Extra-Review ER3 Algebra: Factoring

1.    Factor, completely, each of the following: a.    5a2 + 10ab + 5b2                 b.    -14x3 + 21x + 35x2 c.    56x2+ 40x3 +16x d.    144x3 - 36xy2 e.    a2 - 4ab + 4b2 - 1 f.    y4 - 18 y2 + 81 g.    2x2 - 8y2 + 16y - 8 h.    a2c - 4abc - 9c3 + 4b2c i.    2 - 2y2 - 8x2 - 8xy j.    (x2 - 1) - 2(x + 1) k.    ax + 2ay - 3x2 + 12y2   l.    (p + 1) (p - 6) + 16 (p + 1) m.    45x2 -177xy - 12y2        p.    12x2 - 4x - 21

2.     Solve the following quadratic equations by factoring: a.    x2 +  3x - 28  = 0 b.    x2 - 11x + 24 = 0 c.    10x2 - 13x - 3 = 0 d.    15x2 -  2x  - 8 = 0

3.    Factor the following by completing the square: a.    y2 + 16y -132 b.    2x2 - 8x - 42  c.    2x2 + 5x + 3 d.    4x2 + 4x - 24

4.    Express in simplest form. Note the necessary restrictions: a.                       c.         b.           d.

5.    Perform the following operations. Note the necessary restrictions. a.       c.               b.       d.

6.    The area of rectangle ABCD is given by the expression              (xy + 3x + 7y + 21) m2. Two equal rectangles have been              drawn as shown.     a.    What binomials could represent the dimensions of the                 big rectangle?     b.    What is the perimeter of each small rectangle?

7.    An advertisement is set on a triangular board where            base AB measures (20x) cm and height CH                          measures (10x) cm.        The caption is written on a rectangle with dimensions          24 cm by 6 cm.        a.    Which expression would represent the area of                     triangle ABC?        b.    Express the area of the shaded surface as a                        product of factors.

8.    The right trapezoid ABCD has the following measures             in metres:                                      AB = 5x - 1                                                             CD measures 8 m more than AB           Which expression, in simplest form, represents the area         of trapezoid ABCD?

9.    A big square has a side measuring (y) cm. A square is drawn        exactly inside the big one. The shaded area has a width of        (x) cm.        a.    What expression represents the area of the big square?        b.    What is the side of the smaller square?        c.    What expression, in factored form, represents the               shaded area?                         10.    A public park with an area represented, in m2, by the          algebraic expression:           40xy + 125y + 96x +300                                       includes a rectangular swimming pool set up as shown.          What is the perimeter of the swimming pool?                  New Review # 3 1.    Given the areas of rectangles by their algebraic expressions, factor to determine the binomials         representing their dimensions:           a.    x2 + x – 42                                d.    16x2 + 24x + 9           b.    3x2 + 2x – 8                              e.    6x2 - 5x - 6           c.    9x2 – 30x + 25                          f.    15x2 + 23x + 4 2.    Factor the following polynomials:          a.     x8 - 9                                         d.    x2y - 9y + ax2 - 9a          b.    16  - 25x2                                  e.    (a2 + 6a + 9) - 16          c.    xyz - x3yz                                    f.    (3x + y)2 - (x - y)2     3.    Perform the following operations and give answers in simplest form:                    a.    2x2 - 5x - 12                     x - 4        b.    2c3 + 13c2 + 21c                        c + 3        c.      (x - 1)2 - 9                      x - 4            d.        4x2- 17x - 15                   6x2 - 27 x -15                          4.    The volume of a right prism with a rectangular base is (2x3 + x2 - 22x + 24) m3.         The area of its base is (2x2 + 5x - 12) m2.        What are the three dimensions of this prism?        (Express each dimension as a binomial.) 5.    Solve the following equations:         a.    16 – 25x2 = 0         b.    6x2(3x - 2) + 2x(3x - 2) - 4(3x - 2) = 0         c.    2x2 - x = 15        d.     3x2 - 10x = - 8        e.     6x2 + 4x = 16        f.      18x3 - 15x2 = 18x        g.    10x2 – 30x + 25 = x2         Answers to Extra-Review 3