c**3 + 9*c + 11*c**a + 2 = 0. What is c?
-1
Factor 1/3*x**2 - 20/3 - 8/3*x.
(x - 10)*(x + 2)/3
Let p(h) be the third derivative of -16*h**2 + 0*h**3 + 0*h**4 + 1/210*h**5 + 0*h + 0. Factor p(l).
2*l**2/7
Let b = -30 - -26. Let h be 12/(-8)*b*(-1)/(-18). Find a such that 0*a - h*a**2 + 0 + 1/3*a**4 + 0*a**3 = 0.
-1, 0, 1
Let n(k) be the second derivative of -14/3*k**3 + 8*k**2 - 13*k + k**4 + 0. Find q, given that n(q) = 0.
1, 4/3
Determine f so that -8/5*f**3 + 0*f - f**4 - 4/5*f**2 + 0 - 1/5*f**5 = 0.
-2, -1, 0
Let f be (-56)/(-32)*(36/(-7) - -2) - -6. Suppose 0*k**2 + 1/2*k**3 + 1/4*k**4 - f*k - 1/4 = 0. What is k?
-1, 1
Let c be 7 - (-5 - -8) - 4. Let v(l) be the second derivative of 1/42*l**7 + 0*l**6 - 1/20*l**5 + 0*l**3 + 0*l**2 + c + 2*l + 0*l**4. Factor v(g).
g**3*(g - 1)*(g + 1)
Let z(q) = -6*q**4 + 131*q**3 - 713*q**2 + 360*q + 1215. Let x(n) = 3*n**4 - 66*n**3 + 357*n**2 - 180*n - 609. Let p(i) = 5*x(i) + 3*z(i). Factor p(a).
-3*(a - 10)**2*(a - 2)*(a + 1)
Let v(j) be the third derivative of j**6/600 - j**5/150 - j**4/8 + 6*j**3/5 + 52*j**2. Factor v(o).
(o - 3)**2*(o + 4)/5
Suppose -302*c = -300*c - 8. Let a(o) be the second derivative of -4*o - 4/21*o**3 + 0*o**2 + 1/21*o**c + 0. Determine z, given that a(z) = 0.
0, 2
Let f(j) be the third derivative of 1/210*j**7 - 1/6*j**4 + 43*j**2 - 1/2*j**3 + 0 + 1/30*j**6 + 0*j + 1/30*j**5. Let f(z) = 0. What is z?
-3, -1, 1
Let h(a) be the third derivative of -a**5/330 + a**4/22 - 177*a**2. Factor h(f).
-2*f*(f - 6)/11
Find z such that 3*z + 18/5 + 3/5*z**2 = 0.
-3, -2
Suppose 28*y - 9 = 27*y. Suppose x**3 - 2*x - 22*x**2 + y*x**2 + 14*x**2 = 0. Calculate x.
-2, 0, 1
Let b(c) be the first derivative of c**4/12 - c**3/9 - 20*c**2/3 + 112*c/3 - 2. Factor b(k).
(k - 4)**2*(k + 7)/3
Let g(f) be the third derivative of f**5/180 + 9*f**4/4 + 729*f**3/2 + 407*f**2. Find o, given that g(o) = 0.
-81
Let l(v) be the third derivative of -v**8/1176 + v**6/140 + v**5/105 - 70*v**2. Factor l(w).
-2*w**2*(w - 2)*(w + 1)**2/7
Factor 15*p**3 + 0 + 1/2*p**5 - 22*p**2 - 9/2*p**4 + 12*p.
p*(p - 3)*(p - 2)**3/2
Suppose 5*a + 52 = 31*a. Let b(j) be the second derivative of -1/8*j**a - 7/40*j**6 + 1/8*j**4 + 1/8*j**5 - 2*j + 3/56*j**7 - 1/8*j**3 + 0. Factor b(p).
(p - 1)**3*(3*p + 1)**2/4
Let l = -81 - -163. Let n = -79 + l. Let -2/11*m**n + 2/11 - 2/11*m**2 + 2/11*m = 0. What is m?
-1, 1
Let t = 383619/68 - 5642. Let a = -5/17 - t. Factor 0 + 0*o - a*o**2.
-o**2/4
Let m(i) be the third derivative of i**6/270 + 113*i**5/270 + 406*i**4/27 + 784*i**3/27 - i**2 + 11. Factor m(p).
2*(p + 28)**2*(2*p + 1)/9
Let c be (13 + -10)*13/(-3). Let o = 13 + c. Suppose 0 + 2/3*y**5 + o*y**3 - 4/3*y**4 + 4/3*y**2 - 2/3*y = 0. What is y?
-1, 0, 1
Factor -4/7*p**2 + 0 - 212/7*p.
