Solving Polynomial Equations

We want to solve the given equation by factoring.

Let's start by writing

7 x

as a difference.

2 x^{2} + 7 x - 4 = 0

WriteDiffWrite as a difference

2 x^{2} + 8 x - x - 4 = 0

Factor out

2 x & - 1

FactorOutFactor out

2 x

2 x (x + 4) - x - 4 = 0

FactorOutFactor out

- 1

2 x (x + 4) - (x + 4) = 0

FactorOutFactor out

(x + 4)

(x + 4) (2 x - 1) = 0

To solve this equation, we will apply the Zero Product Property.

(x + 4) (2 x - 1) = 0

ZeroProdPropUse the Zero Product Property

x + 4 = 0 2 x - 1 = 0 (I) (II)

(I):

LHS - 4 = RHS - 4

x = - 4 2 x - 1 = 0

(II):

LHS + 1 = RHS + 1

x = - 4 2 x = 1

(II):

LHS / 2 = RHS / 2

x_{1} = - 4 x_{2} = \frac{1}{2}

Solving Polynomial Equations 1.19 - Solution