the question is Factor the trinomial. Factor out all the common monomials first
21 x^3 - 68 x^2 + 32 x
2007-04-26 18:19:31 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
x(21x^2-68^x+32)
x(7x-4)(3x-8)
2007-04-26 18:31:59 · answer #1 · answered by JO 3 · 0⤊ 0⤋
Hi, Sandy
I hope you remember the distributive rule which says
x * ( c+d+e) = x * c + x * d + x * e
You can also reverse this, in the above trinomial factor the "monomial" x:
21 x^3 - 68 x^2 +32x
= x * ( 21 x^2 - 68x + 32)
Then factor the part of the equation in parentheses. You can use the quadradic equation
or trial and error knowing that the solution is probably a whole number, find numbers a, b, c and d so that
(ax + b)(cx + d) = 21x^2 - 68x +32
so,
a*c = 21
b*d = 32
and ac + bd = -68
Since we assume whole numbers, the possible solutions for a and c are
a c
-- ---
1 21
3 7
7 3
21 1
The possibilities for b and d are
b d
-- --
-1 -32
-2, -16
-4, -8
-8, -4
-16, -2
-32, -1
Go ahead and try all these pairs with each other to find out which satisfy
a*c + b*d = -68
2007-04-27 01:52:09 · answer #2 · answered by m i 5 · 0⤊ 0⤋
OK, factor out "x" first and you're left with:
x(21x^2 - 68x + 32)
Now 21 is the product of 1 x 21 and 7 x 3, but since the middle term has 68 as a coefficient and 32 is pretty large I'll guess first that the coefficients in the factor are 7 and 3. So we have
x (7x - N1)(3x - N2)
Note the two minus signs; it has to be this way since the middle term is negative but the last term is positive.
Playing around with the factors of 32 ultimately gives:
x(7x - 4)(3x -8)
2007-04-27 01:32:00 · answer #3 · answered by Mark S, JPAA 7 · 0⤊ 0⤋
21 x^3 - 68 x^2 + 32 x
x is a common factor so separate it.
x(21 x^2 - 68 x + 32 )
we now have a quadratic
lets ignore the x first to factorize the equation
21 x^2 - 68 x + 32
(7x-4)
(3x-8)
so, 21 x^2 - 68 x + 32 = (7x -4)(3x-8)
and the simplified form of 21 x^3 - 68 x^2 + 32 x is x(7x-4)(3x-8)
2007-04-27 01:29:59 · answer #4 · answered by Kuan T 2 · 0⤊ 0⤋
When the diamond problem gets too complicated, do the quadratic equation, as it ALWAYS will work. Thus, when you plug it into teh formula you get 4624+/- (sq root) 1936 / 42, factor out 1936 and it's a perfect square, 44. Thus, 4624 +/- 44 / 42 and then solve. Sry. hard to do it with no fractions shown! But x is the monomial factor tha should be taken out first.
2007-04-27 01:34:48 · answer #5 · answered by Bri 3 · 0⤊ 0⤋
First factor out the x: x(21x^2-68x+32)
Next factor whats left: x(3x-8)(7x-4)
2007-04-27 01:33:00 · answer #6 · answered by bruinfan 7 · 0⤊ 0⤋