factor completely.
①
$10x^2 + 100x + 250$
②
$3x^2 - 24x + 48$
③
$9x^2 + 30x + 25$
④
$98x^2 + 84x + 18$

Question

Accepted Answer

### Problem 1: $10x^2 + 100x + 250$
# Explanation:
## Step1: Factor out the GCF
First, find the greatest common factor (GCF) of $10x^2$, $100x$, and $250$. The GCF of 10, 100, and 250 is 10.
$10x^2 + 100x + 250 = 10(x^2 + 10x + 25)$
## Step2: Factor the quadratic
The quadratic $x^2 + 10x + 25$ is a perfect square trinomial, since $x^2=(x)^2$, $25 = 5^2$, and $10x = 2 \cdot x \cdot 5$. So, $x^2 + 10x + 25=(x + 5)^2$.
# Answer:
$10(x + 5)^2$

### Problem 2: $3x^2 - 24x + 48$
# Explanation:
## Step1: Factor out the GCF
The GCF of $3x^2$, $-24x$, and $48$ is 3.
$3x^2 - 24x + 48 = 3(x^2 - 8x + 16)$
## Step2: Factor the quadratic
The quadratic $x^2 - 8x + 16$ is a perfect square trinomial, since $x^2=(x)^2$, $16 = 4^2$, and $-8x=-2\cdot x\cdot4$. So, $x^2 - 8x + 16=(x - 4)^2$.
# Answer:
$3(x - 4)^2$

### Problem 3: $9x^2 + 30x + 25$
# Explanation:
## Step1: Identify the perfect square terms
We have $9x^2=(3x)^2$ and $25 = 5^2$.
## Step2: Check the middle term
The middle term is $30x$, and $2\cdot3x\cdot5 = 30x$, which matches the middle term of the trinomial. So, this is a perfect square trinomial.
$9x^2 + 30x + 25=(3x + 5)^2$
# Answer:
$(3x + 5)^2$

### Problem 4: $98x^2 + 84x + 18$
# Explanation:
## Step1: Factor out the GCF
The GCF of 98, 84, and 18 is 2.
$98x^2 + 84x + 18 = 2(49x^2 + 42x + 9)$
## Step2: Factor the quadratic
The quadratic $49x^2 + 42x + 9$ is a perfect square trinomial, since $49x^2=(7x)^2$, $9 = 3^2$, and $42x = 2\cdot7x\cdot3$. So, $49x^2 + 42x + 9=(7x + 3)^2$.
# Answer:
$2(7x + 3)^2$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: \(10x^2 + 100x + 250\)

Step1: Factor out the GCF

Step2: Factor the quadratic

Step1: Factor out the GCF

Step2: Factor the quadratic

Step1: Identify the perfect square terms

Step2: Check the middle term

Answer:

Problem 2: \(3x^2 - 24x + 48\)