Factor Polynomials (Order 4) - As Quadratic (No Hint), Coefficient N

Level 1

This topic focuses on practicing skills related to factoring higher order polynomials, more specifically, polynomials of fourth order. Each problem provides a polynomial in one variable where coefficients involve integer numbers, designated by various letters such as w, y, r, z, n, and p. The task is to factorize these polynomials effectively without the aid of hints, challenging the learner to recognize patterns and apply factoring techniques independently. Several problems include multiple-choice answers illustrating different factorization outcomes, enhancing comprehension through comparison and error analysis. This helps in deepening the understanding of polynomial factorization in algebra.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Factor Polynomials (Order 4) - As Quadratic (No Hint), Coefficient N Worksheet

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Factor Polynomials (Order 4) - As Quadratic (No Hint), Coefficient N
1
Factor this higher order polynomial
A LaTex expression showing 16w to the power of 4 + 32w to the power of 2 + 12
a A LaTex expression showing (4w to the power of 2 + 6)(4w to the power of 2 + 2)
b A LaTex expression showing (12w to the power of 2 - 6)(w to the power of 2 + 2)
2
Factor this higher order polynomial
A LaTex expression showing 25y to the power of 4 - 70y to the power of 2 + 45
a A LaTex expression showing (25y to the power of 2 + 5)(25y to the power of 2 + 9)
b A LaTex expression showing (5y to the power of 2 - 5)(5y to the power of 2 - 9)
3
A LaTex expression showing 9r to the power of 4 - 36
Factor this higher order polynomial
a A LaTex expression showing (3r to the power of 2 + 6)(3r to the power of 2 - 6)
b A LaTex expression showing (9r to the power of 2 - 8)(9r to the power of 2 + 6)
4
Factor this higher order polynomial
A LaTex expression showing 81z to the power of 4 + 99z to the power of 2 + 24
a A LaTex expression showing (9z to the power of 2 + 8)(9z to the power of 2 + 3)
b A LaTex expression showing (24z to the power of 2 + 8)(z to the power of 2 - 3)
5
Factor this higher order polynomial
A LaTex expression showing 64n to the power of 4 - 104n to the power of 2 + 42
a A LaTex expression showing (8n to the power of 2 - 6)(8n to the power of 2 - 7)
b A LaTex expression showing (64n to the power of 2 - 6)(64n to the power of 2 - 7)
6
Factor this higher order polynomial
A LaTex expression showing 49n to the power of 4 - 14n to the power of 2 - 8
a A LaTex expression showing (7n to the power of 2 - 4)(7n to the power of 2 + 2)
b A LaTex expression showing (8n to the power of 2 - 4)(n to the power of 2 + 2)
7
Factor this higher order polynomial
A LaTex expression showing 81p to the power of 4 + 99p to the power of 2 + 30
a A LaTex expression showing (81p to the power of 2 + 6)(8181p to the power of 2 - 5)
b A LaTex expression showing (9p to the power of 2 + 6)(9p to the power of 2 + 5)
8
Factor this higher order polynomial
A LaTex expression showing 16x to the power of 4 + 36x to the power of 2 + 20
a A LaTex expression showing (16x to the power of 2 + 4)(16x to the power of 2 - 5)
b A LaTex expression showing (4x to the power of 2 + 4)(4x to the power of 2 + 5)