(u).
(u - 1)**3*(u + 2)*(u + 9)/2
Let n(m) be the first derivative of m**5/90 - m**4/27 - 4*m**3/27 + 8*m**2/9 - 17*m + 6. Let g(i) be the first derivative of n(i). Factor g(q).
2*(q - 2)**2*(q + 2)/9
Suppose n**4 - 6*n**2 + 31 - 13*n**3 + 6*n**3 - n**2 - 29 + n + 2*n**5 = 0. What is n?
-1, 1/2, 2
Let d(q) be the second derivative of q**4/3 - 32*q**3/3 - 72*q**2 + 4*q + 33. Factor d(k).
4*(k - 18)*(k + 2)
Let p(u) = -u + 1. Let c be p(-4). Suppose 60 = k + 4*k + c*j, 50 = 5*k + 3*j. Factor 41*x**3 + 8*x**5 + 26*x**4 - 2*x**2 + 9*x**2 + k*x**2 + 2*x - 11*x**3.
2*x*(x + 1)**3*(4*x + 1)
Let o = 50216/351561 - -1/50223. Factor 0 + 2/7*a - 3/7*a**2 + o*a**3.
a*(a - 2)*(a - 1)/7
Let b be (18/(-4) + 4)/(8/(-64)). Suppose 8/9*h**3 + 2/9*h**5 - 8/9*h**b + 0*h + 0*h**2 + 0 = 0. Calculate h.
0, 2
Suppose -11*q - 13 = -46. Factor -q*g - 1 + 2*g**2 + 3*g**2 + 0*g**2 - g**2.
(g - 1)*(4*g + 1)
Suppose -4*p + 6 + 14 = 0. Let k(d) be the third derivative of 1/120*d**7 + 0 + 0*d**4 + 0*d + 1/120*d**p + 0*d**3 + 10*d**2 + 3/160*d**6. Factor k(n).
n**2*(n + 1)*(7*n + 2)/4
Let g(r) be the third derivative of r**5/30 - 2*r**4 - 4*r**2 + 34. Factor g(k).
2*k*(k - 24)
Let a be 2/(-30)*2 - 290/(-300)*11. What is u in 3/4*u**4 + 45*u**2 - 75/2*u - a*u**3 - 375/4 = 0?
-1, 5
Let n(l) = -l**2 - 8*l + 5334. Let q be n(69). Factor 27/4 - q*h + 9/4*h**2.
3*(h - 9)*(3*h - 1)/4
Let g = -266 + 266. Let u(p) be the first derivative of g*p**3 - 1/4*p**4 - 2*p + 1 + 3/2*p**2. Factor u(r).
-(r - 1)**2*(r + 2)
Let a = 152 + -150. Find x, given that -2/3 + 1/3*x + 1/3*x**a = 0.
-2, 1
Let v = -4 - -6. Suppose 5*z - 27 + v = 0. Factor -32*u + 48*u**2 - 16*u**2 - 5*u**3 - 2*u**z + 21*u**3 - 4*u**4 - 64.
-2*(u - 2)**2*(u + 2)**3
Let l(c) be the first derivative of 0*c + 2 + 1/26*c**4 - 2/13*c**3 + 2/13*c**2. Factor l(r).
2*r*(r - 2)*(r - 1)/13
Let g(w) be the third derivative of w**6/60 - 3*w**5/10 - 11*w**4/6 + 639*w**2. Let g(o) = 0. What is o?
-2, 0, 11
Suppose 8*m = 2*m - 31*m - 2*m. Factor 1/4*s**2 + 1/4*s**3 + m + 0*s.
s**2*(s + 1)/4
Suppose 15*c - 14*c = 2. Factor 9*i**2 - 12*i**2 - c + 2.
-3*i**2
Let c(w) be the second derivative of 0*w**5 + 0*w**2 - 1/8*w**4 + 1/20*w**6 - 3*w + 0 + 0*w**3. Factor c(v).
3*v**2*(v - 1)*(v + 1)/2
Let m = -14582/189 + -34/189. Let w = m - -80. Solve 4/3*p - 4/3*p**3 + 8/3*p**2 - w = 0.
-1, 1, 2
Solve -1083/4 + 5643/8*t + 15/8*t**3 - 72*t**2 = 0.
2/5, 19
Let u = 999/268 + 35/67. Factor 3/4*f**2 + u*f**3 - 2*f - 1 + 3/4*f**5 + 13/4*f**4.
(f + 1)**3*(f + 2)*(3*f - 2)/4
Let u(b) = 4*b**4 - 8*b**3 - 10*b**2 + 24*b + 20. Let r(g) = -g**4 + 3*g**3 + 3*g**2 - 8*g - 6. Let d(y) = 10*r(y) + 3*u(y). Suppose d(f) = 0. What is f?
