(-2). Solve -1/5*t**2 - 2/5 - b*t = 0.
-2, -1
Suppose 0 = -3*g + 4*q - 8, 19*q + 37 = 3*g + 24*q. Determine b, given that -4/3*b**2 + 4/3*b**g + 0 + 4/3*b**3 - 4/3*b = 0.
-1, 0, 1
Let z be ((-208)/(-128) + -1)*(-1)/(-15). Let r(v) be the first derivative of 1/9*v**3 + 0*v + 1/12*v**2 + z*v**4 - 2. Factor r(c).
c*(c + 1)**2/6
Let b be (-5)/((-40)/(-2))*0. Suppose b = 4*k - 8, 4*x - x + 2 = k. Determine c so that x*c + 3/7*c**2 - 3/7 = 0.
-1, 1
Let r be (-2)/(-13) - 334/(-26). Factor -12 + 2*o**3 + 15*o - 3*o**3 + 5*o**3 - 20*o**2 + r*o.
4*(o - 3)*(o - 1)**2
Let n = 1292 + -1289. Let q = -4 - -9. Suppose -m**4 + 2*m + m**q + m**2 + 0*m**4 - n*m**3 + 0*m = 0. What is m?
-1, 0, 1, 2
Let s(t) = 10*t**4 + 16*t**3 + 8*t**2 + 8. Suppose 3*m = 2*f + 11, m + 3 = 2*m. Let x(g) = g**4 + g**3 + 1. Let n(c) = f*s(c) + 8*x(c). What is l in n(l) = 0?
-2, 0
Let c(p) be the first derivative of p**3/2 + 27*p**2/4 + 21*p + 683. Let c(q) = 0. What is q?
-7, -2
Let j(a) be the second derivative of -1/21*a**3 + 1/21*a**2 + 1/441*a**7 - 41*a - 1/105*a**6 + 1/63*a**4 + 1/105*a**5 + 0. Factor j(k).
2*(k - 1)**4*(k + 1)/21
Let q(j) be the second derivative of 0 + 16*j - 2/35*j**5 + 0*j**2 - 2/21*j**3 + 5/42*j**4 + 1/105*j**6. Factor q(p).
2*p*(p - 2)*(p - 1)**2/7
Factor -10/7*p - 2/7 - 8/7*p**2.
-2*(p + 1)*(4*p + 1)/7
Let i be (-969)/(-665) + 3/(-5). What is h in i - 2/7*h**2 - 1/7*h**3 + 5/7*h = 0?
-3, -1, 2
Let a(q) be the first derivative of q**5/5 + 3*q**4/4 + q**3 + q**2/2 + 133. Factor a(g).
g*(g + 1)**3
Let h = 847/3 - 282. Let g(x) be the first derivative of 0*x + 1 - h*x**3 + 0*x**2. Find u, given that g(u) = 0.
0
Let a = 927/18941 - -6/403. Let j = a + 85/141. Find d, given that j*d**5 + 2/3*d + 0*d**4 + 0*d**2 - 4/3*d**3 + 0 = 0.
-1, 0, 1
Let n(s) be the third derivative of 0*s + 12*s**2 + 0 - 23/210*s**5 - 1/14*s**4 + 23/735*s**7 + 0*s**3 - 1/420*s**6 + 1/168*s**8. Find y such that n(y) = 0.
-3, -1, -2/7, 0, 1
Let d be (-3 - 3) + 16/2. Let t(z) be the third derivative of 0*z**3 + 3*z**d + 1/6*z**4 + 0*z - 1/6*z**5 + 0. Determine f, given that t(f) = 0.
0, 2/5
Factor -3/11*o**2 + 10/11 + 1/11*o**4 + 13/11*o - 5/11*o**3.
(o - 5)*(o - 2)*(o + 1)**2/11
Let g(y) = -5*y**4 + 5*y**3 + 12*y**2 - 2*y - 2. Let n(j) = -3 + 13*j**2 + 8*j**3 - 5*j**3 - 3*j + 2*j**3 - 5*j**4. Let t(f) = -3*g(f) + 2*n(f). Solve t(r) = 0.
-1, 0, 2
Let 3*t**4 + 9*t**3 - 20 + 3*t**2 - 9*t - 16 + 30 = 0. Calculate t.
-2, -1, 1
Factor 73/2*x**3 + 2 + 76*x + 221/2*x**2.
(x + 1)*(x + 2)*(73*x + 2)/2
Suppose -u = -3*m + 43, -3*m - 23 = -6*m + 5*u. Find z, given that 5 + 4*z - 4*z**3 - m + 4*z**2 + 7 = 0.
-1, 1
What is h in -1/3*h - 2/3 + 1/3*h**2 = 0?
