Question

70 points please help

(Also tell me if it says less points on the answer, just write yes or no)
ANSWER BOTH QUESTIONS

Answer 1

• 10(5x -6)
• 3(5x +2)

Explanation:

You want to factor out the greatest common factor from ...

• 50x -60
• 15x +6

Greatest common factor

The greatest common factor is the largest expression that is a factor of both terms. Here, one term is a constant, so the GCF will be the largest constant that is a factor of both the coefficient and the constant.

For these numbers, your familiarity with multiplication tables will tell you the greatest common factors. More formally, you can find the GCF a couple of different ways.

Factoring

You can factor the numbers involved, and identify the set of common factors. The GCF will be the product of the numbers in that set:

• 50 = 2·5²; 60 = 2²·3·5; gcf = 2·5 = 10
• 15 = 3·5; 6 = 2·3; gcf = 3

Euclid's method

Repeatedly divide by the smaller of the two numbers or the remainder, until the remainder is 0. The last divisor is the GCF.

• 60/50 = 1r10; 50/10 = 5r0; gcf = 10
• 15/6 = 2r3; 6/3 = 2r0; gcf = 3

Factored form

Factoring out the greatest common factor, we have ...

• 50x +60 = 10(5x +6)
• 15x +6 = 3(5x +2)

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