Algebra Factoring
In all of these equations we are finding the factor for the answer. We are using grouping, GCF, prime factor, and perfect square as well in these set equations.
Page 345 - 346
#52. Using (45) as the product and (18) as the sum.
18z + 45 + z^2 Equation
(z + 15)(z + 3) Answer
Breaking it down using the FOIL method to verify the answer: z * z = z^2 This is a perfect square.
15 * z = 15z z * 3 = 3z
15 * 3 = 45
In this equation to get the answer we need to use the GCF (Greatest Common Factor) to get the correct answer, which is (z) for the first part of the parentheses and then (3) for the second part of the parentheses. There is also grouping happening in this equation with (3z + 15z).
Putting it all together to solve back to the original equation: z^2 + 3z + 15z + 45 z^2 + 18z + 45
#78. Factor completely. a^4 b + a^2 b^3 Equation a^2 b (a^2 + b^2) Answer
Breaking the answer down to show it equals the answer: a^2 * a^2 * b = a^4 b a^2 * b * b^2 = a^2 b^3
Put the two together to verify that it is the original equation: a^4 b + a^2 b^3
In this equation a^2 is a perfect square. We use the GCF of (a^2 and b). We also use a smaller version of the FOIL method, since there is not as much going on here in this equation.
Page 353
#66. Using trial and error.
8x^2 – 2xy – y^2 Equation
(4x + 1y)(2x – 1y) Answer
Breaking it down using the FOIL method to verify answer:
4x * 2x = 8x^2
4x * -1y = - 4xy
1y * 2x = 2xy
1y * -1y = - y^2
In this equation to get the answer we need to use the prime factor of (2) and the GCF of (y) for the other part of the equation to get the correct answer. We also use grouping with (-4xy + 2xy).
Putting it all back together to verify the equation:
8x^2 - 4xy + 2xy – y^2
8x^2 – 2xy – y^2
In this equation we also have 2 perfect squares (x^2 and
Page 345 - 346
#52. Using (45) as the product and (18) as the sum.
18z + 45 + z^2 Equation
(z + 15)(z + 3) Answer
Breaking it down using the FOIL method to verify the answer: z * z = z^2 This is a perfect square.
15 * z = 15z z * 3 = 3z
15 * 3 = 45
In this equation to get the answer we need to use the GCF (Greatest Common Factor) to get the correct answer, which is (z) for the first part of the parentheses and then (3) for the second part of the parentheses. There is also grouping happening in this equation with (3z + 15z).
Putting it all together to solve back to the original equation: z^2 + 3z + 15z + 45 z^2 + 18z + 45
#78. Factor completely. a^4 b + a^2 b^3 Equation a^2 b (a^2 + b^2) Answer
Breaking the answer down to show it equals the answer: a^2 * a^2 * b = a^4 b a^2 * b * b^2 = a^2 b^3
Put the two together to verify that it is the original equation: a^4 b + a^2 b^3
In this equation a^2 is a perfect square. We use the GCF of (a^2 and b). We also use a smaller version of the FOIL method, since there is not as much going on here in this equation.
Page 353
#66. Using trial and error.
8x^2 – 2xy – y^2 Equation
(4x + 1y)(2x – 1y) Answer
Breaking it down using the FOIL method to verify answer:
4x * 2x = 8x^2
4x * -1y = - 4xy
1y * 2x = 2xy
1y * -1y = - y^2
In this equation to get the answer we need to use the prime factor of (2) and the GCF of (y) for the other part of the equation to get the correct answer. We also use grouping with (-4xy + 2xy).
Putting it all back together to verify the equation:
8x^2 - 4xy + 2xy – y^2
8x^2 – 2xy – y^2
In this equation we also have 2 perfect squares (x^2 and