One factor of $7x^2 + 33x - 10$ is

Analyze the question: We need to factorise the quadratic 7x² + 33x − 10 and find which option is one of its factors.

Concept: For ax² + bx + c, find two numbers whose product is a × c and whose sum is b.

Solution:

a × c = 7 × (−10) = −70 We need two numbers with product −70 and sum +33: these are 35 and −2.

Split the middle term:

7x² + 35x − 2x − 10

Group:

7x(x + 5) − 2(x + 5)

= (7x − 2)(x + 5)

Check by expanding: (7x − 2)(x + 5) = 7x² + 35x − 2x − 10 = 7x² + 33x − 10 ✓

So the factors are (7x − 2) and (x + 5).

Comparing with the options:

• A. 7x + 5 → not a factor
• B. x − 2 → not a factor
• C. 7x − 2 → a factor
• D. x − 5 → not a factor

Quick check using the factor theorem: For 7x − 2, set x = 2/7: 7(4/49) + 33(2/7) − 10 = 4/7 + 66/7 − 70/7 = 0 ✓

Tip: When the constant term is negative, look for two numbers with opposite signs. The larger one takes the sign of the middle term. You can also quickly test options with the factor theorem: if (px − q) is a factor, then x = q/p gives zero.