Which is a factor of x² - 9x + 14?
x - 9, x - 2, x + 5, x + 7
Solution:
Let us factorise the polynomial to find the value of x by splitting the middle term.
Step 1:
Identify the values of a, b and c.
In the above equation, a = 1; is coefficient of x2 , b = - 9; is the coefficient of xand c = 14; is the constant term .
Step 2:
Find the factors of a × c that add up to b.
1 × ( 14) = 14
⇒ - 7 and - 2 are the factors that add up to b.
Step 3:
Split bx into two terms as the sum of factors.
x2 - 7x - 2x + 14 = 0
Step 4:
Take out the common factors.
x (x - 7) - 2 (x - 7) = 0
(x - 2) (x - 7) = 0
We get two values of x, by equating the factors to zero.
x - 2 = 0 and x - 7 = 0
x = 2 and x = 7
Thus, the two values that satisfy the equation are 2 and 7.
Which is a factor of x² - 9x + 14?
x - 9, x - 2, x + 5, x + 7
Summary:
The factors of the equation x2 - 9x + 14 are (x - 2) (x - 7) which satisfies the equation.
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