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tereso536
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Answer:
The Product Sum method of factoring we use on trinomials (ax2+bx+c) with the value of a=1. This is the method that is probably used the most.
example: x2+7x+12 The product is the a value times the c value. In this case 12.
The sum is the b value. In this case 7.
Find the two numbers that multiply to 12 (the product) andadd to 7 (the sum). +4 and +3
These are your two factors. In your two binomials put the x in front and the factors in the back. (x+4)(x+3)
This is your factored expression. To check FOIL back out.
Why does this work???
example:
x2-4x-12
p= -12
s= -4 factors are -6 and +2
so factored answer is (x-6)(x+2)
example:
I'm thinking of a number that could be solved by x2+10x+16=0. What could the number be?
p=16
s=10 factors are +8 and +2
(x+8)(x+2)=0
so either x+8=0 or x+2=0 so either x= -8 or -2 is the
number.
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - {x}^{2} + 7x - 10 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: - {x}^{2} + 2x + 5x - 10 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: - x(x - 2) + 5(x - 2) = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: ( x- 2)( - x + 5) = 0[/tex]
Therefore, there are two solutions for x ;
[tex]\qquad \sf \dashrightarrow \: x - 2 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 2[/tex]
[tex]\qquad \sf \dashrightarrow \: - x + 5 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: - x = - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 5[/tex]