Test Index

CTET Paper II (Mathematics and Science) 8 Feb 2026 Shift 1 Solved Paper

Question : 32 of 150

Marks: +1, -0

​4x ^ 2 + 9y ^ 2 + 12xy - 5(2x + 3y) - 14

is a

Solution:

Concept:

Recognize that

4x^2 + 9y^2 + 12xy = (2x + 3y)^2

. Substitute to simplify the expression into a quadratic.

Explanation:

Rewrite the given expression:

4x^2 + 9y^2 + 12xy - 5(2x + 3y) - 14 = (2x+3y)^2 - 5(2x+3y) - 14

Let

u = 2x + 3y

. Then the expression becomes

u^2 - 5u - 14

Factor the quadratic:

u^2 - 5u - 14 = (u-7)(u+2)

Substitute back

u = 2x+3y

(2x+3y-7)(2x+3y+2)

Thus the factors are

(2x+3y-7)

and

(2x+3y+2)

Answer:

2x + 3y - 7

Go to Question:

Prev Question

Next Question