5.2 Review
Vocabulary
- Binomials
- two terms
- Trinomials
- has three terms
- Factoring
- a method to find products
- Monomial
- An expression that has only one term. This is the first step to factoring.
- Quadratic Equation/Standard form
- one variable that can be written in the form of ax2+bx+c
=0
Factoring Equations
x2+bx+c=(x+m)(x+n)
=x2+(m+n)+mn
ax2+bx+c=(kx+m)(x+n)
=klx2+(kn+lm)x+mn
* Example 1 *
x2-12x-28
-Determine which factoring equation to use. In this case, the equation is
-x2+bx+c=(x+m)(x+n)
=x2+(m+n)+mn
-So…..
x2-12x-28=(x+m)(x+n)
-12 is B and -28 is C
m+n=-12
mn=-28
-Factor
Factors of -28(mn)
[-1, 28]
[-2, 14]
[2, -14]
[-4, 7]
Sum of factors(m+n)-
[27]
[2]
[-12]
[3]
-Solve
m=2, n=-14
>> x2-12x-28=(x+2)(x-14)
* Example 2 *
3x2-17x+10
-use
ax2+bx+c=(kx+m)(x+n)
=klx2+(kn+lm)x+mn
3x2-17x+10=(kx+m)(lx+n)
-k and l are factors of 3 while m and n are factors of 10
-Factor and Solve
(3x-10)(x-1)=3x2-13x+10
(3x-5)(x-2)=3x2-11x+10
(3x-1)(x-10)=3x2-31x+10
(3x-2)(x-5)=3x2-17x+10
-Answer
3x2-17x+10=(3x-2)(x-5)
Tips>> Special Factoring Patterns
Difference of 2 squares
Pattern:
a2-b2=(a+b)(a-b)
Ex: x2-9=(x+3)(x-3)
Perfect square trinomial
a2+2ab+b2=(a+b)2
Ex: x2+12x+36=(x+6)2
a2-2ab+b2=(a-b)2
Ex: x2-8x+16=(x-4)2
*Example 3 *
A) 4x2-25=(2x) 2-5x2 difference of 2 squares
=(2x+5)(2x-5)
B) 49r2-14r+1=(7r) 2 -2(7r)(1)+12 perfect square trinomial
=(7r-1) 2
* Example 4 *
A)5x2-20=5(x2-4) factor
=5(x+2)(x-2)
B)6p2+15p+9=3(2p2+5p+3)
=3(2p+3)(p+1)
Tip>> a quadratic equation/standard form in one variable can be written in the ax2+bx+c=0 form
* Example 5 *
A) x2+3x-18=0 factor
(x+6)(x+3)=0
(x+6)=0 or x-3=0
x=6 or -3
B)2t2-17t+45=3t-5
2t2-20t+50=0 write in standard form
t2-10t+25=0 divide by 2
(t-5)2=0 factor
t-5=0 use 0 product property
x=5
GUIDED PRACTICE :)
1)2x2+x-3(factor the expression)
2)q2+2(factor the expression)
3)x2-2x-8=0(solve the equation)
4)5w2=30w(solve the equation)
5)y=x2+6x+8(write the function in intercept form)
6)y=3x2-8+4(write the function in intercept form)
7)x2-25(equations in special patterns)
8)9s2+12s+4(equations in special patterns)
9)5x2+5x-10(factoring monomials first)
10)u2+7u(factoring monomials first)
11)x2-3x-4=0(equations in standard form)
12)-3b2+3b+90=0(equations in standard form)