Quiz 7 WOODJINA ALDAJU Question 9 of 10 Step 1 of 1 01:06:43 Completely factor the trinomial, if possible. \[ 2 x^{2}+14 x+24 \] Answer How to enter your answer (opens in new window) 2 Points Keypad Keyboard Shortcuts Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used. Not Factorable
Solution
Step 1 ：The given trinomial is \(2x^{2} + 14x + 24\).
Step 2 ：We need to find two numbers that add up to 14 and multiply to 48. The numbers that satisfy these conditions are 6 and 8.
Step 3 ：We can write the middle term (14x) as the sum of 6x and 8x. So, the trinomial becomes \(2x^{2} + 6x + 8x + 24\).
Step 4 ：Next, we factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us \(2x(x + 3) + 8(x + 3)\).
Step 5 ：We can see that \((x + 3)\) is a common factor. Factoring out \((x + 3)\) gives us \((x + 3)(2x + 8)\).
Step 6 ：We can further factor out a 2 from the second term to get \(2(x + 3)(x + 4)\).
Step 7 ：So, the completely factored form of the given trinomial \(2x^{2} + 14x + 24\) is \(\boxed{2(x + 3)(x + 4)}\).
