Fundamental theorem of algebra - Polynomial Functions

Fundamental theorem of algebra

Basic concepts:
Factoring perfect square trinomials: $(a + b)^2 = a^2 + 2ab + b^2$ or $(a - b)^2 = a^2 - 2ab + b^2$
Factoring trinomials
Polynomial synthetic division

Related concepts:
Complex numbers and complex planes

Lessons

Notes:

Fundamental Theorem of Algebra:
• Every polynomial can be factored into a product of linear factors and irreducible quadratic factors.
• A degree n polynomial has exactly n roots.

2.
Discuss the Possible Combinations of Roots
State the possible combinations of roots for each polynomial:

Fundamental theorem of algebra

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AlgebraFactoring perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2(a+b)​2​​=a​2​​+2ab+b​2​​ or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2(a−b)​2​​=a​2​​−2ab+b​2​​

AlgebraFactoring trinomials

AlgebraPolynomial synthetic division

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Factoring perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2(a+b)​2​​=a​2​​+2ab+b​2​​ or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2(a−b)​2​​=a​2​​−2ab+b​2​​

Factoring trinomials

Polynomial synthetic division

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Lessons

Notes:

Fundamental Theorem of Algebra: • Every polynomial can be factored into a product of linear factors and irreducible quadratic factors. • A degree n polynomial has exactly n roots.

1.

2.

Discuss the Possible Combinations of Roots State the possible combinations of roots for each polynomial:

a)

P(x)=a7x7+a6x6+a5x5+a4x4+a3x3+a2x2+a1x+a0P(x) = a_7x^7 + a_6x^6 + a_5x^5 + a_4x^4 + a_3x^3 + a_2x^2 + a_1x + a_0P(x)=a​7​​x​7​​+a​6​​x​6​​+a​5​​x​5​​+a​4​​x​4​​+a​3​​x​3​​+a​2​​x​2​​+a​1​​x+a​0​​

b)

P(x)=x4+...... P(x) = x^4 + ......P(x)=x​4​​+......

Fundamental theorem of algebra

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Algebra
Factoring perfect square trinomials: $(a + b)^2 = a^2 + 2ab + b^2$ or $(a - b)^2 = a^2 - 2ab + b^2$

Algebra
Factoring trinomials

Algebra
Polynomial synthetic division

Factoring perfect square trinomials: $(a + b)^2 = a^2 + 2ab + b^2$ or $(a - b)^2 = a^2 - 2ab + b^2$

or

Fundamental Theorem of Algebra:
• Every polynomial can be factored into a product of linear factors and irreducible quadratic factors.
• A degree n polynomial has exactly n roots.

Discuss the Possible Combinations of Roots
State the possible combinations of roots for each polynomial:

$P(x) = a_7x^7 + a_6x^6 + a_5x^5 + a_4x^4 + a_3x^3 + a_2x^2 + a_1x + a_0$

$P(x) = x^4 + ......$