7.1-7.8 Study Questions
How do you do FOIL Method? (x+1)(x+2)
Do! First Outer Inner and Last Answer: X^2 + 3x + 2
Solve! 4x^2-12x+9
(2x)^2-2(2x)(3)+3^2 =(2x-3)^2 So, 4x^2-12x+9 = (2x-3)^2
Using Special Product Patterns and Mental Math 26x34
(30-4) (30+4) = 30^2 - 4^2 = 900 - 16 = 884
Factor! 54^2 - 48^2
(54 + 48) (54 - 48) =102(6) = 612 So, 54^2 - 48^2 = 612.
Solve! (x-1)^2=0
(x-1)(x-1)=0 x=1 x=1
Factoring Polynomials by Grouping! x^3+3x^2+2x+6
(x^3+3x^2) + (2x+6) = x^2(x+3)+2(x+3) = (x+3)(x^2+2) So, x^3+3x^2+2x+6 = (x+3)(x^2+2)
Solving Equations by Factoring! 2x^2 + 8x = 0
2x(x+4) = 0 2x=0 or x-4=0 x=0 x=4 The roots are x=0 and x=4.
Solving Polynomial Equations! 2x(x-4)=0
2x=0 or x-4=0 x=0 or x=4 The roots are x=0 and x=4
Solve! 2x^3+8x^2=10x
2x^3+8x^2=10x 2x^3+8x^2-10x=0 2x(x^2+4x-5)=0 2x(x+5)(x-1)=0 2x=0 or x+5=0 or x-1=0 x=0 x=-5 x=1
Factor! 4z^2 - 1
2z^2 - 1^2 = (2z+1)(2z-1)
Factoring Completely! 7x^4-28x^2
7x^2(x^2-4) = 7x^2(x^2-2^2) = 7x^2(x+2)(x-2) So, 7x^4-28x^2 = 7x^2(x+2)(x-2)
Factoring x^2 + bx + c When b and c Are Positive Factor: x^2 + 10x + 16
Answer: b=10 and c=16 Factors of 16 1,16 = 17 2,8 = 10 X 4,4 = 8 So, x^2 + 10x + 16 = (x+2)(x+8)
Solve! X^2 - 8x + 12
Answer: (x-2)(x-6)
What is the Leading Coefficient? 2x^3+x^2-5x+12 The leading coefficient is always the number with the highest exponent and the number in front of it.
Answer: 2
Find the value of x^2 - 2x - 35 when x=18.
Answer: 253
Find the Sum. (2x^3 - 5x^2 + x) + (2x^2 + x^3 -1)
Answer: 3x^3 - 3x^2 + x - 1
Factoring out the GCF! Solve! 5x^2 + 15x + 10
Answer: 5(x+1)(x+2)
How to put into standard form? 4+5x^2-x
Answer: 5x^2-x+4
Find the difference. (4n^2 + 5) - (-2n^2 + 2n - 4)
Answer: 6n^2 - 2n + 9
Using the square of a Binomial Pattern! (a+b)^2 (a-b)^2
Answer: a^2 + 2ab + b^2 Answer: a^2 - 2ab + b^2
Sum and Difference Pattern (a+b)(a-b) = a^2 - b^2 Example: (t+5)(t-5)
Answer: t^2 - 25
Multiplying Binomials Using the Distributive Property! (x+2)(x+5)
Answer: x^2 + 7x + 10
What is degree? 2x^3+x^2-5x+12
Sum of the exponents. Degree is 3
The Greatest Common Factor! 4x^4 + 24x^3
The GCF of 4 and 24 is 4. The GCF of x^4 and x^3 is x^3. So, the greatest common monomial factor of the terms is 4x^3. So, 4x^4 + 24x^3 = 4x^3(x+6)
Find each product. (3x+4)^2
a=3x b=4 equation used: a^2 + 2ab + b^2 (3x)^2 + 2(3x)(4)+(4)^2 Answer: 9x^2 + 24x + 16
Solve! n^2+8n+16
n^2 + 2(n)(4) + 4^2 =(n+4)^2 So, n^2+8n+16 = (2x-3)^2.
Factor! 2x^2 - 5x - 7
no GCF! a and c! A= 2 and C=-7 find b! B= -5 Find Factors of 2 amd -7 1,2 1,-7 1,2 7,-1 1,2 -1,7 1,2 -7,1 Possible factorization (x+1)(2x-7) (x+7)(2x-1) (x-1)(2x+7) (x-7)(2x+1) Middle Term -7x + 2x = -5x ! -x + 14x = 13x X 7x - 2x = 5x X x - 14x = -13x X So, 2x^2 - 5x -7 = (x+1)(2x-7)
Factor each polynomial! 4x^2 + 13x + 3
no GCF! take a and c find factors of 4 and 3 factors of 4 factors of 3 Possible factorization 1,4 1,3 (x+1)(4x+3) 1,4 3,1 2,2 1,3 Middle term 3x+4x=7x X x+12x=13x ! 6x+2x=8x X Find Middle Term! Answer: x+12x=13x
How would I do this? (x+5)(x^2-3x-2)
step 1 - x multiplied by everything step 2 - 5 multiplied by everything step 3 - x(x^2 - 3x - 2) x^2 - 3x -2 X x +5 ------------ 5x^2 - 15x -10 x^3 - 3x^2 - 2x ----------------- x^3 + 2x^2 - 17x - 10
Factor! x^2 - 25
x^2 - 5^2 So, x^2 - 25 = (x + 5)(x - 5)
