Question

factor the expression completely. 35x² + 63x⁴

Explanation:

Step1: Identify the GCF of coefficients and variables

First, find the greatest common factor (GCF) of the coefficients 35 and 63. The factors of 35 are 1, 5, 7, 35; the factors of 63 are 1, 3, 7, 9, 21, 63. So the GCF of 35 and 63 is 7. For the variable part, \(x^2\) and \(x^4\) have the GCF \(x^2\) (since the lowest power of \(x\) is 2). So the GCF of the two terms is \(7x^2\).

Step2: Factor out the GCF

Factor out \(7x^2\) from each term: \(35x^2 + 63x^4 = 7x^2(5 + 9x^2)\) (because \(35x^2\div7x^2 = 5\) and \(63x^4\div7x^2 = 9x^2\)).

Answer:

\(7x^2(9x^2 + 5)\) (or \(7x^2(5 + 9x^2)\))