CTET Paper II (Mathematics and Science) 7 Feb 2026 Shift 1 Solved Paper

Concept:Recognize $4x^2 + 16y^2 - 16xy$ as $(2x-4y)^2$. Let $k = 2x-4y$ to simplify the expression into a quadratic in $k$, then factorize.Explanation:First, rewrite the middle term: $4x^2 + 16y^2 - 16xy = (2x)^2 + (4y)^2 - 2(2x)(4y) = (2x-4y)^2$.The expression becomes $5(2x-4y) + 6(2x-4y)^2 - 6$.Let $k = 2x-4y$. Then the expression is $6k^2 + 5k - 6$.Factor this quadratic: look for two numbers whose product is $6 \times (-6) = -36$ and sum is $5$. These are $9$ and $-4$.So $6k^2 + 5k - 6 = 6k^2 + 9k - 4k - 6 = 3k(2k+3) - 2(2k+3) = (3k-2)(2k+3)$.Substitute $k$ back: $3k-2 = 3(2x-4y)-2 = 6x-12y-2 = 2(3x-6y-1)$.Hence one factor is $3x-6y-1$. The other factor $2k+3 = 2(2x-4y)+3 = 4x-8y+3$ does not match the options.Thus, the correct factor among the choices is $3x-6y-1$.Answer:$3x-6y-1$ (Option C)