Polynomials: Factoring trinomials of the form x^4 + bx^2 + c Quiz
Quiz Overview
Description
This quiz focuses on factoring trinomials of the form
x^4 + bx^2 + c. 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. Then express the middle term, bx^2, 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^2 + p)(x^2 + q).
Example:
x^4 - x^2 - 110
The two factors which when multiplied give -110 but when added give -1 are 10 and -11, so express -x^2 as
10x^2 - 11x^2.
x^4 + 10x^2 - 11x^2 - 110, Now factor the GCF from the first two terms and then from the last two terms.
x^2(x^2 + 10) - 11(x^2 + 10)
(x^2 - 11)(x^2 + 10)
x^4 + bx^2 + c. 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. Then express the middle term, bx^2, 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^2 + p)(x^2 + q).
Example:
x^4 - x^2 - 110
The two factors which when multiplied give -110 but when added give -1 are 10 and -11, so express -x^2 as
10x^2 - 11x^2.
x^4 + 10x^2 - 11x^2 - 110, Now factor the GCF from the first two terms and then from the last two terms.
x^2(x^2 + 10) - 11(x^2 + 10)
(x^2 - 11)(x^2 + 10)