 135*h**2.
5*(h - 1)**3*(7*h - 2)
Let b(u) be the third derivative of u**5/30 + 5*u**4/12 + 2*u**3 - 3*u**2 + 10. Find r such that b(r) = 0.
-3, -2
Let q(m) = 2*m**2 + 29*m - 31. Let g(l) = 2*l**2 + 28*l - 30. Let s(i) = 7*g(i) - 6*q(i). Find d, given that s(d) = 0.
-12, 1
Suppose -43*c + v + 17 = -40*c, -3*v + 3 = 0. Let d(o) be the first derivative of -4/7*o + c - 8/21*o**3 + 5/7*o**2 + 1/14*o**4. Factor d(j).
2*(j - 2)*(j - 1)**2/7
Let o(w) be the first derivative of w**6/3060 + w**5/510 + 32*w**3/3 + w - 44. Let f(l) be the third derivative of o(l). Factor f(h).
2*h*(h + 2)/17
Let j(w) be the third derivative of w**5/90 - 25*w**3/9 + 76*w**2 + 2. Factor j(u).
2*(u - 5)*(u + 5)/3
Suppose 2*r - 11 = -5. Let f(z) be the first derivative of -1 + 0*z - z**r - 3/5*z**4 - 3/25*z**5 - 3/5*z**2. Find q such that f(q) = 0.
-2, -1, 0
Suppose -30 - 4 = -2*m. Let o = m + -8. Let -o*g - 6*g**3 - 4*g**2 + 8*g - g**4 - 3*g**4 - g**5 = 0. Calculate g.
-1, 0
Let w(p) = -p**2 + 12*p + 2. Let d(v) = -2*v**2 + 13*v + 3. Let n = 83 - 81. Let h(s) = n*d(s) - 3*w(s). Suppose h(q) = 0. What is q?
-10, 0
Let y(l) be the second derivative of -2*l**6/45 + 41*l**5/20 - 989*l**4/36 + 215*l**3/6 + 75*l**2/2 - 7*l + 6. Solve y(x) = 0.
-1/4, 1, 15
Suppose 5*k + 1 = 11. Suppose 4*r = k*r + 4. Factor -2*g**3 - 5*g + r*g**5 + 5*g.
2*g**3*(g - 1)*(g + 1)
Let k(p) be the second derivative of p**6/150 + p**5/25 - 31*p**4/60 + 7*p**3/15 + 24*p**2/5 + 351*p. Find i such that k(i) = 0.
-8, -1, 2, 3
Let m = -17791 - -106747/6. Factor 0 + m*h**2 + 1/6*h.
h*(h + 1)/6
Suppose 0 = v - 48 + 45. Suppose -7*g - v*g + 3*g = 0. Factor -1/5*c**4 + g*c**2 + 0*c - 1/5*c**3 + 0.
-c**3*(c + 1)/5
Let g(a) be the third derivative of a**6/540 + a**5/270 - 5*a**4/54 + 8*a**3/27 + 122*a**2. Determine m so that g(m) = 0.
-4, 1, 2
Let d = 1653 - 6609/4. Factor 6*g + d*g**3 - 15/4*g**2 - 3.
3*(g - 2)**2*(g - 1)/4
Suppose -65*o**2 + 5*o**5 + 36*o + 10*o**2 - 56*o - 5*o**4 - 45*o**3 = 0. What is o?
-1, 0, 4
Let m(b) = -18*b**3 - 11*b**2 - 3*b - 3. Let p(q) = -8*q**3 - 5*q**2 - q - 1. Let w(z) = -6*m(z) + 14*p(z). Solve w(f) = 0.
-1, 1
Let x(q) be the second derivative of -q**5/170 - 35*q**4/102 - 247*q**3/51 + 1083*q**2/17 - 156*q. Suppose x(m) = 0. What is m?
-19, 3
Let x be 14/4 + (-5)/10. Suppose 8*k**2 - 225*k + k**4 + 229*k + 0*k**3 + 5*k**x = 0. What is k?
-2, -1, 0
Let v = -4201/2 - -2101. Let 0 - s + v*s**3 - 1/2*s**2 = 0. Calculate s.
-1, 0, 2
Let s(q) be the third derivative of -5*q**8/16 + 55*q**7/42 + 7*q**6/6 - q**5 - 10*q**2 - 10*q. Find u, given that s(u) = 0.
-2/3, 0, 2/7, 3
Let i(d) = d**3 - 8*d**2 + 13*d + 7. Let t be i(6). Factor 8*p + 15 - 11*p + t*p - 5*p**2.
-5*(p - 3)*(p + 1)
Factor -120 - 228*i**2 - 39/2*i**4 - 3/2*i**5 - 264*i - 96*i**3.
