Question

Subtract- 3x² - 5x + 7 from 5x² - 7x + 9

Answer 1

Answer:

2x² - 2x + 2 OR  2(x² - x + 1)

Step-by-step explanation:

(5x² - 7x + 9) - (3x² - 5x + 7)

= 5x² - 7x + 9 - 3x² + 5x - 7

= 5x² - 3x² - 7x + 5x + 9 - 7

= 2x² - 2x + 2

= 2(x² - x + 1)

Answer 2

To subtract : $3 x^{2}-5 x+7$ from $5 x^{2}-7 x+9$

Solution :

• To subtract given algebraic expression, we subtract like terms together

• Removing parenthesis and changing sign we subtract given expressions.  

              $\begin{array}{l}\left(5 x^{2}-7 x+9\right)-\left(3 x^{2}-5 x+7\right) \\=5 x^{2}-7 x+9-3 x^{2}-5 x+7 \\=2 x^{2}-12 x+16\end{array}$

• Dividing equation by 2 we get, $x^{2}-6 x+8$
• Finding factors of above expression  

            $\begin{aligned}x^{2}-6 x+8 &=x^{2}-4 x-2 x+8 \\&=x(x-4)-2(x-4) \\&=(x-4)(x-2)\end{aligned}$

Hence, on subtracting $3x^{2} -5x +7$ from $5 x^{2}-7 x+9$  we get $(x-4)(x-2)$.