+ 3)**2
Let t(v) be the first derivative of -2*v**3/9 + 8*v/3 + 123. Factor t(g).
-2*(g - 2)*(g + 2)/3
Suppose -i = j - 4, -2 + 12 = 3*i + 5*j. Find k, given that 20*k - 6*k**2 - k**2 - i*k**3 + 7*k**2 = 0.
-2, 0, 2
Let v(h) be the first derivative of h**6/3 - 4*h**5/5 - 2*h**4 + 4*h**3/3 + 3*h**2 - 281. What is w in v(w) = 0?
-1, 0, 1, 3
Let n(t) be the first derivative of -1/4*t**3 - 1/8*t**2 + 0*t - 4 - 1/20*t**5 - 3/16*t**4. Factor n(a).
-a*(a + 1)**3/4
Suppose -x + 3*x - 2 = 0. Let r = x + 4. Factor 12*p**2 - 3*p**2 - 2*p**3 + r*p**3 + 6*p.
3*p*(p + 1)*(p + 2)
Let u be (-136)/(-36) - (-4)/18. Let h(j) be the second derivative of 0*j**3 + j + 0 - 1/42*j**7 + 0*j**5 + 0*j**2 + 0*j**u + 1/15*j**6. Factor h(l).
-l**4*(l - 2)
Let c(p) be the first derivative of 26*p**5/5 - 119*p**4/2 + 556*p**3/3 - 40*p**2 + 384. Factor c(s).
2*s*(s - 5)*(s - 4)*(13*s - 2)
Let a(q) = -13*q + 3. Let l be a(2). Let i = -20 - l. Factor -i*s**4 + 4 - 4 + 6*s**3 + 0*s**3 - 3*s**2.
-3*s**2*(s - 1)**2
Let v = -2/119 + -103/952. Let p = 5/8 + v. Determine f so that -1/4*f**3 - p*f**2 + 1/2 + 1/4*f = 0.
-2, -1, 1
Let n(m) = -m**3 - 654*m**2 - 139962*m - 10077708. Let l(g) = -g**2 + g - 2. Let i(f) = 6*l(f) - n(f). Factor i(j).
(j + 216)**3
Let p(t) be the second derivative of t**7/84 - 11*t**6/60 + 7*t**5/8 - 25*t**4/24 - 310*t. Solve p(z) = 0.
0, 1, 5
Let z(c) = 3*c**4 + 22*c**3 - 12*c**2 - 58*c + 45. Let w(b) = -11*b**4 - 89*b**3 + 49*b**2 + 231*b - 180. Let h(q) = 2*w(q) + 9*z(q). Factor h(l).
5*(l - 1)**2*(l + 3)**2
Let v(s) be the third derivative of -s**2 + 1/4*s**4 + 13/30*s**5 + 0 + 4/105*s**7 + 0*s**3 + 4/15*s**6 + 0*s. Factor v(x).
2*x*(x + 3)*(2*x + 1)**2
Suppose 5*t + 26 = 4*b, 2*t = -3*b - 3 + 11. Let g(v) be the first derivative of -1 - 1/7*v**2 + 1/14*v**b - 2/21*v**3 + 2/35*v**5 + 0*v. Factor g(n).
2*n*(n - 1)*(n + 1)**2/7
Let r = 39 - 37. Let a = -13 - -29. Factor 4*k**2 + r*k**2 + a*k + k**2 + 6 - 2.
(k + 2)*(7*k + 2)
Let f(h) = h**2 - 2. Let u be f(-2). Factor u*a**5 + 18*a**3 + 0*a**3 - 12*a**4 + 24*a**4.
2*a**3*(a + 3)**2
Let l be (-1)/((-37)/9 - -4). Suppose -5*x - 8 = -l*x. Factor -4/7*h**x + 2/7*h**3 + 0 + 0*h.
2*h**2*(h - 2)/7
Let j(a) = a**2 - 4. Let p(x) = -4*x**2 - 8*x - 18. Let m(s) = -4*j(s) + p(s). Factor m(f).
-2*(2*f + 1)**2
Let y(s) be the first derivative of -2*s**3/3 - 6*s**2 - 227. What is l in y(l) = 0?
-6, 0
Let c(k) be the third derivative of 1/90*k**5 + 0*k - 1/36*k**4 + 0 - 15*k**2 - 2/9*k**3. Solve c(a) = 0 for a.
-1, 2
Let y(s) be the second derivative of -s**7/14 - s**6/30 + 3*s**5/20 + s**4/12 - 78*s. Suppose y(u) = 0. What is u?
-1, -1/3, 0, 1
Determine r, given that 128*r - 172 + 7*r**2 - 39*r**2 + 441 - 24*r**2 + 4*r**3 + 243 = 0.
