factor 7x^4+51x^2+14
Let's factor in :
Let's define:
You can transform this expression into:
Given the quadratic form , let's compute the discriminant: . Here , and
ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product: = = ■Multiplications are done before additions and subtractions: =
ⓘ Multiplications are done before additions and subtractions: = = = =
ⓘ Start from and move back on the number line: =
Since , the equation has two roots:
The quadratic formula gives = =
ⓘ The square root of a number is the positive number whose square is that number: = ; =
ⅰ =
ⓘ The numerator and the denominator are computed before the division: =
We divide the numerator and denominator of by the common factor: , which gives the new expression:
The quadratic formula gives = =
ⓘ The square root of a number is the positive number whose square is that number: = ; =
ⅰ =
ⓘ The numerator and the denominator are computed before the division: =
ⓘ We simplify the fraction by dividing the numerator and the denominator by , their greatest common divisor: = =
A trinomial with roots and is ; bringing the coefficient into the brackets: =
Factors found:
ⓘ A square being never negative, is never zero and cannot be factored in ℝ
▶Factored expression:
