Factor 7x2-16x+4

What are the x-intercepts for the graph of y = x2 + 5x - 6?

We can use grouping to solve this quadratic because it can be factored.

x2+5x-6=0

x2 +6x-x-6=0

(x2+6x)-(x+6)=0

x(x+6)-(x+6)=0

(x-1)(x+6)=0

Next we can use the zero product property

x-1=0

x=1

or

x+6=0

x=-6

Solve: (x+9)^2 + 11(x+9)+18=0

2*9=18 and 2+9=11, therefore...
(x+9)^2 + 11(x+9)+18=
((x+9)+2)((x+9)+9)=
(x+11)(x+18)=0
Solution:
{-11, -18}

Solve this equation: d^2-5d+6=0

then...we'll use grouping to solve.

After looking at the factors 6 and 1 we notice that they don't quite work, so let's try 3 and 3:


Next we factor out the greatest common factors then we group them:


so that



Finally, because of the zero product property we can see that
x=3 or x=2 

Express 9x^2-42x+49 in the form (ax+b)^2 where a and b are constants.

Factor: x^2+8xy+15y^2

We look for a pair of terms that multiply to 15y^2 and add properly to 8y and we discover 3y and 5y will work: 
X^2+8xy+15y^2=
X^2+x(3y+5y)+15y^2=
X^2+3xy +5xy+15y^2=
(X^2+3xy)+(5xy+15y^2)=
x(x+3y)+5y(x+3y)=
(x+5y)(x+3y) 

:)

 
We'll use grouping - there are many ways...but grouping works well for this problem 
 
 
 
 
or 
 
which leads to 
v=1/3 
or v=1

3x^2+11x+10 factor using ac method show all steps

3x^2+11x+10 

ac = 30 
with 5+6=11 
so we write: 

3x^2+11x+10= 
3x^2+6x+5x+10= 
3x(x+2)+5(x+2)= 
(3x+5)(x+2)

solve. 6c^2-11c-72=0

6c^2-11c-72=0 

 

 

c=9/2 or c=-8/3

solve 7x^2+10x=8

7x^2+10x=8
7x^2+10x-8=0
7x^2+14x-4x-8=0
7x(x+2)-4(x+2)=0
(7x-4)(x+2)=0 
x=-2 or x=4/7 

:)

Factor: 4x^2 - 16x - 9

4x^2-16x-9=0 


4x^2 - 16x = 9 
4(x^2-4x)=9 

4(x^2-4x+4)=9+4(4) 
4(x-2)^2=25 
(x-2)^2=25/4 

x-2=5/2
2x-4=5
2x-9=0 
or 

x-2=-5/2
2x-4=-5
2x+1=1 


(2x-9)(2x+1)=0

Factor: 8a^2 - 26a + 15

We need a pair of numbers that add to -26 and multiply to 120. After searching we find -20 and -6. 

 
rearranging and placing parentheses... 
 
removing gcds and factoring... 

 


:)

Factor trinomial 4x^2+7x-2

We look for a pair of numbers that "add" to 7 and multiply to -8 and discover -1 and 8 

4x^2+7x-2= 
4x^2+(8x-x)-2= 

4x^2+8x-x-2= 

(4x^2+8x)-(x+2)= 

4x(x+2)-1(x+2) 

(4x-1)(x+2) 



:)

Factor the quadratic expression

Factor quadratic trinomials by grouping

Factor the quadratic trinomial by grouping

Advanced Factoring

Solution:

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