y2-7y+6-4y2+8y-4

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 6 and whose sum is -7.

-6,-1

Write the factored form using these integers.

(y-6)(y-1)-4y2+8y-4

(y-6)(y-1)-4y2+8y-4

Factor 4 out of -4y2+8y-4.

Factor 4 out of -4y2.

(y-6)(y-1)4(-y2)+8y-4

Factor 4 out of 8y.

(y-6)(y-1)4(-y2)+4(2y)-4

Factor 4 out of -4.

(y-6)(y-1)4(-y2)+4(2y)+4(-1)

Factor 4 out of 4(-y2)+4(2y).

(y-6)(y-1)4(-y2+2y)+4(-1)

Factor 4 out of 4(-y2+2y)+4(-1).

(y-6)(y-1)4(-y2+2y-1)

(y-6)(y-1)4(-y2+2y-1)

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-1⋅-1=1 and whose sum is b=2.

Factor 2 out of 2y.

(y-6)(y-1)4(-y2+2(y)-1)

Rewrite 2 as 1 plus 1

(y-6)(y-1)4(-y2+(1+1)y-1)

Apply the distributive property.

(y-6)(y-1)4(-y2+1y+1y-1)

Multiply y by 1.

(y-6)(y-1)4(-y2+y+1y-1)

Multiply y by 1.

(y-6)(y-1)4(-y2+y+y-1)

(y-6)(y-1)4(-y2+y+y-1)

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(y-6)(y-1)4((-y2+y)+y-1)

Factor out the greatest common factor (GCF) from each group.

(y-6)(y-1)4(y(-y+1)-1(-y+1))

(y-6)(y-1)4(y(-y+1)-1(-y+1))

Factor the polynomial by factoring out the greatest common factor, -y+1.

(y-6)(y-1)4((-y+1)(y-1))

(y-6)(y-1)4(-y+1)(y-1)

Combine exponents.

Factor -1 out of -y.

(y-6)(y-1)4(-(y)+1)(y-1)

Rewrite 1 as -1(-1).

(y-6)(y-1)4(-(y)-1(-1))(y-1)

Factor -1 out of -(y)-1(-1).

(y-6)(y-1)4(-(y-1))(y-1)

Rewrite -(y-1) as -1(y-1).

(y-6)(y-1)4(-1(y-1))(y-1)

Raise y-1 to the power of 1.

(y-6)(y-1)4⋅-1((y-1)1(y-1))

Raise y-1 to the power of 1.

(y-6)(y-1)4⋅-1((y-1)1(y-1)1)

Use the power rule aman=am+n to combine exponents.

(y-6)(y-1)4⋅-1(y-1)1+1

Add 1 and 1.

(y-6)(y-1)4⋅-1(y-1)2

Multiply 4 by -1.

(y-6)(y-1)-4(y-1)2

(y-6)(y-1)-4(y-1)2

(y-6)(y-1)-4(y-1)2

Cancel the common factor of y-1 and (y-1)2.

Factor y-1 out of (y-6)(y-1).

(y-1)(y-6)-4(y-1)2

Cancel the common factors.

Factor y-1 out of -4(y-1)2.

(y-1)(y-6)(y-1)(-4(y-1))

Cancel the common factor.

(y-1)(y-6)(y-1)(-4(y-1))

Rewrite the expression.

y-6-4(y-1)

y-6-4(y-1)

y-6-4(y-1)

Move the negative in front of the fraction.

-y-64(y-1)

-y-64(y-1)

Simplify (y^2-7y+6)/(-4y^2+8y-4)