Algebra 1 Common Core Student Edition, Grade 8-9

9 Lesso n Ch eck

Do y o u k n o w H OW?

Factor each expression. Check your answer.

1. x2 + 7x + 12


2. r2 - 13r + 42


3. p2 + 3p - 40


4. a2 + 12 ab + 32 b2


5. The area of a rectangle is given by th e trinom ial
   n2 - 3n - 28. W hat are th e possible dim ensions of
   th e rectangle? Use factoring.

Do yo u UN DERSTAN D? ( f f l lPRACTICES

Tell whether the sum of the factors of the constant

term should be positive or negative when you factor

the trinomial.

6. s2 + s - 30


7. w2 + 11 w+ 18


8. x2 20


9. Reasoning U nder w h at circum stances should you
   look at pairs of negative factors of th e co n stan t term
   w h en factoring a trinom ial of th e form x2 + bx + c?

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses

^ Practice Complete.

10. k2 + 5k + 6 = {k + 2){k +■)


11. t2 — lOt + 24 = (t - 4)(t -■)

Factor each expression. Check your answer.

14. y2 + 6y+ 5 15. t2+10f+16


15. n2 — \5n + 56 18. r2 - U r + 2 4

Complete.

20. q2 + 3q - 54 = {q - 6 ){q +■)


21. n2 - 5n - 50 = {n + 5 ){n -# )

Factor each expression. Check your answer.

24. r2 + 6r - 27 25. w2 ~ 7 w ~ 8
    27. x 2 + 5x - 6 28. v2 + 5v - 36

MATHEMATICAL

PRACTICES

See Problems 1 and 2.

11. x2 - 7x + 10 = (x - 5)(x -■)


12. v2 + I2 v + 20 = ( v + 10)(y +■)
    16. x 2 + 15x + 56
    19. q2 — 8q + 12

See Problem 3.

21. z 2 — 2z - 48 = (z - 8)(z + ■)

23. y2 + 8y - 9 = (y + 9)(y -■)
    26. z2 + 2z — 8
    29. n2 — 3 n — 10


24. Carpentry The area of a rectangular desk is given by th e trinom ial d 2 - 7d - 18. ^ e e Problem 4.
    W hat are th e possible dim ensions of th e desk? Use factoring.


25. Design The area of a rectangular rug is given by th e trinom ial r2 - 3r — 4. W hat are
    th e possible dim ensions of th e rug? Use factoring.

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