How do you factor by grouping 6x^4 + 7x^2 - 5?

3 Answers
bp
Jun 24, 2015

(2x^2 -1)(3x^2 +5)

Explanation:

To factorise the expression split the middle term and rewrite the expression 6x^4 +10x^2 -3x^2 -5

2x^2( 3x^2 +5) - (3x^2 +5)

(2x^2 -1)(3x^2 +5)

bp
Jun 25, 2015

Hi Alan, just consider x^2 as y, so that we get a simple quadratic expression 6y^2 +7y-5, which can be factorised easily by splitting the middle term.

Explanation:

Hi Alan, just consider x^2 as y, so that we get a simple quadratic expression 6y^2 +7y-5, which can be factorised easily by splitting the middle term.

To do this we multiply the coefficient of y^2 and the constant term. We get -30. Now split this in two parts such that sum is +7 and the product -30. That is how we arrive at 10 and -3

Nghi N.
Jun 28, 2015

Factor: y = 6x^4 + 7x^2 - 5

Explanation:

Call X = x^2 -> f(X) = 6X^2 + 7X - 5

To factor f(X) I use the new AC Method.
Converted f'(X) = X^2 + 7X - 30.
Factor pairs of (-30)-> (-2, 15)(-3, 10). This sum is 7 = b.
p' = -3 and q' = 10
p = (p')/a = -3/6 = -1/2 and q = (q')/a = 10/6 = 5/3

Factored form: f(X) = 6(X - 1/2)(X + 5/3) = (2X - 1)(3X + 5)

f(x) = (2x^2 - 1)(3x^2 + 5) = (xsqrt2 - 1)(xsqrt2 + 1)(3x^2 + 5)

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