = the quotient you get from dividing P(x) by (x-a)
Let R/(x-a) = the remainder you get from dividing P(x) by (x-a). (Note: With a divisor like (x-a) R will just be some number. There will be no x's in the remainder.)
In other words:

Let's multiply both sides by (x-a):

On the right side we need to use the Distributive Property:

Now we can cancel out some (x-a)'s:

leaving:

Therefore

Since (a-a) is zero and zero times anything is zero and zero + R is R:

This is why the remainder, after dividing a polynomial, P(x), by (x-a) is the value of P(a). And synthetic division is a quick, simple, compact way to do this type of division.
RELATED QUESTIONS
hi, i need some help on this please. use synthetic division to find the remainder when... (answered by jim_thompson5910)
Use synthetic division for each, write the quotient and remainder: (2x^4-3x^3+ix^2-x-5i) (answered by midwood_trail)
Hi I Im the 7th grade and im doing Pre Algebra homework.and i just cant seem to figure... (answered by jim_thompson5910,Earlsdon,drj)
I need help with this question Use synthetic division to find the remainder (x3-3x+10 (answered by jim_thompson5910)
Can any help me with this problem? I am supposed to use synthetic division to find the... (answered by Fombitz)
this problem says use synthetic division to divide (3x^3 - 7x^2 - 22x + 8) by (x-4) I... (answered by stanbon)
I am needing some help please. My son needs help with this one. Use a polynomial long (answered by jsmallt9)
Hi im in 9th grade, and my grade in algebra is a D. I reallly need help... (answered by robertb)
Please help with this problem i have a test tonite Use synthetic division and the... (answered by stanbon)