Sat math ( and ! )
r(x) = 2(x^2-11x+3)+7(x+m)
in the polynomial defined above, m is a constant. if r(x) is divisible by x, what is m?

  m = -6/7

Step-by-step explanation:

The constant term in the sum is ...

  2·3 +7·m = 6+7m

In order for r(x) to be divisible by x, this value must be zero:

  6 + 7m = 0

  6/7 + m = 0 . . . . . divide by 7

  m = -6/7 . . . . . . . . subtract 6/7

Step-by-step explanation:

is constant.

has no remainder. This would mean is a factor of .

By factor theorem if x-c is a factor of r then r(c)=0.

We have that x or x-0 is a factor of r:

By factor theorem if x-0 is a factor of r then r(0)=0.

So let's plug in 0 for x:

Now again we have r(0)=0 since x is a factor of r.

Subtract 6 on both sides:

Divide both sides by 7:

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Another way.

So since is divisible by that means when we divide by we will have no fractions.

So let's do that:

I'm going to get my fractions together.

Distribute the 2 to the terms in the ( ) next to it. Distribute 7 to the terms in the ( ) next to it:

Reorder using commutative property of addition:

Combine like terms ( the fractions too since the denominators are the same):

Again we wanted no fraction.

A fraction is 0 when the numerator is 0.

If we find when 6+7m is 0, then we have found the value of m for which x divides r(x).

6+7m=0

Subtract 6 on both sides:

7m=-6

Divide both sides by 7:

m=-6/7.

step-by-step explanation:

answers available in this download

(pearson%2c%25202012)%2520bbs.pdf& usg=aovvaw1obmtxnfghfgxhx0urh_je

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