QuestionFactor the trinomial: $5x^{2} + 24x + 16$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is a trinomial of the form $ax^ + bx + c$ . We need to factor this trinomial into two binomial expressions of the form $(dx + e)(fx + g)$

STEP 2

The trinomial $5x^2 +24x +16$ can be factored by finding two numbers that multiply to $a \cdot c =5 \cdot16 =80$ and add to $b =24$ .

STEP 3

The two numbers that satisfy these conditions are8 and10, since $8 \cdot10 =80$ and $8 +10 =24$ .

STEP 4

We rewrite the middle term of the trinomial as the sum of the terms $8x$ and $10x$ . This gives us $x^2 +8x +16x +16$

STEP 5

We group the terms to prepare for factoring by grouping $(5x^2 +8x) + (16x +16)$

STEP 6

We factor out the greatest common factor from each group $x(5x +8) +2(8x +10)$

STEP 7

We notice that the expressions in the parentheses are not the same, which is necessary for factoring by grouping. To fix this, we need to factor out a2 from the second group $x(5x +) +2(4x +)$

STEP 8

Now that the expressions in the parentheses are the same, we can factor by grouping $(x +2)(5x +8)$ So, the factored form of the trinomial $5x^2 +24x +16$ is $(x +2)(5x +8)$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms