Attempt to factor each expression to find any similarities or differences.
4x^2+10x+4
See solution.
Practice makes perfect
Let's try factoring each one to see if there are any similarities. We can begin by checking for perfect squares in the first and last terms of the first expression.
4x^2-36x+ 81 ⇒ (2x)^2-36x+ 9^2
Next, we can verify if the entire expression is a perfect square. Let's check if the middle term, -36x, is equal to -2 times the first and second roots.
-2( 2x)( 9) ⇒ -36x
Now, we can determine if it's a positive or negative square. The middle term is negative. Therefore, we need to subtract 9.
( 2x- 9)^2
We can factor the other terms to check if they factor similarly.
Expression
Step 1
Step 2
Answer
25x^2+10x+1
(5x)^2+10x+ 1^2
2( 5x)( 1) = 10x
( 5x+ 1)^2
4x^2+10x+4
(2x)^2+10x+ 2^2
2( 2x)( 2) ≠= 10x
no even factor
9x^2-24x+16
(3x)^2-24x+ 4^2
-2( 3x)( 4) ≠= -24x
( 3x- 4)^2
We can identify that each of the expressions is a perfect square except for 4x^2+10x+4. Therefore, 4x^2+10x+4 is the expression that does not belong.
