April 23, 2014

Homework Help: Algebra

Posted by Tomika on Tuesday, June 26, 2007 at 9:58am.

1. x^3+2x^2+x+12/x+3
2. 45a^6b^10/5a^3b^2

Note that x^3+2x^2+x+12 is zero for
x = -3, therefore

(x^3+2x^2+x+12)/(x+3) has no remainder. You can divide using long division, but this is not the preferred method if you are doing the calculation by hand. If you make an error, you'll usually have to start all over again. The following method is more transparant. We put:

x^3+2x^2+x+12 = (a x^2 + b x + c) (x+3)

Work out the right hand side:

(a x^2 + b x + c) (x+3) =

a x^3 + (3 a + b) x^2 + (c + 3 b)x + 3 c

Equate the coefficients of the powers of x on both sides.

Equating coefficient of x^3 yields:

a = 1 (1)

Equating coefficient of x^2 yields:

3 a + b = 2 (2)

Equating coefficient of x yields:

c + 3 b = 1 (3)

Equating constant term yields:

3 c = 12 (4)

Inserting (1) in (2) gives:

b = -1

(4) implies that c = 4 and we see that (3) is already satisfied. The fact that there is an extra equation that is automatically satisfied has to do with the fact that the remainder is zero. If you write down the equation:

x^3+2x^2+x+12 = (a x^2 + b x + c) (x+q)

for arbitrary q, then this can only be valid if the remainder is zero. If you then proceed as above then you can rearrange the four equations into three equations for a b and c and one that says that q^3+2q^2+q+12 = 0, i.e. that q is a zero of the polynomial and that the remainder is thus zero.

Answer this Question

First Name:
School Subject:

Related Questions

Algebra 1b! - 1. Find the excluded value of x for the polynomomial expression ...
Math--help help help - 1)when a certain polynomial is divided by x - 3, the ...
Algebra - Swimming space. The length of a rectangular swimming pool is 2x-...
Math-helpppppp - 1)when a certain polynomial is divided by x - 3, the quotient ...
algebra - please help with the following problem using the substitution method y...
Algebra - Divide using long division: 6x3 + 19x2 + x 10 divided by 2x -1 ...
Algebra - Hello all - I would like to check my work on 2 problems. Solve by ...
math - hi, i need help with solving this equation for "y" 2x+3y=-2 2x+3y=-2 Get ...
Math - Write an equation in slope-intercept form of the line whose parametric ...
Algebra--Correction? - Solve the absolute value equation. I I will represent ...