-2, 0, 1
Let j(r) = 4*r**2 - 2*r + 1. Let l be j(2). Solve 3*y**2 - y**4 + 5*y - 5 + 1 + 2*y**3 + 4*y - l*y = 0.
-1, 2
Let o(s) be the third derivative of 4*s**2 + 1/5*s**5 + 1/15*s**6 + 0 - 2/105*s**7 + 0*s**4 + 0*s + 0*s**3. Factor o(c).
-4*c**2*(c - 3)*(c + 1)
Let t(o) be the second derivative of 1/72*o**6 + 2*o**2 + 7*o + 0 + 5/9*o**3 - 5/24*o**4 + 0*o**5. Let p(l) be the first derivative of t(l). Solve p(n) = 0.
-2, 1
Solve 4/7*q**4 + 0 + 0*q**2 - 116/7*q**3 + 0*q = 0 for q.
0, 29
Let u(b) be the first derivative of 7*b**5/30 + 41*b**4/12 + 52*b**3/3 + 88*b**2/3 - 64*b/3 + 141. What is k in u(k) = 0?
-4, 2/7
Let g(x) be the third derivative of -11/480*x**6 + 0*x + 3/280*x**7 - 14*x**2 + 0 + 0*x**3 + 1/120*x**5 + 0*x**4. Factor g(c).
c**2*(c - 1)*(9*c - 2)/4
Let l be (-20)/(30/9 + -4). Let -h**2 + l*h - 4*h**2 - 25*h = 0. What is h?
0, 1
Solve 12 + 4*k - 20 - 25*k**4 + 5*k**5 + k + 50*k**2 - 10*k**3 - 17 = 0 for k.
-1, 1, 5
Determine l, given that 256 - 97*l**2 - 64*l + 0 + 101*l**2 = 0.
8
Let v be (8/(-15))/((-21)/(-15))*(-180)/120. Factor 12/7*i - 20/7*i**2 + v*i**4 + 0 + 4/7*i**3.
4*i*(i - 1)**2*(i + 3)/7
Let l = 140 + -202. Let o = l + 62. Find w, given that -4/9*w + o*w**2 - 2/9*w**4 + 4/9*w**3 + 2/9 = 0.
-1, 1
Let j be -3*1 + (-16)/(-4). Factor 5*t**4 - 20*t - 23 + 10*t**2 + 20*t**3 + j + 7.
5*(t - 1)*(t + 1)**2*(t + 3)
Let d(g) be the second derivative of g**6/20 - 9*g**5/40 + 3*g**4/8 - g**3/4 + 31*g. Factor d(s).
3*s*(s - 1)**3/2
Let c = 0 + 12. Suppose c + 8*l**2 + 60*l + 0*l**5 + 12*l**3 - 2*l**5 - 86*l - 4*l**4 = 0. Calculate l.
-3, -2, 1
Let n(p) = 2*p - 21. Let g = 75 + -63. Let f be n(g). Factor 0 + 0*w + 0*w**2 + 1/2*w**4 + 0*w**f.
w**4/2
Let q(z) be the first derivative of -1/24*z**6 - 7/8*z**4 + 3/10*z**5 + 1/2*z - 49 + 4/3*z**3 - 9/8*z**2. Suppose q(b) = 0. Calculate b.
1, 2
Suppose c - 6*c + 100 = 0. Let c*b**2 + 20*b**3 - 4*b**4 - 4*b**4 + 13*b**4 = 0. What is b?
-2, 0
Let g(t) be the first derivative of t**8/3360 - t**6/720 + 2*t**3/3 - 1. Let l(a) be the third derivative of g(a). Factor l(x).
x**2*(x - 1)*(x + 1)/2
Factor 1/5*y**2 - 27/5*y + 26/5.
(y - 26)*(y - 1)/5
Let j(s) be the second derivative of 5/12*s**4 + 0 + 0*s**2 + 26*s + 1/6*s**6 + 1/2*s**5 + 0*s**3. Factor j(g).
5*g**2*(g + 1)**2
Let n(y) = -20*y**2 + 95*y - 524. Let t = 22 + -16. Let s(b) = -7*b**2 + 32*b - 175. Let k(i) = t*n(i) - 17*s(i). Suppose k(r) = 0. What is r?
13
Suppose 55*n = -25*n - 11*n. Factor -8/5*t**3 - 4/5*t + n - 2/5*t**4 - 2*t**2.
-2*t*(t + 1)**2*(t + 2)/5
Suppose u - 8 = -5*c - 3, -5*u = c - 1. Let g(q) be the first derivative of 3/20*q**4 + 0*q**3 + 6 - 3/10*q**2 + u*q. Solve g(h) = 0.
-1, 0, 1
Factor -6*l - 38*l**3 - 50*l**2 - 26*l - 14*l**4 - 8 - l**5 - l**5.
-2*(l + 1)**3*(l + 2)**2
Let z(i) be the first derivative of i**4/28 - 15*i + 12. Let l(g) be the first derivative of z(g). Determine j so that l(j) = 0.
