Question

By factorising the expression 3x² + 26x + 51, find two factors of 32 651​

Answer 1

The two factors of 32651 are 103 and 317

Explanation:

The given expression is $3x^{2} +26x+51$

We need to factor the expression and using the factor we need to determine the two factors of 32651

Let us first determine the factor of the expression $3x^{2} +26x+51$

Let us break the expression into two groups.

$\left(3 x^{2}+9 x\right)+(17 x+51)$

Let us factor out 3x and 17x, we get,

$3 x(x+3)+17 (x+3)$

Simplifying, we get,

$(x+3)(3 x+17)$

Thus, the factors of the expression is $(x+3)(3 x+17)$

Now, we shall determine the factor of 32651

$3x^2 + 26x + 51 = 32651$

Subtracting both sides by 51, we get,

$3x^2 + 26x = 32600$

Rewriting the above expression, we get,

$3x^2 + 26x = 30000 + 2600$

$3x^{2} +26x= 3(100^2) + 26(100)$

Thus, the value of x is 100

Substituting the value of x in the factor $(x+3)(3 x+17)$, we get,

$(100+3)(3(100)+17)=103\times317=32651$

Thus, the two factors of 32651 is 103 and 317