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mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
A student incorrectly factoredExplain this error. x² +4 as (x + 2)².
Evaluate for p = -4, q = -2, and r = 5. 5p + 6r² p² + q- 1
A student solved the following equation incorrectly as shown.The student gave { -4} as the solution set. Give the correct solution set. 3x² + 12x = 0 3x (x + 4) = 0 x + 4 = 0 x = − 4
Factor.6x2 + 11x - 35
When a student was given the polynomial 4x2 + 2x - 20 to factor completely on a test, the student lost some credit when her answer wasGive the correct answer. (4x + 10) (x - 2).
Which is not a factored form of the trinomial -x2 + 16x - 60? A. (x 10) (-x+6) C. (-x+ 10) (x - 6) B. (-x-10) (x + 6) D. 1(x 10) (x - 6)
Factor completely.30a + am - am2
The following exercises are of mixed variety. Factor each polynomial.k4 - 16
Factor out the greatest common factor.6r3t - 30r2t2 + 18rt3
Which sum of squares can be factored? Factor it.A. x2 + 100 B. 9m2 + 25 C. t2 + 16 D. 4x2 + 64
A student solved the following equation incorrectly as shown.The student gave the solution set as {-4, 3, 7}. Give the correct solution set. x = 7 x = 7 7(x+4)(x 3) = 0 or x + 4 = 0 or x - 3=0 or x = -4 or x=3
Simplify.3x2 - 4x + 4 + 9x - x2
Which is the completely factored form of the trinomial 4x2 - 4x - 24? A. 4(x-2)(x+3) C. 4(x + 2)(x - 3) B. 4(x + 2)(x + 3) D. 4(x-2)(x-3)
Factor. -2x2 - x + 36
Factor completely.16x2 + 144
The following exercises are of mixed variety. Factor each polynomial.3p4 - 3p3 - 90p2
Factor out the greatest common factor.12q2b + 8qb2 - 20q3b2
Which of the following trinomials are perfect squares? A. x² 8x 16 C. 924 + 30z² + 25 - B. 4m² +20m + 25 D. 25p²-45p + 81
Simplify.-2(m - 3)
A student solved the following equation incorrectly as shown.The student gave the solution set as {4, 9}. Give the correct solution set. (x - 3)(x + 2) = 6 or x + 2 = 6 or x = 4 x3 = 6 x = 9
Factor.3x + by + bx + 3y
Which is the completely factored form of the trinomial 2x6 - 5x5 - 3x4? A. x4(2x + 1)(x − 3) C. (2x5 + x4) (x-3) B. x4(2x - 1)(x + 3) D. x³(2x² + x)(x-3)
Match each polynomial in Column I with the method or methods for factoring it in Column II. The choices in Column II may be used once, more than once, or not at all. I (a) ab 5a + 3b - 15 (b) z² - 3z + 6 (c) 25x² + 100 (d) r². 24r + 144 (e) 2y2 + 36y + 162 II A. Factor out the GCF. B. Factor a
Factor completely.-x2 + 3x + 10
Factor out the greatest common factor.21x2 + 35x
Which of the following binomials are sums or differences of cubes?A. 64 + r3 B. 125 - p6 C. 9x3 + 125 D. (x + y)3 - 1
Perform the indicated operations.2.5(6.5) - 0.15
Solve each equation. 0= (sx) (01 + x)
Solve. 2x 5 + 3x = 4(x + 2)
Factor each polynomial. p2 - 16
The following exercises are of mixed variety. Factor each polynomial.225p2 + 256
Factor by grouping.4m + nq + mn + 4q
Which of the following can be solved using the zero-factor property? A. 25x² + 20x + 4 = 0 C. 2x² 128 = 0 B. 3x² = 15x D. x(4x 15) - 30 = 0
Which is not a valid way of starting the process of factoring the trinomial 12x2 + 29x + 10? A. (12x C. (6x ) (x )(2x ) B. (4x D. (8x ) (3x ) (4x ) )
Which of the following binomials are differences of squares?A. 64 - k2 B. 2x2 - 25 C. k2 + 9 D. 4z4 - 49
Which of the following are quadratic equations? A. 2x + 3 = 6 D. 2x³ + x² - 6x = 0 B. x² E. x² + 160 3x + 2 = 0 C. 5t² + 3t = 2 F. 3x² x = 0
Let ƒ(x) = x2 - 9, g(x)= 2x, and h(x) = x - 3. Find each of the following. (f- g)(-3)
Find each product. 324 22³ + 2-5 22-5
Evaluate. Express answers in standard notation. 5 x 10-3 25 × 10²
Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (f - h)(x)
Use the FOIL method to find each product. (m + 5)(m - 8)
Let ƒ(x) = x2 - 9, g(x)= 2x, and h(x) = x - 3. Find each of the following. (f + h)(x)
Evaluate. Express answers in standard notation. 18 x 10-3 x 24 x 104 8 x 105 x 2 × 10-⁹
Evaluate. Express answers in standard notation. 15 x 10-4 × 12 × 105 4 x 10³ x 5 x 10-8
Identify each polynomial as a monomial, binomial, trinomial, or none of these. Give the degree.4z2 - 11z + 2
The planet Mercury has an average distance from the sun of 3.6 × 107 mi, and the average distance from Venus to the sun is 6.7 × 107 mi.(a) How long would it take a spacecraft traveling at 1.55 × 103 mph to travel from Venus to Mercury? Give the answer in hours, in standard notation.(b) Use the