-1, 2
Let t = 1579 - 1574. Let w(u) be the second derivative of -1/3*u**4 + 1/5*u**t + 2/15*u**6 + 8*u + 0 - 2/3*u**3 + 0*u**2. Factor w(h).
4*h*(h - 1)*(h + 1)**2
Let g = -81 - -84. Let c(r) be the third derivative of 0 + g*r**2 + 2/27*r**3 + 2/135*r**5 + 5/108*r**4 + 0*r + 1/540*r**6. Factor c(l).
2*(l + 1)**2*(l + 2)/9
Let m(q) be the first derivative of -q**4/8 - q**3 + q**2/4 + 3*q + 230. Let m(r) = 0. Calculate r.
-6, -1, 1
Let h = -115 + 119. Let -16*m - 7 - h + 2*m**4 + 16*m**3 + 12*m**2 - 3 = 0. What is m?
-7, -1, 1
Find d, given that 3/5*d**3 + 417/5*d**2 + 14283/5 + 14697/5*d = 0.
-69, -1
Let a(m) = 2*m**2 + m - 3. Let k(y) be the second derivative of 0*y**3 - 1/2*y**2 + 0 + y + 1/12*y**4. Let c(u) = -3*a(u) + 7*k(u). Let c(w) = 0. What is w?
1, 2
Let g(s) be the third derivative of 5/48*s**4 + 4*s**2 + 5/12*s**3 - 1/48*s**6 + 0 + 0*s - 1/24*s**5. Factor g(t).
-5*(t - 1)*(t + 1)**2/2
Let y(t) = 2*t**3 - 4*t**2 + 13*t + 13. Let j(h) = h**3 - 3*h**2 + 14*h + 14. Let x(f) = -6*j(f) + 4*y(f). Suppose x(b) = 0. Calculate b.
-4, -1, 4
Let n be 16/(-33)*-3 - (-210)/385. Factor 18/5*c**n + 27/5*c + 3/5*c**3 + 12/5.
3*(c + 1)**2*(c + 4)/5
Let x(n) be the first derivative of n**3/18 + 44*n**2/3 + 3872*n/3 + 236. Factor x(d).
(d + 88)**2/6
Let r(q) be the second derivative of -3*q**5/20 + q**4/2 + q**3/2 - 3*q**2 - 78*q. Suppose r(y) = 0. Calculate y.
-1, 1, 2
Let p(o) be the first derivative of -o**6/6 + 2*o**5/5 - 2*o**3/3 + o**2/2 + 20. Factor p(u).
-u*(u - 1)**3*(u + 1)
Let u be 6/(-10)*(671/66 + -11). Suppose -v = -0*v - 5. Suppose -u*p**v - 1/2*p**2 + 0*p + 0 + 1/2*p**3 + 1/2*p**4 = 0. Calculate p.
-1, 0, 1
Let a(b) = 3*b**2 - 53*b - 337. Let u be a(-5). Factor 0*t - 2/3*t**4 + 2/3*t**2 + 0 - 2/3*t**5 + 2/3*t**u.
-2*t**2*(t - 1)*(t + 1)**2/3
Let p(o) be the third derivative of o**6/420 + 3*o**5/70 + o**4/6 - 8*o**3/7 + 6*o**2 + 11*o. Determine r so that p(r) = 0.
-6, -4, 1
Let q = 582 - 582. Factor 0 - 1/4*n**5 + 0*n + 0*n**2 + 1/4*n**3 + q*n**4.
-n**3*(n - 1)*(n + 1)/4
Suppose 3*i + 20 = 7*i. Factor -56*y**4 + 57*y**4 + 3*y**2 + 0*y**2 - i*y**3 + y**5.
y**2*(y - 1)**2*(y + 3)
Let i(j) be the third derivative of -35*j**8/48 - 151*j**7/6 + 367*j**6/3 + 161*j**5 + 60*j**4 - 322*j**2. Let i(x) = 0. Calculate x.
-24, -2/7, 0, 3
Suppose -4*m + 5*x = -125, m + 3*x = -3*m + 85. Suppose 0*w**2 + m - w - 19 - 12 + w**2 = 0. Calculate w.
-2, 3
Factor 4*j**3 + 0 - 4/5*j**5 - 12/5*j**2 - 4/5*j**4 + 0*j.
-4*j**2*(j - 1)**2*(j + 3)/5
Let k(t) be the first derivative of -3*t**4/4 + 20*t**3 - 159*t**2/2 + 102*t - 209. Factor k(r).
-3*(r - 17)*(r - 2)*(r - 1)
Suppose 5*o + 9 = 5*s - 26, -s + 13 = -4*o. Suppose -5 = t - 5*z - 2, -7 = -s*t + 3*z. Factor 2/11*b**t - 4/11*b + 2/11.
