Rewrite the trinomial with the x -term expanded, using the two factors. Then, group the first two and last two terms together and find the GCF of each. and fill the b;anks with them

Question

Factor 5x^2+16x+12. Rewrite the trinomial with the x -term expanded, using the two factors. Then, group the first two and last two terms together and find the GCF of each.

Trinomial: (5x^2+10x)+(___+12)

GCF:_____(x+2)+6(___)

Answer 1

To factor the trinomial 5x^2 + 16x + 12, we need to find two binomial factors that, when multiplied, result in the given trinomial.

Step 1: Multiply the coefficient of the quadratic term (5) by the constant term (12). The result is 60.

Step 2: Look for two numbers that multiply to give 60 and add up to the coefficient of the linear term (16). In this case, those numbers are 10 and 6.

Step 3: Rewrite the trinomial with the x-term expanded using the two factors:

(5x^2 + 10x) + (6x + 12)

Step 4: Group the first two and last two terms together:

5x(x + 2) + 6(x + 2)

Step 5: Find the GCF of each group:

GCF of (x + 2) = (x + 2)

GCF of 5x + 6 = 1

Putting it all together:

Trinomial: (5x^2 + 10x) + (6x + 12)

GCF: (x + 2) + 6

Therefore, the factored form of 5x^2 + 16x + 12 is (x + 2)(5x + 6).

Answer 2

5x²+16x+12

(5x²+10x)+(6x+12) Since 10 is given and the middle term is 16, the other term must be 6. Now, factor out the GCF from both terms. 5x and 6

5x(x+2)+6(x+2) The binomial GCF is (x+2)

(x+2)(5x+6)