Question

Factor 16x^2 + 49. Check your work.

Answer 1

Answer:

$16x^2+49=(x-\frac{7i}{4})(x+\frac{7i}{4})$

Step-by-step explanation:

Given : Expression $16x^2+49$

To find : Factor the expression ?

Solution :

The given expression is a quadratic function $y=ax^2+bx+c$ the solution is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

On comparing with general form,

a=16, b=0, c=49

Substitute in the formula,

$x=\frac{-0\pm\sqrt{0^2-4(16)(49)}}{2(16)}$              

$x=\frac{\pm\sqrt{-3136}}{32}$          

$x=\frac{\pm56i}{32}$      

$x=\frac{56i}{32},\frac{-56i}{32}$      

$x=\frac{7i}{4},\frac{-7i}{4}$              

Factors are $(x-\frac{7i}{4}),(x+\frac{7i}{4})$        

Therefore, $16x^2+49=(x-\frac{7i}{4})(x+\frac{7i}{4})$