2*(b - 1)**2/11
Let x(k) = 3*k**2 - 5*k + 4. Let b be (-17)/(-15) - 6/45. Let v be x(b). Solve 1/2*u**3 + 0 + 0*u + 0*u**v + 0*u**4 - 1/2*u**5 = 0 for u.
-1, 0, 1
Let x(v) be the second derivative of 1/35*v**5 + 0*v**2 + 0 + 2/7*v**3 - 3*v - 4/21*v**4. Factor x(s).
4*s*(s - 3)*(s - 1)/7
Let l(a) be the third derivative of a**6/120 - a**5/40 + a**4/48 - 28*a**2. Find g such that l(g) = 0.
0, 1/2, 1
Let k(w) be the first derivative of 1 - 1/3*w**3 - 2*w**2 - 5*w. Let q(a) = -a**2 - 5*a - 6. Let x(c) = -6*k(c) + 5*q(c). Factor x(n).
n*(n - 1)
Let q be (-34)/(3 - 48/15). Solve -4*n**3 + 4*n + q*n**2 - 170*n**2 = 0 for n.
-1, 0, 1
Let y(n) be the third derivative of n**8/2520 + n**7/1575 - n**6/900 - n**5/450 - 62*n**2. Let y(s) = 0. What is s?
-1, 0, 1
Let c(x) = -x**3 + 30*x**2 - 30*x + 67. Let n be c(29). Let l be -3 + -1 + -1 + n/5. Solve -3/5*v**3 - 4/5*v**5 + 0 - l*v**4 + 16/5*v**2 + 4/5*v = 0 for v.
-2, -1/4, 0, 1
Let q(z) be the third derivative of -z**5/300 + 8*z**4/15 + 13*z**3/6 - z**2 + 116*z. Factor q(x).
-(x - 65)*(x + 1)/5
Let p(a) be the third derivative of -a**5/50 + 12*a**4/5 - 576*a**3/5 + 9*a**2. Factor p(b).
-6*(b - 24)**2/5
Let u(t) = t**2 - 744*t + 46132. Let z(a) = 12*a**2 - 9672*a + 599718. Let c(x) = 27*u(x) - 2*z(x). Factor c(p).
3*(p - 124)**2
Let r(u) be the first derivative of 2*u**6/3 - 29*u**5/5 + 67*u**4/4 - 17*u**3 + 9*u**2/2 - 156. Let r(i) = 0. Calculate i.
0, 1/4, 1, 3
Let h(u) be the first derivative of 25*u**4/4 - 35*u**3/3 + 5*u**2 + 33. Factor h(t).
5*t*(t - 1)*(5*t - 2)
Let m be ((-6)/(-4) - -1)*120/3600. Let q(t) be the first derivative of 0*t**2 + 1/5*t**5 + 0*t + 0*t**3 + m*t**6 + 0*t**4 - 3. Factor q(f).
f**4*(f + 2)/2
Suppose 5*v + l - 24 = 0, -4*v = 2*l + l - 28. Solve 23*n**3 - 45*n**2 - v*n**3 - n**4 + 2*n**3 - 2*n**4 + 39*n - 12 = 0.
1, 4
Let d(v) be the second derivative of v**6/60 - 3*v**5/20 + 13*v**4/24 - v**3 + v**2 - 11*v + 4. Factor d(j).
(j - 2)**2*(j - 1)**2/2
Suppose 201 = 29*w + 38*w. Let y(v) be the second derivative of 0 + 0*v**2 + 3/10*v**5 + 1/10*v**6 + 1/4*v**4 - 5*v + 0*v**w. Determine i, given that y(i) = 0.
-1, 0
Let f be 24/9 - 10/15. Find n such that -2 - 10*n + 3 - 11 - 2*n**2 - f = 0.
-3, -2
Let k(y) = 18*y**2 - 18*y + 12. Let t be k(-6). Find b such that -50 - 1 - 3960*b**2 + 3993*b**4 + 3 - 4322*b**3 + 10130*b**3 + t*b = 0.
-2, 2/11
Let m(w) be the first derivative of -9*w**6/4 + 153*w**5/10 - 69*w**4/8 - 125*w**3/6 + 26*w**2 - 10*w - 21. Suppose m(g) = 0. What is g?
-1, 1/3, 2/3, 5
Let n be ((-21)/(-27) - 1) + 776/(-72). Let w be (-14)/(-44) - 2/n. What is l in 0*l**2 - w*l**3 + 0 + 0*l = 0?
0
Let o(p) be the second derivative of -p**5/20 + 2*p**4/3 - p**3 - p**2 - 7*p. Let z be o(7). Find g, given that 14*g**3 + g - g - 17*g**3 + 3*g**z = 0.
-1, 0, 1
Let p(y) be the third derivative of y**9/2160 - y**8/560 + y*