Question

Factor 50t^2-20t-30=??

Answer 1

The answer is 10(t-1) (5t+3).

An algebraic equation of the second degree in x is a quadratic equation. Typically, a quadratic equation is expressed in standard form as,$ax^2 + bx + c = 0$.

And the factor is a number or algebraic expression that divides another number evenly without leaving any remainder.

To factor the given quadratic equation, first, take the common factor of the equation. Therefore,

$50t^2-20t-30=10(5t^2-2t-3)$

Using the sum-product pattern, we can write 2t as 3t-5t. Therefore,

$50t^2-20t-30=10(5t^2+3t-5t-3)$

Now, find the common factor between the pairs within the bracket. We get,

$50t^2-20t-30=10(t(5t+3)-1(5t+3))$

Finally, rewriting the above terms by factoring out the greatest common factor, we get,

$50t^2-20t-30=10(t-1)(5t+3)$

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Answer 2

Answer: 10 (5t+3) (t-1)

Step-by-step explanation:

Given, 50t²-20t-30

Here we take 10 as the common factor:

⇒ 10(5t²-2t-3)

Then, we use the sum-product pattern to divide the 2t into two parts:

⇒ 10(5t²-5t+3t-3)

Taking the common factor from the two pairs, we get:

⇒ 10 [5t(t-1) + 3(t-1)]

⇒ 10 (5t+3) (t-1)

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