How do you factor this?

Question

x²+8x+7

I know the common factors are 1 and 7. My book says to rewrite bx: 8x = x+7x. Why did it chose that term, and how do how do I rewrite it?

Answer 1

Substitute x + 7x in for 8x:

x² + x + 7x + 7

Now partial factor out the common terms:

x(x + 1) + 7(x + 1)

now factor out the (x + 1):

(x + 1) * (x + 7)

Answer 2

Hello like this
x^2 +8x + 7
( x +1 )(x + 7 )
to check use the foil mrthod where F = Mult. first terms by first terms
o = mult. outside terms by outside terms

i = mult. inside terms by insidr terms

l = lmult. last terms by last terms

( x + 1 )( x + 7 )

F = ( x ) ( X ) = x^2

O = ( x ) ( 7 ) = 7x

I = ( 1 ) ( x ) = 1 x

L = ( 7 ) ( 1 ) = 7

add the O and I term

( 1x + 7x = 8x
to get the middle term

Answer 3

consider the general form of quadratic equation: x²+bx+c

suppose m and n are its two factors (there can be only two factors - or less)

then we can say x²+bx+c has been factored into (x-m) and (x-n)

in other words, x²+bx+c = (x-m)(x-n)
=(x²+x(-m-n)+mn

equating both sides, we get

b = -(m+n) and c = mn

in other words, "b" is the negative of sum of the roots (m+n) and "c" is the product of the roots

doing it reverse now... given x²+8x+7 we need to find two numbers that become 7 when multiplied and -8 when added

by experience we know the numbers can be only -1 and -7

so here m= -1 and n= -7

so the equation is expressed as (x+1)*(x+7)

we need not always rely on experience if we apply the formula for quadratic equations....

once we know the values of m and n, we can rewrite the given equation and write steps for factoring

note that the sign of m and n has to be reversed when writing in the equation

Answer 4

x^2 + 8x + 7 = 0

(x + 1) (x + 7) = 0

Answer 5

As I said..........