-2, 8
Let v(f) be the second derivative of -f**5/20 - 5*f**4/12 + 17*f**3/6 + 21*f**2/2 - 31*f. Solve v(h) = 0 for h.
-7, -1, 3
Suppose -6*l + 14 + 10 = 0. Let 45*a**2 + 0*a + l*a**3 - 27*a**2 - 26*a**2 + 4*a = 0. Calculate a.
0, 1
Let j(i) = i**3 - i**2 - i. Let a(t) = -t**2 + 8*t + 2. Let z be a(8). Let k(w) = 2*w**2 - w + w**2 + 3*w - w**2. Let f(g) = z*j(g) + k(g). Factor f(v).
2*v**3
Let l(b) be the second derivative of -b**8/17920 + b**7/960 - 37*b**4/12 - 5*b. Let d(z) be the third derivative of l(z). Find u, given that d(u) = 0.
0, 7
Let u(g) = 2*g**2 - 11*g - 7. Let f(t) = 26 - 2*t - 25 + 3*t. Let b(o) = -14*f(o) - 2*u(o). Factor b(a).
-4*a*(a - 2)
Let b be (19/228)/(25/(-30) + 1). Find w, given that -b - 3/2*w - 3/2*w**2 - 1/2*w**3 = 0.
-1
Let b(r) be the first derivative of r**5/15 + 65*r**4 + 25350*r**3 + 4943250*r**2 + 481966875*r + 610. Suppose b(z) = 0. What is z?
-195
Let r(q) be the first derivative of -5/2*q**4 + 8*q**2 + 14/3*q**3 - 8*q - 8. Suppose r(h) = 0. Calculate h.
-1, 2/5, 2
Suppose 3*b = 36 - 15. Factor 4*u**2 - b*u**2 + 8*u - u**2.
-4*u*(u - 2)
Let t = 1211 + -1206. Let d(k) be the first derivative of 1/22*k**4 - 5 - 1/11*k**6 + 2/11*k**2 - 2/11*k**t + 10/33*k**3 + 0*k. Suppose d(m) = 0. Calculate m.
-1, -2/3, 0, 1
Determine h so that 0 + 4/3*h**2 - 4/3*h + h**3 = 0.
-2, 0, 2/3
Suppose 3*i**2 + 5/3*i**3 + 0 - 14/3*i = 0. What is i?
-14/5, 0, 1
Suppose -m - 12*m = -26. Factor 4 + 2*p**3 + 73*p**2 - 79*p**m - 2*p + 0*p**3 + 2.
2*(p - 3)*(p - 1)*(p + 1)
Let b(h) be the second derivative of 2*h**7/21 - 8*h**6/15 + h**5 - 2*h**4/3 + 75*h. Determine a so that b(a) = 0.
0, 1, 2
Let t = 27 + -26. Let x be (3 + t)*3/4. Solve -3*b + 4*b - 2*b**3 + b**2 - 1 + b**x = 0.
-1, 1
Let c(l) be the third derivative of l**8/56 + 3*l**7/40 + 3*l**6/32 - l**5/80 - 3*l**4/32 + 2*l**2 - 443. Factor c(r).
3*r*(r + 1)**3*(8*r - 3)/4
Let k(i) = 95*i - 3405. Let m be k(36). Find p, given that m*p**2 - 15*p**3 - 15/2*p + 3/2 - 3/2*p**5 + 15/2*p**4 = 0.
1
Suppose 158/13*y + 48/13*y**2 - 2/13*y**3 + 108/13 = 0. Calculate y.
-2, -1, 27
Suppose 110 = 593*n - 538*n. Suppose -72/11*p**n + 0 - 194/11*p**3 - 8/11*p - 144/11*p**4 - 32/11*p**5 = 0. What is p?
-2, -1/4, 0
Let -389344 + 363952*q + 9498*q**2 - 91*q**4 + 15342*q**2 + 548*q**3 + 279*q**4 - 96*q**4 - 88*q**4 = 0. What is q?
-46, 1
Let u(g) be the third derivative of g**6/120 + 5*g**5/12 + 25*g**4/24 + 14*g**3/3 + g**2 + 45. Let x be u(-24). Factor -1/2*i**x - 1/2*i**2 + 0 + i**3 + 0*i.
-i**2*(i - 1)**2/2
Let b be (4 + -29)*11/(-55). Let i(k) be the first derivative of 3/4*k**4 + 2*k**3 + 0*k + 0*k**2 + 2 - 3/5*k**b. Factor i(r).
-3*r**2*(r - 2)*(r + 1)
Let k(c) = 5*c**3 - 10*c**2 + 32*c + 124. Let s(x) = -4*x**3 + 11*x**2 - 32*x - 125. Let z(l) = -3*k(l) - 4*s(l). Factor z(q).