-3*(i + 2)**4*(i + 5)/2
Suppose 2*j - n = 10, -40 + 0 = -5*j + 5*n. Factor 0 - 6*r**3 + r + 7/2*r**4 + 3/2*r**j.
r*(r - 1)**2*(7*r + 2)/2
Let m(p) be the first derivative of p**4 + 2*p**3/3 - 3*p**2/2 - 7. Let b be m(2). Factor -2*f**2 + 4*f**2 + 16 + 5*f + b - 25*f.
2*(f - 5)**2
Factor 10*s**2 + 0 - 8*s**3 + 1/2*s**4 + 1/2*s**5 + 0*s.
s**2*(s - 2)**2*(s + 5)/2
Let c be ((-14)/(-3))/(-7)*(0 - 12). Suppose -4*k - 22 = -2*x, -c*x + 4*x - 4 = 4*k. Factor 0 - 3/2*n - 3/4*n**2 + 3/4*n**x.
3*n*(n - 2)*(n + 1)/4
Let n(j) be the first derivative of -j**8/1120 + j**7/224 - j**6/120 + j**5/160 - 2*j**3/3 - 13. Let b(r) be the third derivative of n(r). Solve b(o) = 0.
0, 1/2, 1
Let n(f) = -f**2 - 7*f. Let d be n(-7). Suppose d = -l, 5*w - 10 = -0*w + 4*l. Factor 6*b**4 + w*b**5 + 3*b**3 - 5*b**5 + 6*b**5.
3*b**3*(b + 1)**2
Let 55*r**4 + 160*r**2 + 1000 - 1550*r + 665/2*r**3 + 5/2*r**5 = 0. Calculate r.
-10, -4, 1
Let f(u) be the second derivative of -u**6/50 + 21*u**5/50 + 51*u**4/20 + 38*u. Factor f(s).
-3*s**2*(s - 17)*(s + 3)/5
Suppose -8 + 0 = -r. Factor -10*m + m**2 - r*m + 21*m.
m*(m + 3)
Let v(u) be the first derivative of -u**4/3 - 52*u**3/9 - 92*u**2/3 - 64*u - 149. Factor v(x).
-4*(x + 2)*(x + 3)*(x + 8)/3
Let b(a) be the second derivative of 3*a**5/40 - 57*a**4/8 + 210*a**3 - 588*a**2 - 340*a. Factor b(z).
3*(z - 28)**2*(z - 1)/2
Suppose -20 = -9*r + 4*r. Factor r*o**3 - o**3 - 2*o**2 - o**2.
3*o**2*(o - 1)
Let q(r) be the second derivative of 5/2*r**3 + 7/2*r**2 + 0 + 3/4*r**4 - 45*r + 1/20*r**5. Suppose q(h) = 0. Calculate h.
-7, -1
Let t(o) be the first derivative of -o**4/54 - 4*o**3/27 - 4*o**2/9 - 41*o - 39. Let d(v) be the first derivative of t(v). What is g in d(g) = 0?
-2
Factor -2/3*l**2 + 0 + 164/3*l.
-2*l*(l - 82)/3
Let u(y) be the first derivative of 28*y**5/5 - 215*y**4 - 248*y**3/3 - 39. Solve u(n) = 0.
-2/7, 0, 31
Let p = -128 + 131. Let z(q) = 3*q**2. Let i(j) = 2*j**2. Let g(b) = p*i(b) - z(b). Factor g(a).
3*a**2
Let i(t) be the first derivative of -1/20*t**5 - 1/16*t**4 - 4 + 1/24*t**6 + 0*t**2 + 1/12*t**3 + 0*t. Factor i(l).
l**2*(l - 1)**2*(l + 1)/4
Let r be ((-6)/(-48))/(5/18*(-12)/(-20)). Factor r*g**2 + 45/4 + 6*g.
3*(g + 3)*(g + 5)/4
Suppose -2*x = 4*o - 3*x - 13, -5*x = 3*o + 19. Factor 4*a**2 - a**3 - 3*a**4 - o*a**3 + 3*a**2 - a**2.
-3*a**2*(a - 1)*(a + 2)
Let g be 4/(9 + (-67)/8). Factor 0*r - 16/5*r**3 - 2/5*r**4 + 0 - g*r**2.
-2*r**2*(r + 4)**2/5
Factor 1/6*w**2 + 722/3 - 38/3*w.
(w - 38)**2/6
Let c(m) be the second derivative of m**5/50 - m**4/2 - 34*m**3/15 - 270*m. What is i in c(i) = 0?
-2, 0, 17
Factor -23*m**3 - 4212 + 49*m**3 - 5*m**4 - 545*m**2 + 104*m**3 - 288 - 3900*m.
