2x^2+9x+42x2+9x+4
First multiply the constant 44 with the coefficient of x^x which is 22
The result is 88
Now find factors of 88 such that they add up to the coefficient of xx here it is +9+9.
Let us list out the pairs which multiply to give 88
These are 1,81,8, 2,42,4, -1,-8−1,−8 and -2,-4−2,−4
Let us check if these add up to +9+9
1xx8=8 and 1+8 =91×8=8and1+8=9 this works. Using this we shall split the middle term. 9x = 1x+8x9x=1x+8x
2x^2+9x+42x2+9x+4
=2x^2+1x+8x+4=2x2+1x+8x+4 This is called splitting the middle term.
Now we would do factor by grouping.
=(2x^2+1x)+(8x+4)=(2x2+1x)+(8x+4)
GCF from each group is taken out.
=x(2x+1) + 4(2x+1)=x(2x+1)+4(2x+1)
Now we have (2x+1)(2x+1) as the common factor, so it is factored out.
=(2x+1)(x+4)=(2x+1)(x+4) Answer
