Explore: Finding Unknowns in Polynomial Equations Solutions

Finding an unknown coefficient or constant in a polynomial equation combines the operations with polynomials and solving equations.
When comparing like terms in an equation, it is important to look at both sides of the equation.
To check your answer, substitute the values back into the given equation. Then make sure both sides of the equation are equal .

Find the missing values, M and N.
$(2 x + M) (N x - 1) = 8 x^{2} + 10 x - 3$

Implement

$2 N x^{2} - 2 x + M N x - M = 8 x^{2} + 10 x - 3$

$\begin{array}{rcl} 2 N x^{2} & = & 8 x^{2} \\ 2 N & = & 8 \\ N & = & 4 \end{array}$

$\begin{array}{rcl} - M & = & - 3 \\ M & = & 3 \end{array}$

$(2 x + 3) (4 x - 1) = 8 x^{2} + 10 x - 3$

Explain

Find the missing value, P.
$(x^{2} - P x + 7) - (6 x^{2} - 5 x + 3) = - 5 x^{2} - 3 x + 4$

$x^{2} - P x + 7 - 6 x^{2} + 5 x - 3 = - 5 x^{2} - 3 x + 4$

$\begin{array}{rcl} - P x + 5 x & = & - 3 x \\ - P + 5 & = & - 3 \\ - P & = & - 8 \\ P & = & 8 \end{array}$

Check
$\begin{array}{rcl} (x^{2} - 8 x + 7) - (6 x^{2} - 5 x + 3) & = & - 5 x^{2} - 3 x + 4 ✓ \end{array}$