Question

Tell whether the quadratic expression can be factored with integer coefficients. If it can, find the factors. $$b^{2}+14 b+35$$

Short answer

Yes, the quadratic expression can be factored with integer coefficients. The factors are \((b+5)\) and \((b+9)\).

Step-by-step solution

Identify the coefficients

First, identify the coefficients in the quadratic expression. Here, \(a=1\), \(b=14\), and \(c=35\).

Search for two numbers that add up to b and multiply to c

Now, find two numbers that both add up to \(b=14\) and multiply to \(c=35\). These numbers are 5 and 9, because \(5+9=14\) and \(5 \times 9=35\).

Write down the factors

With these two numbers, write down the factors of the expression: \(b^{2}+14b+35\) can be factored as \((b+5)(b+9)\).