Which of the following simplifies to the same expression as 4x2−3x2+5x−24
4
x
2
−
3
x
2
+
5
x
−
24
?(1 point)
Responses
(x+8)(x−3)
left parenthesis x plus 8 right parenthesis left parenthesis x minus 3 right parenthesis
4x(x−6)
4 x left parenthesis x minus 6 right parenthesis
(x+6)(x−4)
left parenthesis x plus 6 right parenthesis left parenthesis x minus 4 right parenthesis
2(x−12)
None of the given options simplify to the same expression as 4x^2−3x^2+5x−24.
To find the expression that simplifies to the same expression as 4x^2 − 3x^2 + 5x − 24, we need to factor the given expression.
Step 1: Combine like terms.
4x^2 − 3x^2 + 5x − 24
= (4x^2 − 3x^2) + 5x − 24
= x^2 + 5x − 24
Step 2: Factor the quadratic expression x^2 + 5x − 24.
We need to find two numbers whose product is -24 and whose sum is 5.
The factors of -24 are:
1, -24
-1, 24
2, -12
-2, 12
3, -8
-3, 8
4, -6
-4, 6
Among these factors, the pair that adds up to 5 is 8 and -3.
So, x^2 + 5x − 24 can be factored as:
(x + 8)(x - 3)
Therefore, the expression that simplifies to the same expression as 4x^2 − 3x^2 + 5x − 24 is:
(x + 8)(x - 3)