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Quadratic factorization of the form ax² + bx + c

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Quadratic factorization of the form ax² + bx + c

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ax²+bx+c=0

a(x²+b/ax)=-c

a(x+b/2a)²-b²/4a=-c

a(x+b/2a)²=(b²-4ac)/4a

∴(x+b/2a)²=(b²-4ac)/4a²

When b²-4ac>0, x=(-b±√△)/2a.

When b²-4ac=0, x=-b/2a.

When b²-4ac<0, there is no real solution.

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Factor x ² + 8 x + 12.

x ² + 8 x + 12 = ( x )( x )

12 can be factored in a variety of ways:

(1)(12), (–1)(–12), (2)(6), (–2)(–6), (3)(4), (–3)(–4)

Only one of those pairs of factors sum to 8, namely (2)(6), so

x ² + 8 x + 12 = ( x + 2)( x + 6)

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Factoring Quadratics of the Form x² + bx + c 

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Factoring Quadratics of the Form x² + bx + c 

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To factor polynomials of the form x ² + bx + c, begin with two pairs of parentheses with x at the left of each.

( x )( x )

Next, find two integers whose product is c and whose sum is b and place them at the right of the parentheses.

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A perfect square trinomial is a special type of trinomial. When the binomial terms are multiplied by itself, then the resulting term is called a perfect square trinomial.

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The difference of two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the difference of the square roots and the other shows the sum of the square roots.

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A common factor is a whole number which is a factor of two or more numbers.

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Binomial is a polynomial with only terms. For example, x + 2 is a binomial, where x and 2 are two separate terms.