Use factoring to solve each equation for real values of the

Use factoring to solve each equation for real values of the variable.

x³ + 4x² - 21x = 0

8b³ - 10b² + 3b -0

y⁴ - 50x² + 49 = 0

Please solve and show your work, thankyou.

Solution

1) x^3 + 4x^2 - 21 x =0

x ( x^2 + 4x - 21 ) = 0

x ( x + 7) ( x - 3 ) = 0

2) 8b^3 - 10b^2 + 3b = 0

b ( 8b^2 - 10b + 3 ) = 0

b ( 2b-1 ) ( 4b - 3 ) = 0

3) y^4 - 50y^2 + 49 = 0

let y^2 = a

equation becomes

a^2 - 50 a + 49 = 0

(a-1)(a-49) = 0

a = y^2

(y^2 - 1) ( y^2 - 49 ) = 0

further factoring y^2-1 and y^2 - 49 by applying difference of squares formula

(y-1)(y+1)(y-7)(y+7) = 0