Factor Polynomials (Order 4) - As Quadratic (With Hint), Coefficient N

Level 1

This math topic focuses on the skill of factoring higher order polynomials, specifically quartic (fourth-order) polynomials. The problems guide students to factor these polynomials by transforming them into quadratic forms using provided hints. Each question presents a polynomial and a suggested substitution, hinting at a transformation into a simpler quadratic equation for easier factoring, with multiple-choice answers provided for each problem. This approach educates on identifying and applying appropriate algebraic transformations and factoring techniques to solve quadratic and higher-order polynomial equations.

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 (With Hint), Coefficient N Worksheet

Factor Polynomials (Order 4) - As Quadratic (With Hint), Coefficient N

$A LaTex expression showing 49r to the power of 4 + 70r to the power of 2 + 16\\ \\ \text{hint:}\\q to the power of 2 + 10q + 16\\q=7r to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (7r to the power of 2 + 2)(7r to the power of 2 + 8)

A LaTex expression showing (49r to the power of 2 + 2)(1649r to the power of 2 - 8)

$A LaTex expression showing 16y to the power of 4 - 52y to the power of 2 + 40\\ \\ \text{hint:}\\p to the power of 2 - 13p + 40\\p=4y to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (40y to the power of 2 - 8)(y to the power of 2 + 5)

A LaTex expression showing (4y to the power of 2 - 8)(4y to the power of 2 - 5)

$A LaTex expression showing 36m to the power of 4 - 4\\ \\ \text{hint:}\\t to the power of 2 - 4\\t=6m to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (36m to the power of 2 + 6)(36m to the power of 2 - 9)

A LaTex expression showing (6m to the power of 2 + 2)(6m to the power of 2 - 2)

$A LaTex expression showing 16m to the power of 4 + 32m to the power of 2 + 15\\ \\ \text{hint:}\\q to the power of 2 + 8q + 15\\q=4m to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (4m to the power of 2 + 5)(4m to the power of 2 + 3)

A LaTex expression showing (15m to the power of 2 + 5)(m to the power of 2 - 3)

$A LaTex expression showing 25w to the power of 4 - 49\\ \\ \text{hint:}\\q to the power of 2 - 49\\q=5w to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (25w to the power of 2 - 7)(25w to the power of 2 - 7)

A LaTex expression showing (5w to the power of 2 + 7)(5w to the power of 2 - 7)

$A LaTex expression showing 64r to the power of 4 - 104r to the power of 2 + 36\\ \\ \text{hint:}\\m to the power of 2 - 13m + 36\\m=8r to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (8r to the power of 2 - 4)(8r to the power of 2 - 9)

A LaTex expression showing (r to the power of 2 - 4)(64r to the power of 2 + 9)

$A LaTex expression showing 36t to the power of 4 - 84t to the power of 2 + 48\\ \\ \text{hint:}\\p to the power of 2 - 14p + 48\\p=6t to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (6t to the power of 2 - 6)(6t to the power of 2 - 8)

A LaTex expression showing (t to the power of 2 - 6)(48t to the power of 2 + 8)

$A LaTex expression showing 25r to the power of 4 + 5r to the power of 2 - 30\\ \\ \text{hint:}\\w to the power of 2 + 1w - 30\\w=5r to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (25r to the power of 2 - 5)(25r to the power of 2 - 6)

A LaTex expression showing (5r to the power of 2 - 5)(5r to the power of 2 + 6)