Solve the following problem on Algebra 2 Factoring
Find a and b in order that x3 - 6x2 + ax + b is exactly divisible by x2 - 3x + 2
Solution to Example 3 of Algebra 2 Factoring
Let f(x) = x3 - 6x2 + ax + bWe can factorize x2 - 3x + 2 using the knowledge of factorization of Quadratic Polynomials. x2 - 3x + 2 = x2 - x - 2x + 2= x(x - 1) - 2(x - 1) = (x - 1)(x - 2) f(x)[ = x3 - 6x2 + ax + b] is exactly divisible by x2 - 3x + 2 ⇒ f(x) is exactly divisible by (x - 1)(x - 2) ⇒ (x - 1) and (x - 2) are factors of f(x) ⇒ f(1) = 0 and f(2) = 0 f(1) = 1 - 6 + a + b = a + b - 5 = 0 ⇒ a + b = 5...........(i) f(2) = (2)3 - 6(2)2 + a(2) + b = 8 - 24 + 2a + b = 2a + b - 16 f(2) = 0 ⇒ 2a + b - 16 = 0 ⇒ 2a + b = 16..........(ii) (ii) - (i) gives (2a + b) - (a + b) = 16 - 5 ⇒ 2a + b - a - b = 11⇒ a = 11 Using this value of a in (i), we get 11 + b = 5 ⇒ b = 5 - 11 = -6 Thus a = 11, b = -6. Thus Factor Theorem in Factoring Polynomials helped us to find a and b,for x3 - 6x2 + ax + b to be exactly divisible by x2 - 3x + 2 as a = 11 and b = -6. Ans.
Exercise on Algebra 2 Factoring
Solve the Following Problems on Algebra 2 Factoring :
Factorize x3 + 6x2 + 11x + 6
Factorize 2x3 - x2 - 15x + 18
Find l and m in order that x4 - x3 + lx2 + mx + 4 is exactly divisible by x2 - x - 2
For Answers See at the bottom of the Page.
Progressive Learning of Math : Algebra 2 Factoring
Recently, I have found a series of math curricula (Both Hard Copy and Digital Copy) developed by a Lady Teacher who taught everyone from Pre-K students to doctoral students and who is a Ph.D. in Mathematics Education.
This series is very different and advantageous over many of the traditional books available. These give students tools that other books do not. Other books just give practice. These teach students “tricks” and new ways to think.
These build a student’s new knowledge of concepts from their existing knowledge. These provide many pages of practice that gradually increases in difficulty and provide constant review.
These also provide teachers and parents with lessons on how to work with the child on the concepts.
The series is low to reasonably priced and include
There is an exclusive, Parent Information Page provides YOU with detailed reports of your child’s progress so you can monitor your child’s success and give them encouragement. These Reports include
Time spent using the program
Personalized remediation curriculum designed for your child
Details the areas of weakness where your child needs additional help
Provides the REASONS WHY your child missed a concept
List of modules accessed and amount of time spent in each module
Creates reports that can be printed and used to discuss issues with your child’s teachers
These reports are created and stored in a secure section of the program, available exclusively to you, the parent. The section is accessed by a password that YOU create and use. No unauthorized users can access this information.