Evaluate. Assume that all variables represent nonzero real numbers.y0
Use the FOIL method to find each product. (p + 4)(p-6)
Identify each polynomial as a monomial, binomial, trinomial, or none of these. Give the degree.-6p4q - 3p3q2 + 2pq3 - q4
Let ƒ(x) = x2 - 9, g(x)= 2x, and h(x) = x - 3. Find each of the following. (f - h)(-3)
Evaluate. Assume that all variables represent nonzero real numbers.30 + (-3)0
Give the numerical coefficient and the degree of each term.14p5
Identify each polynomial as a monomial, binomial, trinomial, or none of these. Give the degree.8s3t - 4s2t2 + 2st3 + 9
Evaluate. Assume that all variables represent nonzero real numbers.50 + (-5)0
Give the numerical coefficient and the degree of each term.-z2
Combine like terms. 5z4 + 3z4
Use the information given in the previous two exercises to find the number of minutes necessary for light from the sun to reach Earth.Data from in Previous The average distance from Earth to the sun is 9.3 × 107 mi. How long would it take a rocket, traveling at 2.9 × 103 mph, to reach the
Evaluate. Express answers in standard notation. 0.05 × 1600 0.0004
Use the FOIL method to find each product. (4k+ 3) (3k - 2)
Evaluate. Assume that all variables represent nonzero real numbers.-30 + 30
Let ƒ(x) = x2 - 9, g(x)= 2x, and h(x) = x - 3. Find each of the following. (f + h) (-2)
Give the numerical coefficient and the degree of each term.x/10
Evaluate. Express answers in standard notation. 0.003 x 40,000 0.00012
Combine like terms. 8r5 - 2r5
Evaluate. Assume that all variables represent nonzero real numbers.-50 + 50
Use the FOIL method to find each product. (5w+ 2) (2w - 5)
Give the numerical coefficient and the degree of each term.504p3r5
Let ƒ(x) = x2 - 9, g(x)= 2x, and h(x) = x - 3. Find each of the following. (g + h)(-10)
Evaluate. Express answers in standard notation. 15,000 X 0.25 0.0075 X 50,000
Combine like terms. -m3 + 2m3 + 6m3
Evaluate. Assume that all variables represent nonzero real numbers.-40 - m0
For each polynomial,(a) Write in descending powers (b) Identify as a monomial, binomial, trinomial, or none of these(c) Give the degree9k + 11k3 - 3k2
Use the FOIL method to find each product. (3x-2)(5x-1)
Let ƒ(x) = x2 - 9, g(x)= 2x, and h(x) = x - 3. Find each of the following. (g- h) (10)
Evaluate. Express answers in standard notation. 400,000 X 0.05 0.008 × 25,000
Combine like terms. 3p4 + 5p4 - 2p4
Evaluate. Assume that all variables represent nonzero real numbers.-80 - k0
Factor.11z2 - 44z
Match each polynomial in Column I with the method or methods for factoring it in Column II. The choices in Column II may be used once, more than once, or not at all. I (a) 49x² - 81y² (b) 125z6 + 1 (c) 88r²55s² (d) 64a³-8b⁹ (e) 50x² - 128y4 II A. Factor out the GCF. B. Factor a difference
Factor out the greatest common factor.12p2 - 6p
Factor completely.x2 + 5y + 5x + xy
Factor.10x2y5 - 5x2y3 - 25x5y3
Find each product. (4z + 2) (2²-32 - 5)
The total population of the United States was recently estimated at 321,400,000. Of this amount, about 72,000 Americans were centenarians, that is, age 100 or older. Write the three boldfaced numbers using scientific notation. 100
Write each number in standard notation.2.7 × 10-6
For each pair of functions, find (a) (ƒ + g)(x) and (b) (ƒ - g)(x). f(x) = 4x² + 8x − 3, g(x) = −5x² + 4x − 9 -
Find each product. 5m - 3n 5m + 3n
Evaluate. Assume that all variables represent nonzero real numbers.190
Identify each polynomial as a monomial, binomial, trinomial, or none of these. Give the degree.7m - 22
For each pair of functions, find (a) (ƒ + g)(x) and (b) (ƒ - g)(x). f(x) = 3x² − 9x + 10, g(x) - = -4x² + 2x + 12
Find each product. 2k + 6q 2k - 6q
Write each number in standard notation. -2.89 × 10-2
Write each number in standard notation. 1.21 × 106
Find two polynomial functions defined by ƒ(x) and g(x) such that each statement is true. (f + g)(x) = 3x³ = x + 3 -
Find each product. -b² + 3b + 3 2b + 4
Find two polynomial functions defined by ƒ(x) and g(x) such that each statement is true. S = x + ₂x = (x)(8 — f) - -
Evaluate. Assume that all variables represent nonzero real numbers.-80
Identify each polynomial as a monomial, binomial, trinomial, or none of these. Give the degree.6x + 15
Write each number in standard notation.-7.68 × 10-4
Evaluate. Assume that all variables represent nonzero real numbers.-100
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