What is the completely factored form of the expression 16x² + 8x + 32?

Solution:

Given expression is 16x² + 8x + 32

Grouping the common factors,

16x² + 8x + 32

= 8 [2x² + x + 4]

Here D = b² -4ac 

= -31 < 0.

Note:

For a quadratic expression ax² + bx + c, cannot be factored into linear factors if the discriminant b² -4ac < 0.

Hence the completely factored form of the expression 16x² + 8x + 32 is 8 [2x² + x + 4]

What is the completely factored form of the expression 16x² + 8x + 32?

Summary:

The factored form of the expression 16x² + 8x + 32 is 8[2x² + x + 4].