Step 1

Let consider a quadratic polynomial

\(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}\)

Steps to factorize quadratic polynomial

i) Multiply the highest degree and lowest degree coefficient i.e. a and c

ii) Add or subtract two numbers to find the coefficient b such that multiplication of these two give the multiplication from step i)

iii) write in factorization form by taking common part out from the polynomial

Step 2

Given polynomial

\(\displaystyle{15}{x}^{{2}}+{7}{x}-{4}\)

\(\displaystyle{15}{x}^{{2}}+{12}{x}-{5}{x}-{4}\ldots\ldots\ldots..{\left[{12}\cdot{\left(-{5}\right)}={15}\cdot{\left(-{4}\right)}\right]}\)

\(3x ( 5x + 4) -1 ( 5x +4 )\)

\((3x -1) ( 5x + 4)\)