Question

# Factor the given polynomial. 15x^2+7x-4

Polynomial factorization
Factor the given polynomial.
$$\displaystyle{15}{x}^{{2}}+{7}{x}-{4}$$

2021-03-09

Step 1
$$\displaystyle{a}{x}^{{2}}+{b}{x}+{c}$$
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
$$\displaystyle{15}{x}^{{2}}+{7}{x}-{4}$$
$$\displaystyle{15}{x}^{{2}}+{12}{x}-{5}{x}-{4}\ldots\ldots\ldots..{\left[{12}\cdot{\left(-{5}\right)}={15}\cdot{\left(-{4}\right)}\right]}$$
$$3x ( 5x + 4) -1 ( 5x +4 )$$
$$(3x -1) ( 5x + 4)$$