Answer :
Let's solve the problem step-by-step to determine which expression is equivalent to [tex]\( 2x^2 - 14x + 24 \)[/tex].
### Step 1: Identify the quadratic polynomial
The given quadratic expression is:
[tex]\[ 2x^2 - 14x + 24 \][/tex]
### Step 2: Factor the quadratic expression
We need to find factors that multiply to give the quadratic expression and whose product expands back to the original expression.
### Step 3: Rewriting the quadratic expression in factored form
We can express the quadratic expression in the form:
[tex]\[ 2(x - 4)(x - 3) \][/tex]
### Step 4: Verification (optional step):
To ensure correctness, we can expand the factored form:
[tex]\[ 2(x - 4)(x - 3) = 2 [x^2 - 3x - 4x + 12] = 2 [x^2 - 7x + 12] = 2x^2 - 14x + 24 \][/tex]
Thus, the correct factored form of the quadratic expression [tex]\( 2x^2 - 14x + 24 \)[/tex] is:
[tex]\[ 2(x - 4)(x - 3) \][/tex]
### Step 5: Select the answer from the given options
The equivalent expression is:
B. [tex]\( 2(x - 3)(x - 4) \)[/tex]
The correct answer is [tex]\( \boxed{2 (x - 3) (x - 4)} \)[/tex].
### Step 1: Identify the quadratic polynomial
The given quadratic expression is:
[tex]\[ 2x^2 - 14x + 24 \][/tex]
### Step 2: Factor the quadratic expression
We need to find factors that multiply to give the quadratic expression and whose product expands back to the original expression.
### Step 3: Rewriting the quadratic expression in factored form
We can express the quadratic expression in the form:
[tex]\[ 2(x - 4)(x - 3) \][/tex]
### Step 4: Verification (optional step):
To ensure correctness, we can expand the factored form:
[tex]\[ 2(x - 4)(x - 3) = 2 [x^2 - 3x - 4x + 12] = 2 [x^2 - 7x + 12] = 2x^2 - 14x + 24 \][/tex]
Thus, the correct factored form of the quadratic expression [tex]\( 2x^2 - 14x + 24 \)[/tex] is:
[tex]\[ 2(x - 4)(x - 3) \][/tex]
### Step 5: Select the answer from the given options
The equivalent expression is:
B. [tex]\( 2(x - 3)(x - 4) \)[/tex]
The correct answer is [tex]\( \boxed{2 (x - 3) (x - 4)} \)[/tex].
