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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Factor completely x² - 10x + 25.
(x - 5)(x - 5), (x + 5)(x + 5), (x + 5)(x - 5), (x - 25)(x - 1)
Solution:
Given is a quadratic polynomial.
Step 1: Identify the values of a, b and c.
In the above equation, a is coefficient of x2 = 1,
b is the coefficient of x = -10 and
c is the constant term = 25.
Step 2: Solve for x by factoring polynomial by splitting the middle term.
Multiply a and c and find the factors that add up to b.
1 × (25) = 25
⇒ -5 and -5 add up to b. -5 is a factor of 25.
Step 3: Split bx into two terms.
x² - 5x - 5x + 25
Step 4: Take out the common factors by grouping.
x(x - 5) - 5(x - 5)
(x - 5) (x - 5) or (x - 5)2
Thus the factors of the given polynomial x² - 10x + 25 are (x - 5) (x - 5)
Factor completely x² - 10x + 25.
(x - 5)(x - 5), (x + 5)(x + 5), (x + 5)(x - 5), (x - 25)(x - 1)
Summary:
The factors of the equation x² - 10x + 25 are (x - 5) (x - 5).
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