Question

Tell whether the quadratic expression can be factored with integer coefficients. If it can, find the factors. $$w^{2}-6 w+16$$

Short answer

No, the quadratic expression \(w^{2}-6 w+16\) cannot be factored with integer coefficients because its discriminant is negative.

Step-by-step solution

Calculate the Discriminant

The discriminant of a quadratic equation of the form \( ax^2+bx+c \) is given by \( b^2-4ac \). For the quadratic equation \( w^2-6w+16 \), \( a \) is equals to 1, \( b \) equals to -6, and \( c \) equals to 16. Therefore, the discriminant is \( (-6)^2-4*1*16 = 36-64 = -28

Analyzing the Discriminant

The discriminant is negative (-28), which tells us that there are no real solutions for \( w \) in the quadratic equation. Therefore, the quadratic expression can't be factored with integer coefficients.