Algebra Know-It-ALL

Tables 22-1 through 22-5 show how we can convert the above equations to polynomial
standard form. Note the last step in Table 22-5. To be “true to form,” the polynomial should
show the terms by descending powers of the variable. The term containing x^2 should come
first, then the term containing x, and finally the constant.

Table 22-1. Conversion of x^2 = 2 x + 3 to polynomial

standard form.

Statements Reasons

x^2 = 2 x+ 3 This is the equation we are given

x^2 − 2 x= 3 Subtract 2x from each side

x^2 − 2 x− 3 = 0 Subtract 3 from each side

Table 22-2. Conversion of x= 4 x^2 − 7 to polynomial

standard form.

Statements Reasons

x= 4 x^2 − 7 This is the equation we are given

− 4 x^2 +x=−7 Subtract 4x^2 from each side

− 4 x^2 +x+ 7 = 0 Add 7 to each side

Table 22-3. Conversion of x^2 + 4 x= 7 +x to

polynomial standard form.

Statements Reasons

x^2 + 4 x= 7 +x This is the equation we are given

x^2 + 4 x− 7 =x Subtract 7 from each side

x^2 + 3 x− 7 = 0 Subtract x from each side

Table 22-4. Conversion of x− 2 =− 8 x^2 − 22 to

polynomial standard form.

Statements Reasons

x− 2 =− 8 x^2 − 22 This is the equation we are given

8 x^2 +x− 2 =−22 Add 8 x^2 to each side

8 x^2 +x+ 20 = 0 Add 22 to each side

Table 22-5. Conversion of 3 +x= 2 x^2 to polynomial

standard form.

Statements Reasons

3 +x= 2 x^2 This is the equation we are given

− 2 x^2 + 3 +x= 0 Subtract 2x^2 from each side

− 2 x^2 +x+ 3 = 0 Commutative law for addition

Second-Degree Polynomials 365