Question

factories using factor theoremx^4-7x^3+9x^2+7x-10​

Answer 1

$\mathfrak{\huge{\blue{\underline{\underline{AnswEr :}}}}}$

Φ ${x}^{4} - 7 {x}^{3} + 9 {x}^{2} + 7x - 10$

⇒${x}^{4} - 7 {x}^{3} + 10 {x}^{2} - {x}^{2} + 7x - 10$

⇒${x}^{2} ( {x}^{2} - 7x + 10) - 1( {x}^{2} - 7x + 10)$

⇒$( {x}^{2} - 1)( {x}^{2} - 7x + 10)$

⇒${x}^{2} - 1 = 0 \: Or, \: {x}^{2} - 7x + 10 = 0$

⇒${x}^{2} = 1$

✿ $\boxed{ \red{x = ±1}}$

Φ $Now, \: ( {x}^{2} - 7x + 10 = 0)$

⇒${x}^{2} - 5x - 2x + 10 = 0$

⇒$x(x - 5) - 2(x - 5) = 0$

⇒$(x - 2)(x - 5) = 0$

⇒$(x - 2) = 0 \: Or, \: (x - 5) = 0$

✿ $\boxed{ \red{x = 2 \: \: Or, \: \: x = 5}}$

† Solutions of this Polynomial are

$\huge\boxed{ \purple{x = ±1 \: , \: \: 2 \: \: or, \: \: 5}}$

Answer 2

$\mathtt{\large{\underline{\underline{AnswEr :}}}}$

Φ ${x}^{4} - 7 {x}^{3} + 9 {x}^{2} + 7x - 10$

⇒${x}^{4} - 7 {x}^{3} + 10 {x}^{2} - {x}^{2} + 7x - 10$

⇒${x}^{2} ( {x}^{2} - 7x + 10) - 1( {x}^{2} - 7x + 10)$

⇒$( {x}^{2} - 1)( {x}^{2} - 7x + 10)$

⇒${x}^{2} - 1 = 0 \: Or, \: {x}^{2} - 7x + 10 = 0$

⇒${x}^{2} = 1$

★ $\boxed{ \pink{x = ±1}}$

Φ $Now, \: ( {x}^{2} - 7x + 10 = 0)$

⇒${x}^{2} - 5x - 2x + 10 = 0$

⇒$x(x - 5) - 2(x - 5) = 0$

⇒$(x - 2)(x - 5) = 0$

⇒$(x - 2) = 0 \: Or, \: (x - 5) = 0$

★ $\boxed{ \pink{x = 2 \: \: Or, \: \: x = 5}}$