Algebra Examples

$8 x^{4} - 4 x^{3} + 10 x^{2}$ , $2 x^{2}$

Step 1

If $2 x^{2}$ is a factor of the polynomial, then it must be a root of the polynomial. To determine if the factor is a root, first find the value of $x$ when the factor $2 x^{2}$ is equal to $0$ .

$2 x^{2} = 0$

Step 2

Solve the equation for $x$ .

$x = 0$

Step 3

Replace $x$ with $0$ in $8 x^{4} - 4 x^{3} + 10 x^{2}$ to find if it is a root of the polynomial.

$8 {(0)}^{4} - 4 {(0)}^{3} + 10 {(0)}^{2}$

Step 4

Simplify each term.

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Step 4.1

Raising $0$ to any positive power yields $0$ .

$8 \cdot 0 - 4 {(0)}^{3} + 10 {(0)}^{2}$

Step 4.2

Multiply $8$ by $0$ .

$0 - 4 {(0)}^{3} + 10 {(0)}^{2}$

Step 4.3

Raising $0$ to any positive power yields $0$ .

$0 - 4 \cdot 0 + 10 {(0)}^{2}$

Step 4.4

Multiply $- 4$ by $0$ .

$0 + 0 + 10 {(0)}^{2}$

Step 4.5

Raising $0$ to any positive power yields $0$ .

$0 + 0 + 10 \cdot 0$

Step 4.6

Multiply $10$ by $0$ .

$0 + 0 + 0$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $0$ and $0$ .

$0 + 0$

Step 5.2

Add $0$ and $0$ .

$0$

Step 6

Since $x = 0$ is a root of the polynomial, $2 x^{2}$ is a factor of the polynomial.

$2 x^{2}$ is a factor of $8 x^{4} - 4 x^{3} + 10 x^{2}$