Find the largest value of n such that 3x^2 +nx + 72 can be factored as the product of two linear factors with integer coefficients.

n = 217

Step-by-step explanation:

The quadratic expression that we have to factorize is 3x² + nx + 72.

So, we have to find factors of (3 × 72) i.e. 216.

Now, we can write 216 as

(1 × 216), Hence, 1 + 216) = 217

(2 × 108), Hence, 2 + 108 = 110

(3 × 72), Hence, 3 + 72 = 75

(4 × 54), Hence, 4 + 54 = 58

So on.

Therefore, to factorize 3x² + nx + 72, the maximum value of n which can be put in place of n to factorize the expression is 217. (Answer)

x = 25

step-by-step explanation:

a^2+b^2=c^2

7^2+24^2=c^2

49+576=625

sqrt625=25

x=25

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