# Question #da2fb

Oct 31, 2016

$2. 9$
$4. 10$

#### Explanation:

I'll do questions $2$ and $4$.

$2.$ We need to factor the numbers within the square roots.

$\implies 5 \sqrt{4 \times 3} - 2 \sqrt{25 \times 3} + 3 \sqrt{9 \times 3}$

$\implies 5 \left(2\right) \sqrt{3} - 2 \left(5\right) \sqrt{3} + 3 \left(3\right) \sqrt{3}$

$\implies 10 \sqrt{3} - 10 \sqrt{3} + 9 \sqrt{3}$

$\implies 9 \sqrt{3}$

The numerical coefficient is $9$.

$4.$ This is a trinomial factoring problem. When we want to factor a trinomial of the form $y = a {x}^{2} + b x + c , a \ne 1 , 0$, we need to find two numbers that multiply to $a c$ and that add to $b$.

$\implies 10 {r}^{2} - 8 r + 35 r - 28$

$\implies 2 r \left(5 r - 4\right) + 7 \left(5 r - 4\right)$

$\implies \left(2 r + 7\right) \left(5 r - 4\right)$

The value of $a + b + c + d$ is $2 + 7 + 5 - 4 = 10$

Hopefully this helps!