suppose we want to find lim(x→4) (x² + 3x - 28)/(x² - 11x + 28). if x = 4, the numerator is 0 and the…

suppose we want to find lim(x→4) (x² + 3x - 28)/(x² - 11x + 28). if x = 4, the numerator is 0 and the denominator is 0. this means the limit is 0 the question is wrong the limit is undefined an algebraic reduction is possible factoring: x² + 3x - 28 = x² - 11x + 28 =

suppose we want to find lim(x→4) (x² + 3x - 28)/(x² - 11x + 28). if x = 4, the numerator is 0 and the denominator is 0. this means the limit is 0 the question is wrong the limit is undefined an algebraic reduction is possible factoring: x² + 3x - 28 = x² - 11x + 28 =

Answer

Explanation:

Step1: Factor the numerator

We use the formula for factoring quadratic $ax^{2}+bx + c$. For $x^{2}+3x - 28$, we need two numbers that multiply to $- 28$ and add up to $3$. The numbers are $7$ and $-4$. So $x^{2}+3x - 28=(x + 7)(x - 4)$.

Step2: Factor the denominator

For $x^{2}-11x + 28$, we need two numbers that multiply to $28$ and add up to $-11$. The numbers are $-4$ and $-7$. So $x^{2}-11x + 28=(x - 4)(x - 7)$.

Answer:

$x^{2}+3x - 28=(x + 7)(x - 4)$ $x^{2}-11x + 28=(x - 4)(x - 7)$