(q - 8)**2*(q + 2)
Determine d so that 3*d**5 + 446*d**3 + 24*d - 3*d**4 + 428*d**3 - 889*d**3 + 12 + 3*d**2 = 0.
-1, 2
Factor 5*c + 0*c**2 + 128 - 131 - 3*c + c**2.
(c - 1)*(c + 3)
Let b(a) be the third derivative of -a**6/45 - a**5/90 + a**4/72 + a**2. Let b(s) = 0. What is s?
-1/2, 0, 1/4
Find w, given that 2*w + 2*w**2 + 2*w**3 + 0*w - 2*w + w - 2 - 3*w = 0.
-1, 1
Let c(n) be the third derivative of 0 + 1/120*n**5 + 1/240*n**6 + 0*n - 1/48*n**4 - 1/12*n**3 + 28*n**2. Suppose c(b) = 0. What is b?
-1, 1
Suppose 3*h = 5*v + 2*h + 541, 2*h + 322 = -3*v. Let i = -105 - v. Let 4/5*b**2 + 4/5*b**4 + 1/5*b + 6/5*b**i + 1/5*b**5 + 0 = 0. Calculate b.
-1, 0
Let t = 75407/3 + -25125. Find o, given that -64/3 - 4/3*o**2 - t*o = 0.
-4
Let c(q) = -q**3 + 5*q**2 + 4. Let r be c(6). Let p = r - -35. Let -15*g - 3*g**2 + 7*g**3 + 9*g**3 - 9 - 18*g**3 + 5*g**p = 0. What is g?
-1, 3
Let w(a) = a**2 + 3*a - 4. Suppose 4*l + 3 + 17 = 0. Let z be w(l). Let 12*p**3 + z*p**4 + 8 + 0*p**4 + 2*p**4 - 18*p**2 + 2*p**2 - 12*p = 0. What is p?
-2, -1, 1/2, 1
Let c be 108/5*240/32. Solve 39*k + c + 2*k**3 + 4*k**2 + 159*k + 4*k**2 + 30*k**2 = 0 for k.
-9, -1
Let g(l) = -l - 1. Suppose 5*b = 5*t, 0*t = -3*t - 3. Let z(j) = -4*j**2 - 56*j - 116. Let f(y) = b*z(y) + 16*g(y). Determine v, given that f(v) = 0.
-5
Let d(f) be the third derivative of -3*f**6/320 + f**5/80 + 3*f**4/16 - f**3/2 + 6*f**2. Factor d(z).
-3*(z - 2)*(z + 2)*(3*z - 2)/8
Factor 12 + 3/4*p**3 - 27/4*p**2 + 9/2*p.
3*(p - 8)*(p - 2)*(p + 1)/4
Let j(z) = -z**2 + z + 1. Suppose 2 = p + 5. Let l(u) = 9*u**2 + 18*u + 6. Let n(m) = p*j(m) + l(m). Factor n(v).
3*(v + 1)*(4*v + 1)
Let n(s) be the first derivative of -1/18*s**3 - 1/72*s**4 - 2 - 1/12*s**2 + 2*s. Let a(x) be the first derivative of n(x). Factor a(q).
-(q + 1)**2/6
Let s be (21/28)/(6/40). Suppose -4*r - 5*g = -41, -5*r = -4*r + s*g - 29. Solve 6/5*l**3 - 21/5*l - 3/5*l**r + 2*l**2 + 9/5 - 1/5*l**5 = 0.
-3, 1
Let y(o) be the first derivative of -2*o**2 + 24*o - 4/3*o**3 + 6. Factor y(q).
-4*(q - 2)*(q + 3)
Let u(k) be the third derivative of -6*k**2 + 4 + 0*k + 0*k**3 - 5/48*k**4 - 13/240*k**5 + 1/160*k**6. Factor u(s).
s*(s - 5)*(3*s + 2)/4
What is t in 1/6*t**2 + 7/2 + 5/3*t = 0?
-7, -3
Find v, given that -1/3*v**3 + 2/3 + v**2 + 5/3*v - 1/3*v**4 = 0.
-1, 2
Let h(s) be the first derivative of -3*s**4/8 + 9*s**3/4 + 231*s**2/8 + 27*s - 428. Factor h(u).
-3*(u - 9)*(u + 4)*(2*u + 1)/4
Solve -42*k - 35*k**2 + 0*k**3 - 57*k + 0*k**3 - 5*k**3 + 39*k = 0.
-4, -3, 0
Let t(s) be the second derivative of -3*s**5/20 + s**4/2 + 2*s**3 - 12*s**2 - s + 18. Suppose t(r) = 0. What is r?
-2, 2
Let c(d) be the second derivative of -1/110*d**5 - 48/11*d**2 - 35*d - 40/33*d**3 + 0 - 1/6*