factor the trinomial.
1. m^2-7m-30
2. z^2+65z+1000
3.x^2-45x+450
4.d^2-33d-280
1. factorize m^2-7m-30
Look for two numbers such that their product is -30 and the sum/difference is -7.
1*30 nope
2*15 nope
3*10 yes, 3*(-10)=30, 3-10=-7
So
m^2-7m-30=(m-10)(m+3)
thanks , i get it now but can you explain number 2 please
For #2, you need to find two numbers that multiply together to get 1000, and add up to 65. This is easier because it is all positive, so we don't need to worry where the negative sign goes.
1000=1*1000 nope (sum too big)
1000=2*500 nope
1000=4*250 nope
1000=5*200 nope
1000=10*100 nope (sum still too big)
1000=20*50 nope (sum=70, getting close)
1000=25*40 yesss! (sum =65)
Can you take it from here?
To factor a trinomial, you need to find two binomials that, when multiplied together, equal the given trinomial.
1. Factoring the trinomial m^2 - 7m - 30:
For this trinomial, we need to find two numbers that multiply to -30 and add up to -7.
After some trial and error, we can see that -10 and 3 satisfy these conditions.
Therefore, the factored form of the trinomial is: (m - 10)(m + 3).
2. Factoring the trinomial z^2 + 65z + 1000:
Here, we need to find two numbers that multiply to 1000 and add up to 65.
By analyzing the factors of 1000, we find that 40 and 25 fit these conditions.
Therefore, the trinomial can be factored as: (z + 40)(z + 25).
3. Factoring the trinomial x^2 - 45x + 450:
Similarly, we are looking for two numbers that multiply to 450 and add up to -45.
By examining the factors of 450, we see that -15 and -30 satisfy these conditions.
So, the factored form of the trinomial is: (x - 15)(x - 30).
4. Factoring the trinomial d^2 - 33d - 280:
Again, we need to find two numbers that multiply to -280 and add up to -33.
After some exploration, we find that -40 and 7 meet these criteria.
Therefore, the trinomial can be factored as: (d - 40)(d + 7).
Remember that factoring trinomials sometimes involves trial and error, but with practice, you'll become more efficient at recognizing patterns and finding the correct factors.