Find the second factor of 9x^2 + 16 + 1

Question

asked Jun 1, 2024 107k views

1 Answer

LeafGlowPath · Answer 1 · 2024-06-07T03:56:11+0000

Answer:

$\sf (3x + 1)$

Explanation:

To find the second factor, we need to determine what to multiply
$\sf (3x + 1)$ by to get the given product
$\sf 9x^2 + 6x + 1$ .

Let the second factor be
$\sf (ax + b)$ . Now, we can perform the multiplication and equate it to the given product:

$\sf (3x + 1)(ax + b) = 9x^2 + 6x + 1$

Now, distribute the terms:

$\sf 3x(ax + b) + 1(ax + b) = 9x^2 + 6x + 1$

Simplify further:

$\sf 3ax^2 + 3bx + ax + b = 9x^2 + 6x + 1$

Now, equate the corresponding coefficients:

Coefficient of
$\sf x^2$ :
$\sf 3a = 9$

$\sf \Rightarrow$
$\sf a =(9)/(3)= 3$

2. Coefficient of
$\sf x$ :
$\sf 3b + a = 6$

$\sf \Rightarrow$
$\sf 3b + 3 = 6$

$\sf \Rightarrow$
$\sf b =(6-3)/(3)=1$

So, the second factor is
$\sf (ax + b) = (3x + 1)$ .