Polynomial Operations and Factoring
Simple Quadratic Equations
These questions will test your knowledge of operations involving
polynomial operations and factoring simple quadratic equations. Solve the following equations.
问答题
For x=4,
3x2-5x+9=______
【正确答案】
【答案解析】To solve the equation, substitute 4 for x:
3(42)-5(4)+9= 3(16)-20+9=
48-20+9=37
问答题
(5x3+3x-12)-(2x3-6x+17)=______
【正确答案】
【答案解析】To add or subtract polynomials, combine like terms (remember to keep track of
the negative signs!):
(5x3+3x-12)-(2x3-6x+17)
(5x3-2x3)+(3x+6x)-(17-12)
3x3+9x-5
问答题
(4x2+2x)(x-6)=______
【正确答案】
【答案解析】Use the Distributive Property to multiply each term of one polynomial by each
term of the other (remember to use the FOIL method).
(4x2+2x)(x-6) First terms:
(4x2)(x)=4x3 Outside terms:
(4x2)(-6)=-24x2 Inside terms:
(2x)(x)=2x2 Last terms: (2x)(-6)=-12x
Now place the terms in decreasing order of the exponents:
4x3-22x2-12x
问答题
What are the solution sets for
x2+2x-48?
【正确答案】
【答案解析】Find two numbers whose product is -48 and sum is 2.8 and -6 are the only possible numbers. Therefore, the solution sets are (x-6) and (x+8).
问答题
(x-4) and (2x+3) are the solution sets for what
equation?
【正确答案】
【答案解析】The solution sets are given, so multiply the two sets together to find the
original equation, using the FOIL method: (x-4)(2x+3)
=2x2+3x-8x-12 =2x2-5x-12