10. $$ 2 x^{2}-24 x+70 $$ 12. $$ 44+15 a+a^{2} $$

Question

UpStudy AI · Accepted Answer

Sure, let's factor each of the given quadratic expressions.

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**10. $$ 2x^{2} - 24x + 70 $$**

**Step 1: Factor Out the Greatest Common Factor (GCF)**
  
The GCF of the terms $$2x^2$$, $$-24x$$, and $$70$$ is **2**.

$$
2x^{2} - 24x + 70 = 2(x^{2} - 12x + 35)
$$

**Step 2: Factor the Quadratic Inside the Parentheses**

We need to factor $$x^{2} - 12x + 35$$. We look for two numbers that multiply to **35** and add up to **-12**.

- **Factors of 35:** 1 & 35, 5 & 7
- **Which pair adds to -12?** $$ -5 $$ and $$ -7 $$ (since $$-5 \times -7 = 35$$ and $$-5 + -7 = -12$$)

$$
x^{2} - 12x + 35 = (x - 5)(x - 7)
$$

**Final Factored Form:**

$$
2x^{2} - 24x + 70 = 2(x - 5)(x - 7)
$$

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**12. $$ a^{2} + 15a + 44 $$**

**Step 1: Factor the Quadratic**

We need to factor $$a^{2} + 15a + 44$$. We look for two numbers that multiply to **44** and add up to **15**.

- **Factors of 44:** 1 & 44, 2 & 22, 4 & 11
- **Which pair adds to 15?** $$4$$ and $$11$$ (since $$4 \times 11 = 44$$ and $$4 + 11 = 15$$)

$$
a^{2} + 15a + 44 = (a + 4)(a + 11)
$$

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**Summary of Factored Forms:**

10. $$ 2x^{2} - 24x + 70 = 2(x - 5)(x - 7) $$

12. $$ a^{2} + 15a + 44 = (a + 4)(a + 11) $$
10. $$ 2x^{2} - 24x + 70 = 2(x - 5)(x - 7) $$ 12. $$ a^{2} + 15a + 44 = (a + 4)(a + 11) $$

10. \( 2 x^{2}-24 x+70 \) 12. \( 44+15 a+a^{2} \)