-5*(m - 15)**2*(m + 2)**2
Suppose 5*i = j - 5, -j - 3*i - 3 = 2*j. Let t(u) be the second derivative of -1/40*u**5 + 2*u + 0*u**2 + j*u**3 - 1/12*u**4 + 0. Solve t(g) = 0 for g.
-2, 0
Let h(r) be the third derivative of 8/5*r**4 + 0*r + 3*r**2 + 0 - 8/15*r**3 - 26/25*r**6 - 118/75*r**5 - 169/1050*r**7. Factor h(f).
-(f + 2)**2*(13*f - 2)**2/5
Let o(j) = 6*j**4 - 27*j**3 - 69*j**2 + 168*j. Let d(v) = -v**4 + 4*v**3 + 10*v**2 - 24*v. Let s(m) = 15*d(m) + 2*o(m). Find h, given that s(h) = 0.
-2, 0, 2
Let v(x) = 8*x**5 - 4*x**4 + x**3 - 10*x**2 + 28*x - 2. Let w(m) = m**5 - m**4 + m**3 + m + 1. Let d(a) = 2*v(a) - 14*w(a). Factor d(q).
2*(q - 1)**3*(q + 3)**2
Let m(h) be the first derivative of -h**4/3 + 8*h**3/9 - 5*h**2/6 + h/3 + 157. Find a, given that m(a) = 0.
1/2, 1
Factor -196/9 - 19/3*x**2 - 2/9*x**3 - 140/3*x.
-(x + 14)**2*(2*x + 1)/9
Let s be 45/6*(-10)/(-15). Suppose -17*x - 10*x**2 + 5*x**4 + s + 17*x = 0. Calculate x.
-1, 1
Let r(a) be the third derivative of 0*a - 7*a**2 + 0 - 2/33*a**4 + 1/66*a**5 + 4/33*a**3 - 1/660*a**6. Factor r(f).
-2*(f - 2)**2*(f - 1)/11
Let i(n) = 2*n**3 - 7*n**2 + 11*n + 3. Let h be i(4). Let b = -251/4 + h. Suppose 0*x + 0 + 0*x**3 + 1/4*x**4 - b*x**2 = 0. Calculate x.
-1, 0, 1
Suppose 3 - 9 = -2*g. Let a(v) be the second derivative of 0*v**2 - 1/165*v**6 + 0 + 1/66*v**4 + 4*v - 1/110*v**5 + 1/231*v**7 + 0*v**g. Factor a(t).
2*t**2*(t - 1)**2*(t + 1)/11
Let -247 - 95*v - 19*v**2 + 14*v**2 + 347 = 0. What is v?
-20, 1
Let j be (-3 + (-187)/(-44))*4. Let a(u) be the third derivative of 0*u - 1/5*u**j + 1/6*u**4 + 2*u**3 + 0 - 1/30*u**6 + 5*u**2. Factor a(v).
-4*(v - 1)*(v + 1)*(v + 3)
Suppose 0*p + 5*p - 14 = -r, -5*p + 3*r = 2. Let b = -215 + 230. Factor -b + 20 + h**2 - 6*h**p.
-5*(h - 1)*(h + 1)
Let z(l) be the second derivative of l**7/252 - 7*l**6/180 - l**5/120 + 7*l**4/72 + 3*l - 5. Solve z(t) = 0 for t.
-1, 0, 1, 7
Let d(v) be the first derivative of 2*v**6/15 + 28*v**5/5 + 71*v**4 + 260*v**3/3 - 2704*v**2 + 35152*v/5 + 166. Let d(n) = 0. What is n?
-13, 2
Let m = 126 + -162. Let j = m - -112/3. Solve -8/3*g - j*g**3 + 4*g**2 + 0 = 0 for g.
0, 1, 2
Find q, given that 22/5*q**2 + 0 + 6/5*q**4 - 12/5*q + 8*q**3 = 0.
-6, -1, 0, 1/3
Let m be (-1)/(12/9*(0 - 9)). Let v(h) be the third derivative of 2/3*h**3 + 0 + 0*h - m*h**4 - 5*h**2 - 1/30*h**5. Determine f so that v(f) = 0.
-2, 1
Suppose -66 = 215*m - 496. Factor -4/3*z**m - 16/3 + 16/3*z.
-4*(z - 2)**2/3
Let t(j) be the second derivative of -j**6/780 - j**5/780 + j**4/78 - 8*j**3/3 + 10*j. Let y(c) be the second derivative of t(c). Let y(x) = 0. Calculate x.
-1, 2/3
Let w(p) be the second derivative of -p**6/480 + 7*p**4/96 - p**3/4 - 26*p**2 + 15*p + 3. Let a(n) be the first derivative of w(n). Solve a(y) = 0.
-3, 1, 2
Let l(v) be the second de