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1001 Algebra II Practice Problems For Dummies
book

1001 Algebra II Practice Problems For Dummies

by Mary Jane Sterling
June 2013
Beginner content levelBeginner
504 pages
9h 8m
English
For Dummies
Content preview from 1001 Algebra II Practice Problems For Dummies

376.    ( x + 4) 2 ( x – 6)

There is only one possible positive real root, so try for a negative root first.

9781118446614-eq180901.eps

Because –4 is a root, (x + 4) is a factor. Writing the coefficients in the bottom row in the corresponding trinomial, you have

x 3 + 2x 2 – 32x – 96 = (x + 4)(x 2 – 2x – 24)

Now factor the quadratic trinomial.

= (x + 4)(x + 4)(x – 6)

The solution x = –4 is a double root, so you can write the factorization as (x + 4)2(x – 6).

377.    ( x – 1)( x + 2)( x + 5)( x – 3)

There are two or no possible positive real roots, so there’s no advantage to trying one type of root or the other. But, trying a positive number first, you have

9781118446614-eq180902.eps

Now, using the coefficients in the bottom row, try a negative number (because you now have two negative and one positive remaining):

9781118446614-eq180903.eps

Because 1 and –2 are roots, (x – 1) and (x + 2) are factors. Writing the coefficients in the bottom row in the corresponding trinomial, you have

x 4 + 3x 3 – 15x 2 – 19x + 30

= (x – 1)(x + 2)(x 2 + 2x – 15)

Now factor the quadratic trinomial.

= (x – 1)(x + 2)(x + 5)(x – 3)

378.    ( x + 2)( x + 3)( x – 1)( x + 4)

There is only one possible positive real root, so try for a negative root first.

Now, ...

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