Factor by grouping

Answer Key - Grade 9 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Noah pairs the terms of xy − 4x + 5y − 20 to find a shared bracket. Which is it factored?

   • (x + 5)(y − 4)
   • x(y − 4) + 5(y − 4)
   • (y − 4)(5x)
   • (x − 4)(y + 5)
2. 2.

   Pia draws xy + 6x − 3y − 18 as two rectangles with a shared side. Which is it factored?

   • (y + 6)(−3x)
   • x(y + 6) − 3(y + 6)
   • (x − 3)(y + 6)
   • (x + 6)(y − 3)
3. 3.

   Ren checks four answers for 2xy + 10x + 3y + 15. Which one is it factored?

   • (2x + 3)(y + 5)
   • (y + 5)(6x)
   • 2x(y + 5) + 3(y + 5)
   • (2x + 5)(y + 3)
4. 4.

   Tala sees that 3x³ − 8 + 12x² − 2x will not group in this order. Reordered and grouped, it is (x + ▢)(3x² − 2). What number goes in the box?

   4
5. 5.

   Zee has to move the terms of 2x³ − 15 + 10x² − 3x before grouping. Grouped, it is (x + ▢)(2x² − 3). What number goes in the box?

   5
6. 6.

   Ari reorders 5x³ − 12 + 30x² − 2x so pairs share a factor. Factored, it is (x + ▢)(5x² − 2). What number goes in the box?

   6
7. 7.

   Esme groups x³ + 3x² + 4x + 6 as x²(x + 3) + 2(2x + 3). What does this grouping show?

   • It factors as (x + 3)(x² + 2).
   • It is already factored, since each pair has been factored on its own.
   • The brackets differ, so this grouping does not factor it.
   • It factors as (2x + 3)(x² + 2).
8. 8.

   Jun tries grouping x³ + 5x² + 3x + 9 and gets x²(x + 5) + 3(x + 3). What does this show?

   • The brackets differ, so this grouping does not factor it.
   • It factors as (x + 3)(x² + 3).
   • It is already factored, because each pair has its own common factor.
   • It factors as (x + 5)(x² + 3).
9. 9.

   Kira draws 2x²(x + 2) + 3(x + 3) for 2x³ + 4x² + 3x + 9 as two rectangles. What does this grouping show?

   • It is already factored, since each pair shows a common factor.
   • It factors as (x + 2)(2x² + 3).
   • It factors as (x + 3)(2x² + 3).
   • The brackets differ, so this grouping does not factor it.
10. 10.

    Luz writes x³ − 2x² + 5x − 15 = x²(x − 2) + 5(x − 3). What does this grouping show?

    • It factors as (x − 2)(x² + 5).
    • The brackets differ, so this grouping does not factor it.
    • It factors as (x − 3)(x² + 5).
    • It is already factored.