You can factor trinomials with the form ax2 + bx + c in one of two ways: (1) factor out a GCF, or (2) find two binomials whose product is that trinomial. When finding the two binomials whose product is a particular trinomial, you work from the factors of the constant term and the factors of the coefficient of the lead term to create a sum or difference that matches the coefficient of the middle term. This technique can be expanded to trinomials that have the same general format but with exponents that are multiples of the basic trinomial.
Here are the types of things you work on in this chapter:
Be aware of the following when factoring quadratic trinomials:
496–499 Factor out the GCF of each.
496. 12x4y2 − 6x3y3 + 21x2y4
497. 70a2b3c + 63a3b2c2 − 21a4bc3
498. 3(x − 4)3 + 6x(x − 4)2 − 9x2(x − 4)
499. 60x5y − 48x6y2 + 36x2y3
500–511 Factor each trinomial into the product of two binomials.
500. x2 − 8x − 20
501. x2 + 10x + 9
502. y2 − 6y − 16
503. z2 + 2z − 48
504. 2x2 + x − 6
505. 3x2 + 5x − 12
506. 9z2 + 24z + 16
507. 16x2 − 40x + 25
508. w2 − 63w − 64
509. 4x2 + 15x − 25
511. 16x2 − 14x − 15
512–519 Factor the quadratic-like expressions into the product of two binomials.
512. x10 − 5x5 + 4
513. y6 − 4y3 − 21
514. y16 − 25
515. 25a4 − 49b10
516. x−8 − 3x−4 − 18
517. x−6 + 5x−3 + 4
518. 5x1/3 − 11x1/6 + 2
519. 6x2/5 − x1/5 − 12
520–535 Completely factor each trinomial.
520. 5z2 + 30z + 45
521. 18x3 + 12x2 + 2x
522. 4y3 − 8y2 − 12y
523. 6x6 + x5 − x4
525. 96y − 48y2 + 6y3
526. w4 − 13w2 + 36
527. x6 − 9x3 + 8
528. 5x2(x + 3)3 + 15x(x + 3)3 − 50(x + 3)3
529. 4x2(x + 1) − 6x(x + 1) − 4(x + 1)
530. a2(x2 − 81) + 13a(x2 − 81) + 22(x2 − 81)
531. 4y2(x3 − 1) + 4y(x3 − 1) −3(x3 − 1)
532. 300y1/4 + 70y1/8 − 150
533. 6y − 6y1/2 − 12
534. 3x−3 − 19x−2 + 20x−1
535. 12x−2 + 5x−3 − 2x−4