t derivative of 15*x**2 - 20 - 35/3*x**3 + 5*x. Factor q(v).
-5*(v - 1)*(7*v + 1)
Let o(s) be the first derivative of 3*s**7/280 - s**6/30 - s**5/40 + s**4/4 + 14*s**3/3 + 15. Let t(q) be the third derivative of o(q). What is z in t(z) = 0?
-2/3, 1
Let q = -17 + 32. Let j = -10 + q. Let 6*s**4 + 4*s**3 - 2 + 20*s**5 - 18*s**j - 6*s + 0 - 4*s**2 = 0. Calculate s.
-1, 1
Let m(k) be the third derivative of -k**8/84 + 12*k**7/35 - 17*k**6/5 + 244*k**5/15 - 83*k**4/2 + 60*k**3 - 515*k**2. Find x such that m(x) = 0.
1, 3, 10
Suppose -10*i - 80 = -5*i + 5*z, -4*i - 56 = 2*z. Let o be (-14)/(-40) + i/(-30). Solve -3/8*k - 3/8 + o*k**2 = 0 for k.
-1/2, 1
Let y(u) = 6*u**3 - u**2 - 2*u - 10. Let l(q) = -7*q**3 + 2*q**2 + 3*q + 12. Let b(i) = -5*l(i) - 6*y(i). Let b(m) = 0. Calculate m.
-3, -1, 0
Let x(d) be the third derivative of d**9/151200 - d**8/16800 + d**7/6300 - 11*d**5/60 - 8*d**2. Let c(z) be the third derivative of x(z). Factor c(n).
2*n*(n - 2)*(n - 1)/5
Determine r, given that 1/3*r**3 + 7/3*r**2 - 1 - 1/3*r - 4/3*r**4 = 0.
-1, -3/4, 1
Let x(d) = -7*d - 8. Let r be x(7). Let n = 172/3 + r. Solve 4/3*w**3 + n*w**4 + 4/3*w + 1/3 + 2*w**2 = 0 for w.
-1
What is s in 1/2*s**4 + 63/2*s**2 + 17*s**3 - 17*s - 32 = 0?
-32, -2, -1, 1
Let q(a) be the third derivative of a**5/120 + 3*a**4/8 - 10*a**3/3 - 141*a**2. Factor q(p).
(p - 2)*(p + 20)/2
Let j(y) be the first derivative of -2*y**4/3 + 34*y**3/9 - 20*y**2/3 + 8*y/3 - 154. Factor j(h).
-2*(h - 2)**2*(4*h - 1)/3
Let s = 61/5 - 243/20. Let k(a) be the first derivative of -3/8*a**4 - a - 3/2*a**2 - s*a**5 - 13/12*a**3 + 2. Factor k(y).
-(y + 1)**2*(y + 2)**2/4
Let c(k) be the second derivative of 1/100*k**5 + k - 1/75*k**6 + 1/210*k**7 + 0 + 0*k**4 + 0*k**3 + 0*k**2. Suppose c(q) = 0. Calculate q.
0, 1
Factor -61*v**2 + 4 + 58*v + 31/2*v**3.
(v - 2)**2*(31*v + 2)/2
Suppose f = -3*i + 54, -2*f - 2*i = 2*i - 106. Let k = -152/3 + f. Factor -1/3*d**2 - k*d + 0.
-d*(d + 1)/3
Let y(x) be the first derivative of -x**6/180 + x**5/20 - x**4/6 - x**3 + 4. Let m(o) be the third derivative of y(o). Factor m(h).
-2*(h - 2)*(h - 1)
Suppose 0 = 3*s + 29 - 44. Solve 84*i**2 - 3*i**s + 3*i**3 - 84*i**2 = 0.
-1, 0, 1
Let b(y) be the third derivative of y**6/240 + y**5/24 - y**4/6 - y**3 + 2*y**2 - 2*y. Factor b(f).
(f - 2)*(f + 1)*(f + 6)/2
Let u(a) be the second derivative of 2*a**6/105 + a**5/35 - a**4/21 - 2*a**3/21 - 22*a + 2. Factor u(i).
4*i*(i - 1)*(i + 1)**2/7
What is b in 11*b**2 + 9*b**2 - 74*b + 6*b**2 - 28*b**2 = 0?
-37, 0
Let p = 969172/22435 - -4/4487. Factor 176/5*g + 20*g**3 + 32/5 + 16/5*g**4 + p*g**2.
4*(g + 2)**3*(4*g + 1)/5
Suppose 2/13*v**2 + 120/13*v + 1800/13 = 0. What is v?
-30
Let s be (-2)/3*(-45)/6. Suppose s*v - 2*v = 0. Suppose -3*l**4 - l**3 + v*l**2 + 2*l**4 - l**2 + l**5 + 2*l**4 = 0. What is l?
-1, 0, 1
Let b(x) be the third derivative of x**9/12096 + x**8/2016 - x**7/1008 - x**6/72 + 3*x**5/10 - 2*x**2. Let g(k) be the third derivative of b(k). Factor g(h).
5*(h - 1)*(h + 1)*(h + 2)
Solve 2496*z + 5*z**3 + 2*z**3 - 5*z**3 - 294*z**2 + 4*z**3 - 1536 + 3*z**3 = 0 for z.
2/3, 16
Factor 2/3 - 4/9*i**2 - 10/9*i.
-2*(i + 3)*(2*i - 1)/9
Let i(b) = b**3 + 6*b**2 + 2*b + 6. Let f be i(-6). Let n be (f/(-36))/((-8)/(-6)). Factor 1/8*q**2 + 1/8*q - 1/8*q**3 - n.
-(q - 1)**2*(q + 1)/8
Let l be 9/(-15)*30/(-3). Let k = -5 + l. Factor 1 - 2 + k - j - j**4 + j**3 + j**2.
-j*(j - 1)**2*(j + 1)
Let p(c) be the first derivative of c**6/8 - 3*c**5/20 - 63*c**4/16 + 45*c**3/4 - 48. Factor p(y).
3*y**2*(y - 3)**2*(y + 5)/4
Let w(q) = -q**2 + 70*q - 323. Let z be w(65). Factor 1/5*a**z - 1/5*a - 2/5.
(a - 2)*(a + 1)/5
Let f(n) be the first derivative of 1/3*n**3 + 0*n + 6 + 1/6*n**4 + 1/30*n**5 + n**2. Let s(l) be the second derivative of f(l). Solve s(y) = 0.
-1
Let r(a) be the second derivative of -2*a**2 + 0 - 16*a - a**3 + 1/10*a**5 + 0*a**4. Factor r(z).
2*(z - 2)*(z + 1)**2
Let o(p) be the third derivative of -p**8/3024 - 8*p**7/945 - 11*p**6/135 - 16*p**5/45 - 2*p**4/3 - 15*p**2 - 4. Factor o(q).
-q*(q + 2)**2*(q + 6)**2/9
Let c(o) be the first derivative of -25*o - 1/3*o**3 + 5*o**2 + 13. Find t such that c(t) = 0.
5
Suppose 140 = -7*x + 2*x. Let l = x - -59/2. Solve -l*d + 0*d**3 + 9/4*d**2 - 3/4*d**4 + 0 = 0.
-2, 0, 1
Let w(i) be the first derivative of -27 - 48*i**2 - 4*i**3 - 1/8*i**4 - 256*i. Factor w(p).
-(p + 8)**3/2
Find j such that 94*j + 4900 + 3*j**2 - 3*j**2 + 186*j + j**2 + 3*j**2 = 0.
-35
Let b(h) be the third derivative of -2*h**7/105 - h**6/2 - 5*h**5 - 125*h**4/6 + 379*h**2. Find j, given that b(j) = 0.
-5, 0
Let g(r) be the first derivative of -27*r**4/4 + 10*r**3 + 27*r**2/2 - 30*r - 9. Let g(t) = 0. What is t?
-1, 1, 10/9
Let k(q) = 8*q**2 - 40*q - 48. Let l(v) = 7*v**2 - 39*v - 46. Let f(x) = 3*k(x) - 4*l(x). Let f(m) = 0. What is m?
-1, 10
Let b be 1 - 2 - (3 + 5). Let z = b - -28/3. Factor 2*k + 3 + z*k**2.
(k + 3)**2/3
Suppose -111*u + 152*u = 164. Find d, given that 1/2*d**2 + 3/4*d**3 + 0*d + 1/4*d**u + 0 = 0.
-2, -1, 0
Let p(w) be the first derivative of 4*w - 1/2*w**4 + 8/3*w**3 - 38 - 5*w**2. Factor p(k).
-2*(k - 2)*(k - 1)**2
Let n(k) be the second derivative of -k**5/30 + k**4/12 - 13*k**2/2 - 21*k. Let m(p) be the first derivative of n(p). What is w in m(w) = 0?
0, 1
Let t = -14/51 - -15/34. Let z(u) be the third derivative of 0 - t*u**3 + 0*u - 1/20*u**5 + 1/120*u**6 + 1/8*u**4 - 12*u**2. Solve z(d) = 0.
1
Factor 288 + 2/9*b**2 - 16*b.
2*(b - 36)**2/9
Let y(z) be the third derivative of z**6/200 + z**5/20 + z**4/5 + 2*z**3/5 + 2*z**2 + 9*z. Find s such that y(s) = 0.
-2, -1
Let y(o) = 3*o - 4. Let s be y(2). Factor s*d**2 + d**2 - 144*d**3 - 4*d - 9*d**2 + 142*d**3.
-2*d*(d + 1)*(d + 2)
Let x(c) = -c**2 + 7*c + 9. Let h be x(8). Let b(n) = 5*n**2 - 10*n. Let t(i) = i. Let p(j) = h*b(j) + 5*t(j). Find m such that p(m) = 0.
0, 1
Let v(z) be the first derivative of 5*z**6/4 + 21*z**5/10 + 3*z**4/4 - 120. Factor v(s).
3*s**3*(s + 1)*(5*s + 2)/2
Let m(l) be the first derivative of 2*l + 3/2*l**2 + 1/8*l**4 + 7 - 3/4*l**3. Let h(r) be the first derivative of m(r). Factor h(v).
3*(v - 2)*(v - 1)/2
Let r(t) be the first derivative of t**5 - 5*t**4/4 - 5*t**3/3 + 5*t**2/2 - 456. Determine g so that r(g) = 0.
-1, 0, 1
Suppose -3/4*w + 0 + 3/4*w**2 = 0. Calculate w.
0, 1
Suppose 2*n + 5*b = -159 + 50, n - 4*b + 22 = 0. Let a = n - -42. Suppose -6/5*g**4 + 0 - 3/5*g**5 + 0*g + a*g**2 + 0*g**3 = 0. What is g?
-2, 0
Determine u, given that -18*u - 42*u - 2*u**4 + 3*u**4 + 180 + 60*u**3 - 175*u**2 - 6*u**4 = 0.
-1, 1, 6
Let c = -268 + 273. Let o(n) be the third derivative of 1/336*n**8 + 0*n**3 + 0 + 0*n**6 + 1/105*n**7 - 1/24*n**4 + 6*n**2 + 0*n - 1/30*n**c. Factor o(y).
y*(y - 1)*(y + 1)**3
Let w(d) be the third derivative of 2/35*d**7 + 0*d + 0*d**4 - 16*d**2 + 1/84*d**8 + 0*d**5 + 0*d**3 + 1/15*d**6 + 0. Factor w(l).
4*l**3*(l + 1)*(l + 2)
Let c(p) = -p**4 - 7*p**3 + 5*p**2 - 15*p. Let r(k) = -k**4 - 22*k**3 + 15*k**2 - 40*k. Let s(x) = -8*c(x) + 3*r(x). Factor s(m).
5*m**2*(m - 1)**2
Suppose 5*d = 3*x - 6, 0 = x + d - 3*d - 2. Let i be (-108)/324 + (-2)/(-6). Factor -1/3*h**x - 1/3*h**4 + 2/3*h**3 + i + 0*h.
-h**2*(h - 1)**2/3
Suppose -8*z - 4 = -44. Let l(c) be the third derivative of 0*c**3 + 0 + z*c**2 - 1/12*c**4 + 0*c - 1/60*c**5. Let l(u) = 0. Calculate u.
-2, 0
Let y(z) be the second derivative of -24*z + 0 - 5/6*z**3 + 2*z**2 + 1/6*z**4 - 1/80*z**5. Factor y(j).
-(j - 4)*(j - 2)**2/4
Let y be (3/2)/(21/28). Factor 2*n**2 + 0*n**y - 4*n**2 - 3*n**3 + 5*n**2.
-3*n**2*(n - 1)
Let r be 0 - 1 - (-1320)/429. Let g = 239/65 - r. Suppose g*j**4 - 2/5*j**2 - 6/5*j**3 + 0*j + 0 = 0. Calculate j.
-1/4, 0, 1
Let q(k) be the first derivative of k**9/1512 - k**8/280 + k**7/140 - k**6/180 - 3*k**3 + 14. Let r(x) be the third derivative of q(x). Solve r(t) = 0.
0, 1
Let b(f) be the second derivative of -1/5*f**2 - 1/10*f**4 + 1/50*f**5 + 1/5*f**3 + 0 - 13*f. Factor b(r).
2*(r - 1)**3/5
Let 17161/2 + 131*a + 1/2*a**2 = 0. Calculate a.
-131
Determine i so that -45/2 - 9/4*i**2 + 3/4*i**4 - 45/4*i**3 + 141/4*i = 0.
-2, 1, 15
Suppose -4*y = -3*q - 7, 5*q - 4*y + 0 + 1 = 0. Factor -189 - q*s**3 - s**3 - 8*s**2 + 189 + 4*s**4.
4*s**2*(s - 2)*(s + 1)
Let k = 1566/9475 + -2/379. Let p 