-4*p*(p + 53)/7
Let m(n) be the first derivative of -3*n**4/14 + 8*n**3/7 + 33*n**2/7 + 36*n/7 - 16. Factor m(w).
-6*(w - 6)*(w + 1)**2/7
Suppose 89*k - 83*k = 24. Let g(s) be the second derivative of -1/6*s**k + s + 1/3*s**3 + 0 + 0*s**2 + 1/40*s**5. Determine d, given that g(d) = 0.
0, 2
Let x(o) be the second derivative of -o**7/315 - o**6/225 + 4*o**5/75 + 4*o**4/45 - 16*o**3/45 - 16*o**2/15 + 99*o. Find l such that x(l) = 0.
-2, -1, 2
Suppose -n + 9*n - 624 = 0. Solve -158*h - 16 + n*h + 5*h**2 - 4 + 20*h**3 = 0.
-2, -1/4, 2
Let y be (7/5 - 1) + 1. Let l = 12/1483 - -2906/7415. Factor l + 9/5*a + y*a**2.
(a + 1)*(7*a + 2)/5
Let k = -2/101 + 307/202. Let h(f) be the second derivative of -k*f**3 + 3*f**2 + 0 + 1/4*f**4 + 4*f. Factor h(b).
3*(b - 2)*(b - 1)
Let r(v) be the third derivative of 0 + 17*v**2 + 1/60*v**5 - 1/120*v**6 + 1/6*v**4 + 0*v - 2/3*v**3. Factor r(b).
-(b - 2)*(b - 1)*(b + 2)
Let f(m) be the second derivative of -3*m**5/70 + 23*m**4/14 - 143*m**3/7 + 363*m**2/7 - 196*m. Factor f(t).
-6*(t - 11)**2*(t - 1)/7
Factor 3/7*f**2 + 36/7 + 3*f.
3*(f + 3)*(f + 4)/7
Let q(s) = -2*s**2 - 8*s - 6. Suppose 2*o - 6 = 3*o. Let w be (-4)/(-6)*(-27)/o. Let y(p) = -10*p**2 - 40*p - 30. Let m(a) = w*y(a) - 16*q(a). Factor m(r).
2*(r + 1)*(r + 3)
Factor 28*g**3 + 3*g - 6*g**3 + 81 + g**4 + 54*g**2 + 105*g - 10*g**3.
(g + 3)**4
Let i = 43 + -49. Let f(s) = s**2 + 3*s - 14. Let j be f(i). Suppose 1/2*p**j - 1/2*p**2 + 1/4*p + 0 - 1/4*p**5 + 0*p**3 = 0. Calculate p.
-1, 0, 1
Let q(z) be the third derivative of -3*z**7/70 + z**6/10 - z**5/15 - 137*z**2. Factor q(a).
-a**2*(3*a - 2)**2
Solve -828/5*d - 108/5 - 1428/5*d**2 + 32*d**4 + 668/5*d**3 - 64/5*d**5 = 0 for d.
-3, -1/4, 3
Let q(f) be the second derivative of 2 + 4/255*f**6 + 36/17*f**2 - 43/170*f**5 - 24*f + 56/17*f**3 + 5/6*f**4. Find l, given that q(l) = 0.
-1, -1/4, 6
Let u = 2/191 - -175/1528. Let n(q) be the third derivative of -1/80*q**6 + 0*q - u*q**4 + 3/40*q**5 + 0*q**3 + 5*q**2 + 0. Factor n(l).
-3*l*(l - 2)*(l - 1)/2
Determine k, given that 0*k + 0*k**2 + 1/3*k**5 + 0 + 2*k**4 + 5/3*k**3 = 0.
-5, -1, 0
Let p(s) = 8*s - 13*s - 32 + 36*s - 31*s**2 + 0*s**3 - s**3. Let f be p(-32). Factor -2/15*l**2 + f*l + 2/15*l**5 + 2/5*l**3 - 2/5*l**4 + 0.
2*l**2*(l - 1)**3/15
Let s(g) = 2*g**2 - 2*g. Let r be s(0). Let a(d) be the third derivative of -1/120*d**5 + 0*d + r*d**3 + 0 - d**2 + 0*d**4. Factor a(q).
-q**2/2
Let k(f) be the third derivative of -f**8/1680 + f**7/210 - f**6/90 + 5*f**4/12 + f**2. Let s(z) be the second derivative of k(z). Solve s(c) = 0.
0, 1, 2
Let d(i) = 24*i - 1317. Let a be d(55). Let q = -149/4 + 769/20. Factor q - 6/5*z**2 - 3/5*z + 3/5*z**a.
3*(z - 2)*(z - 1)*(z + 1)/5
Factor -2/3*r - 1/3*r**4 + 0*r**3 + 0 + r**2.
