Factor Polynomials (Order 4) - As Quadratic (With Hint), Coefficient 1

Level 1

This math topic focuses on factoring fourth-order polynomials as quadratic expressions, specifically with a leading coefficient of one. Each problem provides a hint by presenting a related quadratic expression for transformation back into the polynomial variable. The challenges include selecting the correct factorization from given options, aiding learners in understanding how to handle higher-degree polynomials by breaking them down into simpler quadratic components. This content forms part of an introductory unit on factoring higher order polynomials.

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Factor Polynomials (Order 4) - As Quadratic (With Hint), Coefficient 1 Worksheet

Factor Polynomials (Order 4) - As Quadratic (With Hint), Coefficient 1

$A LaTex expression showing t to the power of 4 - 13t to the power of 2 + 36\\ \\ \text{hint:}\\n to the power of 2 - 13n + 36\\n=t to the power of 2$

Factor this higher order polynomial

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

$A LaTex expression showing w to the power of 4 + 6w to the power of 2 + 8\\ \\ \text{hint:}\\r to the power of 2 + 6r + 8\\r=w to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (w to the power of 2 + 4)(w to the power of 2 + 2)

A LaTex expression showing (2w to the power of 2 - 4)(w to the power of 2 + 2)

$A LaTex expression showing p to the power of 4 - 14p to the power of 2 + 45\\ \\ \text{hint:}\\q to the power of 2 - 14q + 45\\q=p to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (p to the power of 2 - 5)(p to the power of 2 - 9)

A LaTex expression showing (p to the power of 2 - 5)(4p to the power of 2 + 9)

$A LaTex expression showing w to the power of 4 - 7w to the power of 2 + 10\\ \\ \text{hint:}\\n to the power of 2 - 7n + 10\\n=w to the power of 2$

Factor this higher order polynomial

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

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

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

Factor this higher order polynomial

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

$A LaTex expression showing z to the power of 4 + 11z to the power of 2 + 18\\ \\ \text{hint:}\\p to the power of 2 + 11p + 18\\p=z to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (z to the power of 2 + 9)(7z to the power of 2 - 2)

A LaTex expression showing (z to the power of 2 + 9)(z to the power of 2 + 2)

$A LaTex expression showing x to the power of 4 + 11x to the power of 2 + 24\\ \\ \text{hint:}\\n to the power of 2 + 11n + 24\\n=x to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (x to the power of 2 + 8)(x to the power of 2 + 3)

A LaTex expression showing (x to the power of 2 - 8)(5x to the power of 2 + 3)

$A LaTex expression showing m to the power of 4 + 9m to the power of 2 + 20\\ \\ \text{hint:}\\t to the power of 2 + 9t + 20\\t=m to the power of 2$

Factor this higher order polynomial

A LaTex expression showing (1m to the power of 2 - 4)(m to the power of 2 + 5)

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