B. 4(x^2+ 7x + 12) = (2x + 6)
Answers
Answer:
STEPS USING FACTORING BY GROUPING
4(x
2
+7x+12)=2x+6
Use the distributive property to multiply 4 by x
2
+7x+12.
4x
2
+28x+48=2x+6
Subtract 2x from both sides.
4x
2
+28x+48−2x=6
Combine 28x and −2x to get 26x.
4x
2
+26x+48=6
Subtract 6 from both sides.
4x
2
+26x+48−6=0
Subtract 6 from 48 to get 42.
4x
2
+26x+42=0
Divide both sides by 2.
2x
2
+13x+21=0
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as 2x
2
+ax+bx+21. To find a and b, set up a system to be solved.
a+b=13
ab=2×21=42
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 42.
1,42
2,21
3,14
6,7
Calculate the sum for each pair.
1+42=43
2+21=23
3+14=17
6+7=13
The solution is the pair that gives sum 13.
a=6
b=7
Rewrite 2x
2
+13x+21 as (2x
2
+6x)+(7x+21).
(2x
2
+6x)+(7x+21)
Factor out 2x in the first and 7 in the second group.
2x(x+3)+7(x+3)
Factor out common term x+3 by using distributive property.
(x+3)(2x+7)
To find equation solutions, solve x+3=0 and 2x+7=0.
x=−3
x=−
2
7
Step-by-step explanation: