- r**6/360 + 11*r**3 + 34. Let u(n) be the third derivative of q(n). What is y in u(y) = 0?
-2, 0
Let w(g) be the second derivative of -g**5/60 - 5*g**4/18 - g**3/2 + 73*g. Factor w(c).
-c*(c + 1)*(c + 9)/3
Suppose -1 + 4 = r. Let o(t) be the first derivative of 6*t + t**r - 6 + 9/2*t**2. Let o(m) = 0. What is m?
-2, -1
Let g(i) = -i**3 - 35*i**2 - 198*i - 54. Let d be g(-28). Factor 0 + 4/7*m + 4/7*m**d.
4*m*(m + 1)/7
Let n(v) be the first derivative of v**4/2 - 34*v**3/3 + 44*v**2 - 56*v + 73. Factor n(i).
2*(i - 14)*(i - 2)*(i - 1)
Let i(m) be the first derivative of 2*m**5 + 3*m**4 + m**3/3 - 3*m**2/2 - 11*m - 2. Let u(j) = j**4 + j**3 - 1. Let p(h) = -2*i(h) + 18*u(h). Factor p(c).
-2*(c - 1)*(c + 1)**2*(c + 2)
Let y(s) be the first derivative of s**5 - 35*s**4/2 + 40*s**3 + 136. Factor y(f).
5*f**2*(f - 12)*(f - 2)
Let l be 4/(24/(-30)) - -8. Let d(y) be the first derivative of 1/3*y + 1/3*y**l + 1/12*y**4 + 3 + 1/2*y**2. Factor d(c).
(c + 1)**3/3
Let l(h) = -67*h - 666. Let d be l(-10). Suppose -8/3*j**d + 4/3*j**5 + 8/3*j**2 - 4/3*j**3 + 0*j + 0 = 0. What is j?
-1, 0, 1, 2
Suppose -2*t = -i - 8, 0 = 2*i + i. Let h(c) be the first derivative of 0*c + c**2 - 1 - 4/5*c**5 - 1/3*c**6 + 0*c**t + 4/3*c**3. Factor h(s).
-2*s*(s - 1)*(s + 1)**3
Determine i, given that -11*i**4 - 5*i**4 + 29*i**4 - 4*i**4 - 56*i**2 + 60*i**3 - 13*i**4 = 0.
0, 1, 14
Let m(t) be the third derivative of -t**9/20160 + t**8/2240 - t**6/60 + 29*t**5/60 + 37*t**2. Let l(c) be the third derivative of m(c). Solve l(x) = 0.
-1, 2
Let n be (-228)/(-304) + (15/(-8))/((-3)/2). Factor 1/2*l**2 - 2*l + n.
(l - 2)**2/2
Let i be ((-2)/(-8))/((-6)/24*-1). Let v be i + (-17)/(-5) + 8/(-2). Factor -v*h**3 + 0*h**2 + 0*h - 1/5*h**4 + 1/5*h**5 + 0.
h**3*(h - 2)*(h + 1)/5
Suppose -n + 2*w = -17, -n - 3 + 24 = -3*w. Suppose -3*y + 21 = -n. Let -7*s - 3 - 5*s - 2*s**2 - y*s**2 = 0. What is s?
-1/2
Let g be (-3)/7 - (-312)/42. Let q(w) be the second derivative of 2*w**2 + g*w + 0 + w**3 + 1/6*w**4. Factor q(v).
2*(v + 1)*(v + 2)
Let r(s) be the second derivative of s**7/210 - s**6/120 - s**5/30 - 7*s**2 + 13*s. Let q(p) be the first derivative of r(p). Determine k, given that q(k) = 0.
-1, 0, 2
Let o(z) be the second derivative of -z**4/2 + 23*z**3/6 - 6*z**2 - 9*z. Let l(b) = 25*b**2 - 93*b + 48. Let f(c) = -6*l(c) - 26*o(c). Factor f(d).
2*(d - 6)*(3*d - 2)
Determine f so that -2*f**2 + 65*f - 18*f - 23*f - 48 - f**2 = 0.
4
Let g be 6*3/(-9) - (-20)/6. Let y(z) be the first derivative of -g*z**3 + 2*z**2 + 8*z + 2. Factor y(r).
-4*(r - 2)*(r + 1)
Suppose -3*d + 2 = 4*w, -3*w + 3*d - 3 + 15 = 0. Factor 6*q**2 + 30*q + 4*q**2 - 4*q**2 + 75 - 3*q**w.
3*(q + 5)**2
Let y(u) be the first derivative of 9/4*u - 3/4*u**3 - 3/4*u**2 + 29 + 3/8*u**4. Factor y(k).
3*(k - 1)*(k + 1)*(2*k - 3)/4
Factor -4/9*r - 2/9*r**3 - 16/9 + 10/9*r**2.
-2*(r - 4)*(r - 2)*(r + 1)/9
Let w(m) = -5*m**5 - 6*m**4 - 100*m**3 - 132*m**2 - 4. Let i(t) = 4*t**5 + 9*t**4 + 99*t**3 + 131*t**2 + 3. Let g(p) = -4*i(p) - 3*w(p). Factor g(r).
-r**2*(r + 2)*(r + 8)**2
Let b(q) = q**3 + 14*q**2 + 20*q + 95. Let z be b(-13). Suppose 0 = 5*n - 4*n - 0*n. Determine x, given that 0 + 0*x**2 + 0*x + n*x**3 + 3/4*x**z = 0.
0
Let f(z) be the second derivative of -z**6/12 + 5*z**5/12 - 5*z**4/6 + 5*z**3/6 - 15*z**2/2 - 18*z. Let p(y) be the first derivative of f(y). Factor p(u).
-5*(u - 1)**2*(2*u - 1)
Let y = -34 - -36. Factor -3*f**5 - 7*f**4 + 7*f**5 + 3*f**3 - f**3 + 0*f**5 + f**y.
f**2*(f - 1)**2*(4*f + 1)
Suppose 57*j = 25*j. Let h(p) be the third derivative of j*p**3 + 0*p**4 - 1/720*p**6 + 0*p + 0 - 7*p**2 + 1/180*p**5. Find d, given that h(d) = 0.
0, 2
Let n(a) be the first derivative of a**6/6 - 6*a**5/5 + 9*a**4/4 - 4*a**3/3 + 481. Factor n(h).
h**2*(h - 4)*(h - 1)**2
Let r(u) = u**2 - 1. Let k(n) = -20*n**2 + 4*n + 16. Suppose -43 = -2*a + 25. Suppose -a - 38 = 3*s. Let w(h) = s*r(h) - k(h). Determine o so that w(o) = 0.
-2, 1
Let s = 30 - 24. Find h, given that -3*h**4 - 5 + s + 0 - 4 + 6*h**2 = 0.
-1, 1
Let q be (-1)/(-5) + 0*(-1)/5. Let o(y) be the first derivative of q*y**5 - 10 - 2/3*y**3 + y - 1/2*y**2 - 1/6*y**6 + 1/2*y**4. Factor o(x).
-(x - 1)**3*(x + 1)**2
Let k be (2/(-6))/((-166)/3320). Find t such that 16/3*t**3 - 28/3*t + k*t**2 - 8/3 = 0.
-2, -1/4, 1
Determine x, given that 43717 + 30478 + 540*x**2 - 24300*x - 4*x**3 + 290305 = 0.
45
Let i(r) = -r - 3. Suppose -3*s = -7*s - 12. Let w be i(s). Factor 0*p**4 + w*p**2 - 1/2*p**3 + 0 + 1/2*p**5 + 0*p.
p**3*(p - 1)*(p + 1)/2
Let c be (-20 - 2) + (-5 - -2). Let j = c + 27. Find i, given that 0 + 0*i**j - 1/5*i**3 + 1/5*i = 0.
-1, 0, 1
Let g be (-4)/6*27/(-18). Let q(u) = 6*u**3 - u**2 + 3*u - 2. Let m be q(g). Factor -9 - m*n + 3*n**2 + 5*n - 5*n.
3*(n - 3)*(n + 1)
Suppose 142 - 240 = -49*b. Let q(l) be the first derivative of -3/7*l - 1/21*l**3 + 5 + 2/7*l**b. Find f such that q(f) = 0.
1, 3
Let j = -1416 - -1419. Find u such that 0*u + 5/3*u**j - 5/3*u**2 + 5/3*u**4 - 5/3*u**5 + 0 = 0.
-1, 0, 1
Let j(b) be the third derivative of -b**6/120 - 7*b**5/6 + 6*b**4 - 262*b**2. Determine r, given that j(r) = 0.
-72, 0, 2
What is b in 1305111 + b**3 - 1305111 + 31*b**2 + 58*b = 0?
-29, -2, 0
Let w = -4273997 + 6334063847/1482. Let y = w - 5/114. Determine r, given that 0 - 4/13*r**3 - y*r - 6/13*r**2 = 0.
-1, -1/2, 0
Let w(q) be the second derivative of -3*q**6/40 - 13*q**5/20 - 11*q**4/16 + 5*q**3/12 + 89*q + 1. Solve w(h) = 0.
-5, -1, 0, 2/9
Find c, given that 3/7*c + 5/7*c**2 + 0 - 8/7*c**3 = 0.
-3/8, 0, 1
Let a be 0 + 64 + (-4)/(-4). Let m = a - 65. Solve -7/3*t**3 + 0 + 2/3*t**2 + m*t = 0 for t.
0, 2/7
Let d(q) be the second derivative of 1/90*q**6 + 0*q**3 - 1/30*q**5 - 1/12*q**4 - 7*q + 0 + 0*q**2. Factor d(c).
c**2*(c - 3)*(c + 1)/3
Let u(i) = -6*i**3 - 18*i**2 + 32*i - 20. Let q(g) = 10*g**3 + 35*g**2 - 63*g + 39. Let w(v) = -4*q(v) - 7*u(v). Factor w(j).
2*(j - 4)*(j - 2)*(j - 1)
Let s = -28722 - -28725. Factor 63/4*o - 15/4*o**2 - 49/4 + 1/4*o**s.
(o - 7)**2*(o - 1)/4
Suppose 74 - 689 = -5*l. Let c = l + -119. Factor 2/9*q**5 + 2/9 - 2/3*q**c + 4/9*q**2 + 4/9*q**3 - 2/3*q.
2*(q - 1)**4*(q + 1)/9
Let u be (8/32)/((-2)/(-40)) + -5. Let j = -4/45 + 13/45. Let j*h**2 + 1/5*h**3 + 0*h - 1/5*h**5 + u - 1/5*h**4 = 0. Calculate h.
-1, 0, 1
Factor -17*c**2 - 39*c**2 + 44*c - 35 + 47.
-4*(c - 1)*(14*c + 3)
Let m be (-6)/(-48) + 240/128. Factor -3/2*n**2 - 4*n - m + 1/2*n**4 + n**3.
(n - 2)*(n + 1)**2*(n + 2)/2
Let k(g) = 61*g**2 - g - 11. Let x(q) be the third derivative of q**5/5 - q**3/3 - q**2. Let c(o) = 2*k(o) - 11*x(o). Factor c(n).
-2*n*(5*n + 1)
Let h = -89 - -94. Suppose 3*v = -h*w + 7*w + 9, 4*w + 2*v - 6 = 0. Determine a, given that 4/3*a**5 + 0 - 16/3*a**2 + 4*a**4 + 0*a + w*a**3 = 0.
-2, 0, 1
Let p(l) be the second derivative of l**4/60 - 2*l**3/15 + 2*l**2/5 - 29*l - 6. Determine h so that p(h) = 0.
2
Find t, given that -2/7*t**4 + 6/7*t**2 + 2/7*t - 4/7 - 2/7*t**3 = 0.
-2, -1, 1
Let l(n) = -2*n**4 + 8*n**3 + 6*n**2 - 36*n. Let h(p) = 12*p**4 - 48*p**3 - 36*p**2 + 216*p. Let s(x) = -6*h(x) - 34*l(x). Factor s(b).
-4*b*(b - 3)**2*(b + 2)
Let r(w) be the second derivative of w**4/4 + 15*w**3 + 13*w + 28. Factor r(p).
3*p*(p + 30)
Let m(p) be the third derivative of 1/240*p**6 - 1/16*p**4 - 39*p**2 - 1/24*p**3 + 0 - 1/30*p**5 + 1/336*p**8 + 3/280*p**7 + 0*p. Let m(i) = 0. What is i?
-1, -1/4, 1
Let x = 1023 + -1019. Let i(u) be the third derivative of 1/300*u**5 - 1/30*u**3 + 3*u**2 + 0 + 0*u + 1/600*u**6 - 1/120*u**x. Factor i(j).
(j - 1)*(j + 1)**2/5
Suppose -8*c + 21 = -c. Factor -6*o + 7*o**2 - 7*o**2 + 0*o**2 - 3*o**2 - c.
-3*(o + 1)**2
Let d(p) = 2*p + 18. Let z be d(-8). Determine j so that -5*j**2 - 58 + 57 + 4*j**z - 2*j = 0.
-1
Let c(f) = 6*f**3 + 381*f**2 + 11898*f - 12288. Let y(q) = q**3 - 2*q. Let l(r) = -c(r) + 3*y(r). Find t, given that l(t) = 0.
-64, 1
Let t(v) be the first derivative of v**3/12 + 9*v**2 + 324*v - 98. Determine g, given that t(g) = 0.
-36
Let q be (170/51)/((-4)/(-6)). Let d(b) = 64*b**2 - 90*b + 36. Let s(h) = -64*h**2 + 91*h - 36. Let t(r) = q*d(r) + 6*s(r). What is l in t(l) = 0?
3/4
Let a(g) be the third derivative of g**6/30 - 7*g**5/5 + 34*g**4/3 - 2*g**2 - 9. Determine f so that a(f) = 0.
0, 4, 17
Let y(h) be the 