1. m^2 - 7m - 30
2. z^2 + 65z + 1000
3.x^2 - 45x + 450
4.d^2 - 33 d - 280
The area of a rectangular field is given by the trinomial t2 – 4t – 45. The length of the rectangle is t + 5. What is the expression for the width of the field?
MathMate already did one of them for you
http://www.jiskha.com/display.cgi?id=1329964907
why not try his method for the others.
I will do the last one: d^2 - 33d - 280
280 = 56x5 , difference in factors of 33 ? no
280 = 40x7 , difference in factors of 33 ? YES
-280 = -40 x 7 , (-40) + 7 = -33
so
d^2 - 33d - 280 = (d - 40)(d + 7)
ok, your turn
Show us how you would do the other two.
Please do not insert a new question as a reply to somebody else's question.
All you have to do is factor t^2 - 4t -45
To make it really simple, one of the factors is already given, so
t^2 - 4t - 45 = (t+5)(........)
you know it has to start with (t ......) and end in (.....-9)
so (t+5)(t-9)
does that produce a middle term of -4t ?? , YES
so we are done.
the width is t-9
1000=2x500
1000=4x250
1000=5x200 don't none of them work
To factorize the quadratic expressions, we need to find two numbers that multiply to give the constant term and add up to give the coefficient of the linear term.
Let's factorize each quadratic expression:
1. m^2 - 7m - 30:
We need to find two numbers that multiply to give -30 and add up to give -7.
The numbers are -10 and 3.
So, the factored form is: (m - 10)(m + 3).
2. z^2 + 65z + 1000:
We need to find two numbers that multiply to give 1000 and add up to give 65.
The numbers are 40 and 25.
So, the factored form is: (z + 40)(z + 25).
3. x^2 - 45x + 450:
We need to find two numbers that multiply to give 450 and add up to give -45.
The numbers are -15 and -30.
So, the factored form is: (x - 15)(x - 30).
4. d^2 - 33d - 280:
We need to find two numbers that multiply to give -280 and add up to give -33.
The numbers are -40 and 7.
So, the factored form is: (d - 40)(d + 7).
By factoring the quadratic expressions, we can find their simplified forms.