Factor Polynomials (Order 4) - As Quadratic (No Hint), Coefficient 1

Level 1

This math topic focuses on factoring polynomials of the fourth order, treated as quadratic expressions without hints and where the leading coefficient is 1. The problems require recognizing and applying polynomial factoring techniques to solve expressions that involve complex structural forms, transforming quartic equations into products of quadratic factors. Each problem presents the polynomial and requires students to factor it correctly out of two possible answers, fostering skills in recognizing patterns and applying polynomial division.

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 1 Worksheet

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Factor Polynomials (Order 4) - As Quadratic (No Hint), Coefficient 1
1
Factor this higher order polynomial
A LaTex expression showing w to the power of 4 + 2w to the power of 2 - 15
a A LaTex expression showing (w to the power of 2 - 3)(w to the power of 2 + 5)
b A LaTex expression showing (w to the power of 2 + 3)(w to the power of 2 - 5)
2
A LaTex expression showing t to the power of 4 + 6t to the power of 2 - 16
Factor this higher order polynomial
a A LaTex expression showing (t to the power of 2 - 2)(t to the power of 2 - 8)
b A LaTex expression showing (t to the power of 2 - 2)(t to the power of 2 + 8)
3
Factor this higher order polynomial
A LaTex expression showing w to the power of 4 - 1w to the power of 2 - 12
a A LaTex expression showing (w to the power of 2 - 4)(w to the power of 2 - 3)
b A LaTex expression showing (w to the power of 2 - 4)(w to the power of 2 + 3)
4
Factor this higher order polynomial
A LaTex expression showing w to the power of 4 + 16w to the power of 2 + 63
a A LaTex expression showing (w to the power of 2 + 9)(w to the power of 2 + 7)
b A LaTex expression showing (2w to the power of 2 - 9)(w to the power of 2 + 7)
5
Factor this higher order polynomial
A LaTex expression showing n to the power of 4 + 1n to the power of 2 - 20
a A LaTex expression showing (n to the power of 2 + 4)(20n to the power of 2 - 5)
b A LaTex expression showing (n to the power of 2 - 4)(n to the power of 2 + 5)
6
Factor this higher order polynomial
A LaTex expression showing y to the power of 4 - 17y to the power of 2 + 72
a A LaTex expression showing (y to the power of 2 - 8)(y to the power of 2 - 9)
b A LaTex expression showing (y to the power of 2 - 8)(1y to the power of 2 + 9)
7
Factor this higher order polynomial
A LaTex expression showing x to the power of 4 - 2x to the power of 2 - 8
a A LaTex expression showing (x to the power of 2 - 4)(x to the power of 2 + 2)
b A LaTex expression showing (x to the power of 2 - 4)(8x to the power of 2 + 2)
8
Factor this higher order polynomial
A LaTex expression showing q to the power of 4 - 1q to the power of 2 - 42
a A LaTex expression showing (q to the power of 2 - 7)(q to the power of 2 + 6)
b A LaTex expression showing (1q to the power of 2 + 7)(q to the power of 2 - 6)