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Binomial

ange0780abc — 2022-05-20 13:26:19 UTC

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

Common facto

ange0780abc — 2022-05-20 13:26:21 UTC

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

Difference of Squares

ange0780abc — 2022-05-20 13:26:22 UTC

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.

Perfect Square Trinomials

ange0780abc — 2022-05-20 13:26:24 UTC

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.

Factoring Quadratics of the Form x² + bx + c

ange0780abc — 2022-05-20 13:26:26 UTC

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.

Example 1

ange0780abc — 2022-05-20 13:26:27 UTC

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)

Quadratic factorization of the form ax² + bx + c

ange0780abc — 2022-05-20 13:26:29 UTC

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.