Question

$-x^{2} +7x-10=o$
solve using sum product method

Answer 1

Answer:

Step-by-step explanation: Answer

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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.

Answer 2

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Let's solve ~

$\qquad \sf  \dashrightarrow \: - {x}^{2} + 7x - 10 = 0$

$\qquad \sf  \dashrightarrow \: - {x}^{2} + 2x + 5x - 10 = 0$

$\qquad \sf  \dashrightarrow \: - x(x - 2) + 5(x - 2) = 0$

$\qquad \sf  \dashrightarrow \: ( x- 2)( - x + 5) = 0$

Therefore, there are two solutions for x ;

Case 1

$\qquad \sf  \dashrightarrow \: x - 2 = 0$

$\qquad \sf  \dashrightarrow \: x = 2$

Case 2

$\qquad \sf  \dashrightarrow \: - x + 5 = 0$

$\qquad \sf  \dashrightarrow \: - x = - 5$

$\qquad \sf  \dashrightarrow \: x = 5$