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Factor this polynomial completely x2-8x+16

Factor this polynomial completely x2-8x+16-example-1
User Banesto
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2 Answers

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There are a couple of formulas that we should know about quadratic functions, and this one utilizes this one:

(x - a)^2 = x^2 -2ax + a^2

Notice how x^2 - 8x + 16 fits into the formula:

x^2 - 8x + 16

x^2 - 2*x*4 + 4^2

(x - 4)^2

(x - 4)(x - 4)


Of course, not all expanded quadratic expressions fit into that formula, so there is a universal method to factor quadratic expressions:

x^2 + x(a + b) + ab —> (x + a)(x + b)

Basically, the middle term is the sum of an and b times x, and the last term is the product of an and b. So, if we are using the expression given in the problem, notice how -4 * -4 is 16, and the sum of -4 and -4 is -8. Thus, a and b are both -4 and the factored form is (x - 4)(x - 4)

User Beta Carotin
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1 vote

Answer:

X^2-8x+16

X^2-4x-4x+16

Factorise by gouping terms

X(x-4)-4(x-4)

=(x-4)(x-4)

User Dhia Shalabi
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