-r*(r - 1)**2*(r + 2)/3
Factor -1 - 2/3*h**2 + 1/6*h**3 - 11/6*h.
(h - 6)*(h + 1)**2/6
Suppose l - 8 = m, m + m = 4. Factor 5*a**3 - 4*a**4 + 9*a**4 + 0*a**4 - l*a**2.
5*a**2*(a - 1)*(a + 2)
Let k(o) be the second derivative of o**6/210 + o**5/70 - o**4/12 + 2*o**3/21 + 126*o. Factor k(i).
i*(i - 1)**2*(i + 4)/7
Let t(l) = 7*l**2 - 14*l + 27. Let c(o) = -20*o**2 + 43*o - 81. Let g = 21 - 32. Let d(u) = g*t(u) - 4*c(u). Factor d(p).
3*(p - 3)**2
Let c(g) be the second derivative of -g**8/1680 - g**7/280 - g**6/120 - g**5/120 - 5*g**3/6 - 4*g. Let s(u) be the second derivative of c(u). Factor s(b).
-b*(b + 1)**3
Let z(a) be the third derivative of 0*a**3 + 0*a + 1/96*a**5 - 1/2688*a**8 + 1/48*a**4 - 1/320*a**6 + 0 - 1/336*a**7 + 16*a**2. Suppose z(l) = 0. What is l?
-4, -1, 0, 1
Factor -44*r - 24 + 12*r**2 - 30*r**2 - 4*r**3 - 6*r**2.
-4*(r + 1)*(r + 2)*(r + 3)
Factor 2/5*j**3 - 6/5*j**2 - 2/5*j + 4/5 + 2/5*j**4.
2*(j - 1)**2*(j + 1)*(j + 2)/5
Let y(g) = 11*g**2 + 48*g - 5. Let w(b) = 5*b**2 + 24*b - 2. Let m(f) = -5*w(f) + 2*y(f). Determine s, given that m(s) = 0.
-8, 0
Let b = -242 - -7261/30. Let q(x) be the third derivative of 1/6*x**4 + 0 + b*x**5 + 0*x + 0*x**3 + x**2. Factor q(d).
2*d*(d + 2)
Let s(m) be the second derivative of -m**5/140 - m**4/21 - 13*m - 16. Factor s(w).
-w**2*(w + 4)/7
Let f(u) be the second derivative of 0*u**4 + 0 + 1/6*u**6 + 0*u**5 - 10*u + 0*u**2 + 0*u**3. Find x, given that f(x) = 0.
0
Let f(j) = j**5 + j**4 - j**3 + j**2 + j - 1. Let b(d) = d**4 - 3*d**2 - d + 1. Let n = 19 + -18. Let h(c) = n*f(c) + b(c). Factor h(m).
m**2*(m - 1)*(m + 1)*(m + 2)
Let b(m) be the third derivative of m**8/84 + 4*m**7/105 - m**6/30 - 2*m**5/15 + 2*m**2 + 8. Find h, given that b(h) = 0.
-2, -1, 0, 1
Let a = 14/289 + 1389/1156. Suppose a + 1/12*b**2 - 4/3*b = 0. Calculate b.
1, 15
Let j(x) = -3*x**2 - 5 + 25*x + 3*x**2 - 29*x + x**2. Let v be j(5). Solve -1/4*o**2 + 1/4*o**4 + v + 0*o**3 + 0*o = 0 for o.
-1, 0, 1
Let y(o) be the second derivative of o**5/80 + o**4/12 - 5*o**3/24 - 10*o + 5. Factor y(i).
i*(i - 1)*(i + 5)/4
Let a be 45/15 + (-362)/78. Let r = a + 30/13. What is b in -4/3 - r*b**3 + 0*b**2 + 2*b = 0?
-2, 1
Suppose -5*h - 84 = -3*h. Let n be (-3)/(h/8) - (-8)/(-14). Factor -1/5*g - 1/5*g**2 + n.
-g*(g + 1)/5
Let t(r) = -19*r**3 + 2088*r**2 - 242208*r + 9365363. Let b(g) = -3*g**3 + 348*g**2 - 40368*g + 1560894. Let w(v) = 39*b(v) - 6*t(v). Factor w(l).
-3*(l - 116)**3
Let n = 1915/7 - 273. Let r = 32/11 + -158/77. Suppose -4/7 + n*l**2 - r*l + 6/7*l**3 = 0. Calculate l.
-1, -2/3, 1
Let b(s) be the second derivative of -s**4/12 + 5*s**3/6 + 5*s**2/2 + s. Let d be b(5). Factor 7*h**d - h**3 - 2*h**4 - 7*h**5 - h**5.
-h**3*(h + 1)**2
Let 