Question

Factor the expression over the complex numbers. PLEASE HELP GIVING 25 POINTS!!!!!!!!!!!
1) x^2+20
2) y^2+49
3) y^4-16
4) y^4+12y^2+36
5) y^3+2y^2+16y+32

Answer 1

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Heya

1) x² + 20

= (x)² + (√20)²

Using identity

a² + b² = (a + b)² - 2ab

= (x + √20)² - 2(x)(√20)

= (x + √20)² - 2(x)(√2 × 2 × 5)

= (x + √20)² - 4√5x


2) y² + 49

= (y)² + (7)²

Using identity

a² + b² = (a + b)² - 2ab

= (y + 7)² - 2(y)(7)

= (y + 7)² - 14y



3) y⁴ - 16

= (y²)² - (4)²

Using identity

a² - b² = (a + b)(a - b)

= (y² + 4)(y² - 4)


4) y⁴ + 12y² + 36

= (y²)² + 2(y²)(6) + (6)²

Using identity

a² + 2ab + b² = (a + b)²

= (y² + 6)²


5) y³ + 2y² + 16y + 32

Taking common

= y²(y + 2) + 16(y + 2)

= (y + 2)(y² + 16)

Hope this helps you.