Polynomials: Factoring trinomials of the form x^2 + bx + c where c is positive Quiz
Quiz Overview
Description
This quiz focuses on factoring trinomials of the form
x^2 + bx + c by examining the constant term c (where c is positive). The first step is to examine the constant term, c, and identify two factors of c, which when multiplied give c but when added give b. Because the constant term, c, is positive, the two factors will either be both positive or both negative. Then express the middle term, bx, as the sum of these two factors. Next factor the first two terms and factor the last two terms. The final step is to express as the product of two binomials, (x + p)(x+q).
Example:
x^2 + 5x + 6
The two factors which when multiplied give 6 but when added give 5 are 3 and 2, so express 5x as 3x + 2x.
x^2 + 3x + 2x + 6, Now factor the GCF from the first two terms and then from the last two terms.
x(x + 3) + 2(x + 3)
(x + 2)(x + 3)
x^2 + bx + c by examining the constant term c (where c is positive). The first step is to examine the constant term, c, and identify two factors of c, which when multiplied give c but when added give b. Because the constant term, c, is positive, the two factors will either be both positive or both negative. Then express the middle term, bx, as the sum of these two factors. Next factor the first two terms and factor the last two terms. The final step is to express as the product of two binomials, (x + p)(x+q).
Example:
x^2 + 5x + 6
The two factors which when multiplied give 6 but when added give 5 are 3 and 2, so express 5x as 3x + 2x.
x^2 + 3x + 2x + 6, Now factor the GCF from the first two terms and then from the last two terms.
x(x + 3) + 2(x + 3)
(x + 2)(x + 3)