The process of factoring binomials and quadratic trinomials is pretty much scripted with the various choices available for each format. When you start factoring expressions with more than three terms, you need different techniques to create the factorization — or to recognize that factors may not even exist.
In this chapter on factoring polynomials, you deal with the following situations:
Here are a few things to keep in mind while you work on the factoring:
536. bc − 3b + 2c − 6
537. x2 − abx + xyz − abyz
538. 2x3 − 3x2 + 2x − 3
539. 2xz2 + 8x − 3z2 − 12
540. n3/2 + 2n − 4n1/2 − 8
541. y5/2 − 3y2 + 2y1/2 − 6
542. 4x − 12 + xy − 3y − xz + 3z
543. kx + 4x + ky + 4y + kz + 4z
544–547 Factor each completely, beginning with grouping.
544. x2y2 + 3x2 − xy2 − 3x − 12y2 − 36
545. 2x4 − 4x2 + 3x3 − 6x + x2 − 2
546. m2n + 3m2 − 25n − 75
547. 4x3 + 16x2 − 25x − 100
548–565 Completely factor each expression.
548. 4x3 − 196x
549. 6x5 − 48x2
551. x5 − 13x3 + 36x
552. 16x4 + 23x2 − 75
553. 4x6 − 4x2
554. z6 − 729
555. y8 − 1
556. 64b5 − 64b3 + b2 − 1
557. 27z5 − 243z3 − 8z2 + 72
558. z8 − 17z4 + 16
559. x5 − 2x4 + x3
560. x4 − 8x2 + 16
561. y−3 − 27y−6
562. (x2 − 1)2(3x + 4)2 + (3x + 4)3(x2 − 1)
563. (y3 + 8)4(y2 − 9)−(y2 − 9)2(y3 + 8)3
564. (z + 1)1/2(z3 − 1)2 −(z3 − 1)(z + 1)3/2
565. 4x6 − 25x4 + 500x3 − 3125x