Pre-Algebra Demystified
The point whose coordinates are (5, 3) is: (a) Point A (b) Point B (c) Point D (d) Point E The point whose coordinates are (4, ...
(a) line l (b) line m (c) line n (d) line o The line whose equation is y¼2 is: (a) line l (b) line m (c) line n (d) line o Whi ...
Find y when x¼3 for 2xþy¼8. (a) 2 (b) 1 (c) 2 (d) 4 Find x when y¼3 for 5xþ3y¼16. (a) x¼ 5 (b) x¼ 2 (c) x¼ 2 (d) x¼ 5 ...
(d) 10 8 The slope of a vertical line is: (a) 0 (b) 1 (c) undefined (d) 1 When two lines are parallel, the system is said to ...
CHAPTER 12 Operations with Monomials and Polynomials Monomials and Polynomials Recall from Chapter 7 that an algebraic expressio ...
Monomials: 3x^2 5y 2x^3 y^2 Binomials: xþ2y 3x^2 þx 2yþz Trinomials 3x^2 þ4x12x3yþ 5 Addition of Polynomials Recall in Chapt ...
PRACTICE Add: (6x^2 þ3x8)þ(2x^2 5x9) (3xþ2y2)þ(4x2yþ8) (2xþ5)þ(7x10)þ(3x4)þ(4x6) (3a^2 b^2 2abþ5)þ(a^2 b^2 þ2abþ4) (9m ...
EXAMPLE Subtract (2a3bc)(5a6bc). SOLUTION ð2a3bcÞð5a6bcÞ¼2a3bc5aþ6bþc ¼ð2a5aÞþð3bþ6bÞþðcþcÞ ¼3aþ3b PRACTICE Sub ...
SOLUTION y^5 y^6 ¼y^5 þ^6 ¼y^11 To multiply two monomials, multiply the numerical coefficients (numbers) and add the exponents ...
9ab^4 6ab^2 3ab 7xy3x^2 zð2yz^2 Þ ANSWERS 10x^2 y^2 16a^5 b^2 60x^6 y^4 162a^3 b^7 42x^3 y^2 z^3 Raising a Monomial ...
SOLUTION ð6a^4 b^5 Þ^3 ¼ð 6 Þ^3 a^4 ^3 b^5 ^3 ¼216a^12 b^15 EXAMPLE Find (xy^3 )^4. SOLUTION ðxy^3 Þ^4 ¼ð1xy^3 Þ^4 ¼ð 1 ...
EXAMPLE Multiply x(2xþ3y). SOLUTION xð2xþ3yÞ¼x2xþx3y ¼2x^2 þ3xy EXAMPLE Multiply 5x^2 y(3xþ2y6) SOLUTION 5x^2 yð3xþ2y 6 Þ¼5x ...
SOLUTION Distribute (xþ4) over (xþ2) as shown: ðxþ 4 Þðxþ 2 Þ¼ðxþ 4 Þxþðxþ 4 Þ 2 : Next distribute each point as shown: ¼xxþ 4 ...
2x7x¼5x Hence,ðx 7 Þðxþ 2 Þ¼x^2 5x14. PRACTICE Multiply: (xþ6)(xþ7) (x4)(x6) (xþ9)(x11) (x3)(xþ3) (xþ4)(xþ4) ANSWERS ...
EXAMPLE Square (2x3). SOLUTION ð2x 3 Þ^2 ¼ð2xÞ^2 2 2x 3 þð 3 Þ^2 ¼4x^2 12xþ 9 EXAMPLE Square (3xþ1). SOLUTION ð3xþ 1 Þ^2 ...
SOLUTION ðxþ 2 Þðx^2 þ5x 6 Þ¼ðxþ 2 Þx^2 þðxþ 2 Þ5xþðxþ 2 Þð 6 Þ ¼xx^2 þ 2 x^2 þx5xþ 2 5xþxð 6 Þþ 2 ð 6 Þ ¼x^3 þ2x^2 þ5 ...
(x^2 þ3xþ2)(xþ1) (3x^2 þ2xþ5)(x6) (2x^2 þ4x1)(2x3) (x^3 2x^2 þ2xþ1)(x5) (x^2 þ2xþ7)(x^2 x6) ANSWERS x^3 þ4x^2 þ5xþ 2 3 ...
SOLUTION 15x^5 5x^3 ¼3x^5 ^3 ¼3x^2 EXAMPLE Divide 12x^4 y^6 by 3xy^4. SOLUTION 12x^4 y^6 3xy^4 ¼4x^4 ^1 y^6 ^4 ¼4x^3 y^2 M ...
Division of a Polynomial by a Monomial To divide a polynomial by a monomial, divide each term in the polynomial by the monomial. ...
Quiz Add (2x^2 þxþ1)þ(3x^2 5xþ2). (a) 5x^2 4xþ 3 (b) 6x^2 4xþ 2 (c) 6x^2 5xþ 2 (d) 5x^2 6xþ 3 Add (6xþ2y)þ(4x8y). (a) 10x ...
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