0
Find o, given that 0*o - 2/11*o**4 - 14/11*o**3 + 0*o**2 + 0 = 0.
-7, 0
Let w(m) be the first derivative of m**4/16 - 7*m**3/12 + 5*m**2/4 + 58. Factor w(h).
h*(h - 5)*(h - 2)/4
Let d be 0*(15 - 1780/120). Let t(c) = -2*c**3 - 4*c**2 - 2*c. Let l be t(-2). Factor 0 + 3/4*k**3 + 3*k**l + 0*k**2 + d*k.
3*k**3*(4*k + 1)/4
Let w(t) be the third derivative of t**7/105 - 29*t**6/25 - 29*t**5/30 + 29*t**4/5 + 28*t**3/3 + 15*t**2. Let w(a) = 0. What is a?
-1, -2/5, 1, 70
Let o(x) be the third derivative of 0 + 0*x - 9*x**2 - 1/60*x**5 + 1/24*x**4 + 0*x**3. Factor o(c).
-c*(c - 1)
Let n be ((-6)/544)/((-27)/9). Let d = 547/816 - n. Solve -d - 1/6*x**2 + 2/3*x = 0 for x.
2
Let n(b) be the third derivative of -1/36*b**3 - 3*b**2 - 1/24*b**4 - 1/90*b**6 + 0 - 1/30*b**5 + 0*b. Solve n(f) = 0 for f.
-1/2
Determine a, given that 13/4*a**4 + 1/2*a**3 - 1/4*a**5 - 13/2*a**2 - 1/4*a + 13/4 = 0.
-1, 1, 13
Let u(g) = g**2 + 170*g + 1 + g**3 - 2 - 169*g. Let p(o) = -3*o**3 + 11*o**2 + 5*o - 5. Let x(i) = -2*p(i) + 10*u(i). Solve x(r) = 0 for r.
0, 3/4
What is z in 0 - 2/11*z**4 - 46/11*z**2 - 28/11*z - 20/11*z**3 = 0?
-7, -2, -1, 0
Let z = -44 - -171. Let z*i - 127*i - 3*i**3 = 0. What is i?
0
Let w be (4/22)/((-1505)/(-3311)). Factor -w*d**3 + 0*d + 2/5*d**2 + 0.
-2*d**2*(d - 1)/5
Factor 60492/7 + 3/7*m**2 - 852/7*m.
3*(m - 142)**2/7
Let l = 19 - 17. Factor 3*y - 3*y + y**l - 4.
(y - 2)*(y + 2)
Let o(f) = -f**2 + 12*f - 16. Let x be o(11). Let u be 0/2*4/(-40)*x. Factor 8/9*v + u + 4/9*v**2.
4*v*(v + 2)/9
Let q(f) = -7*f**3 + 8*f**2 - 7*f - 2. Let t(b) = 2*b**3 + 0 + 6*b**3 + 7*b**3 - 15*b**2 + 5 + 15*b. Let h(k) = 5*q(k) + 2*t(k). Factor h(x).
-5*x*(x - 1)**2
Suppose 13*w + 125 = 18*w. Determine s, given that -10*s**5 - 5*s**4 + 11*s**5 - 5*s**4 + w*s**3 = 0.
0, 5
Let o(j) = -4*j - 8. Let z be o(-6). Suppose h = 3*x - z - 22, -4*x = 3*h - 29. Factor -19 - 6*g**2 + 43*g - 16 - 9*g**3 - 7*g + x + 3*g**4.
3*(g - 2)**2*(g - 1)*(g + 2)
Let b(w) be the second derivative of -2*w**7/21 + 31*w**6/5 - 792*w**5/5 + 1872*w**4 - 6912*w**3 - 62208*w**2 - 2*w + 37. Factor b(c).
-2*(c - 12)**4*(2*c + 3)
Let h(z) = z**2 - 11*z + 20. Let p be h(9). Factor 4*m + 3*m**2 - 4*m - p*m - m**4.
-m*(m - 1)**2*(m + 2)
Let z = 224 + -200. Let x(w) = -w**2 + 6*w - 5. Let a be x(4). Factor 6*p**4 + 72*p**3 - 6*p**4 - 16*p**2 - 36*p**4 + 8*p**5 - z*p**a.
4*p**2*(p - 2)**2*(2*p - 1)
Let x = -2173 + 2178. Factor -1/4*t**3 + 1/4*t**4 - 1/4*t**2 + 1/4*t**x + 0*t + 0.
t**2*(t - 1)*(t + 1)**2/4
Let q be -1*((6 - 9) + 0). Solve -1/7*u**q - 4/7*u - 4/7*u**2 + 0 = 0 for u.
-2, 0
Let b(g) = -5*g**4 - 15*g**3 + 20*g**2 + 20*g + 10. Let f(y) = -y**4 + 2*y**2 + 1. Let o(i