- 15*u**2 + 45*u. Let i(p) = p**4 - p**2 - p. Let s(n) = 5*i(n) + j(n). Suppose s(v) = 0. Calculate v.
-1, -2/5, 0, 2/7, 2
Let a(u) be the first derivative of -26 + 1/30*u**5 - 25/6*u + 4/3*u**3 - 5/6*u**2 + 5/12*u**4. Find c such that a(c) = 0.
-5, -1, 1
Suppose 25*c = 8*c - 0*c - 21*c. Factor -7/6*q**4 + 1/3*q - 1/3*q**3 + 7/6*q**2 + c.
-q*(q - 1)*(q + 1)*(7*q + 2)/6
Let f(a) = 5*a**4 + 35*a**3 - 25*a**2 - 110*a + 75. Let c(s) = -3*s**4 - 18*s**3 + 13*s**2 + 54*s - 38. Let b(z) = 5*c(z) + 2*f(z). Factor b(o).
-5*(o - 1)**2*(o + 2)*(o + 4)
Let f be (-2)/26*(-49 + 49). Factor f*x**2 - 4/5*x**3 + 0*x - 2/5*x**4 + 0 + 2/5*x**5.
2*x**3*(x - 2)*(x + 1)/5
Let v = 930 + -19526/21. Let g(i) be the first derivative of 4/7*i - v*i**3 + 1/7*i**2 - 1/14*i**4 - 8. Factor g(r).
-2*(r - 1)*(r + 1)*(r + 2)/7
Let n(t) be the third derivative of t**8/280 - 61*t**7/1575 + 2*t**6/45 + 2*t**5/75 - 2*t**2 + 84. Solve n(r) = 0.
-2/9, 0, 1, 6
Suppose -10 = -5*f - 0*f. Find o such that -2*o**f - o**3 - o**2 - 4*o + 2*o = 0.
-2, -1, 0
Let w(k) be the second derivative of -k**4/96 - k**3/16 - k**2/8 + 2*k - 7. Factor w(g).
-(g + 1)*(g + 2)/8
Solve -28*w**2 - 73895*w**3 + 0*w**2 + 73888*w**3 - 20*w + w**4 = 0 for w.
-2, -1, 0, 10
Suppose -2/5*o**2 - 108/5 + 58/5*o = 0. Calculate o.
2, 27
Let i(p) be the third derivative of -p**5/30 + 77*p**4/12 + 26*p**3 + 340*p**2. Let i(j) = 0. Calculate j.
-1, 78
Let m(j) be the second derivative of 2/5*j**5 - 1/2*j**4 + 0*j**3 - 5*j + 0 + 0*j**2 - 1/15*j**6. Factor m(a).
-2*a**2*(a - 3)*(a - 1)
Suppose -16*u = -14 - 18. Factor 88*o - 68*o - 15*o**3 + 2*o**2 + o**u - 23*o**2.
-5*o*(o + 2)*(3*o - 2)
Let o(p) be the second derivative of -3/20*p**5 + 0*p**3 + 0 + 0*p**2 - 1/10*p**6 + 1/4*p**4 + 1/14*p**7 - 7*p. Factor o(a).
3*a**2*(a - 1)**2*(a + 1)
Let a(g) be the third derivative of 0*g**3 - 1/50*g**5 + 0 + 1/30*g**6 + 0*g**4 - 33*g**2 - 8/525*g**7 + 0*g. Factor a(z).
-2*z**2*(2*z - 1)*(4*z - 3)/5
Let j(m) be the first derivative of -3*m**4/28 - 4*m**3/7 + 15*m**2/14 + 133. Let j(s) = 0. What is s?
-5, 0, 1
Find x such that 51/8*x**5 - 201/8*x**4 + 147/4*x**3 - 93/4*x**2 + 3/8 + 39/8*x = 0.
-1/17, 1
Let p(q) be the first derivative of 0*q + 0*q**5 + 0*q**3 + 16/5*q**2 + 1/15*q**6 - 4/5*q**4 - 10. Factor p(s).
2*s*(s - 2)**2*(s + 2)**2/5
Let h(k) be the second derivative of -k**6/150 + 9*k**5/100 + 7*k**4/20 + 11*k**3/30 + 21*k. Factor h(p).
-p*(p - 11)*(p + 1)**2/5
Let a(o) = o**5 + o. Let c(r) = r**5 - r**4 + 4*r**3 + 4*r**2 + 2*r. Let y(z) = 4*a(z) - 2*c(z). Factor y(k).
2*k**2*(k - 2)*(k + 1)*(k + 2)
Let -132/5 - 36/5*t**2 - 166/5*t - 2/5*t**3 = 0. What is t?
-11, -6, -1
Let w be (-106)/(-10) + (-9)/15. Let p = w + -8. Factor c**p - 4*c**3 + 6*c**4 + c**2 - 4*c**4.
2*c**2*(c - 1)**2
Let l(g) be the first derivative of g**3/6 - 21*g**2/2 + 41*g/2 + 349. Factor l(u).
(u - 41)*(u - 1)/2
Let v be (-159)/(-12) + 3/(-12). Suppose 6*m - v = 5. Factor 1/3*p**2 - 1/3*p**m - 1/3 + 1/3*p.
-(p - 1)**2*(p + 1)/3
Suppose v = 2*g - 8, 0 = -4*g + 2*v + v + 20. Let c(p) = -p**4 - p**3 - p**2. Let a(d) = -2*d**3. Let x(h) = g*c(h) + a(h). Let x(u) = 0. Calculate u.
-1, 0
Let l(m) be the second derivative of 8*m + 0 + 0*m**2 + 0*m**3 - 1/5*m**5 + 1/6*m**4 + 1/15*m**6. Let l(b) = 0. What is b?
0, 1
Suppose 0 = -76*p + 417 + 267. Factor -51/5*x + 6/5 + p*x**2.
3*(x - 1)*(15*x - 2)/5
What is l in -6*l**2 - 56/9*l + 2/9*l**3 + 0 = 0?
-1, 0, 28
Let g(t) be the third derivative of 1/9*t**3 + 7/72*t**4 + 0*t + 0 + 4*t**2 - 1/45*t**5. Suppose g(w) = 0. Calculate w.
-1/4, 2
Let q(w) be the first derivative of 4/15*w**3 - 8/5*w + 2/5*w**2 - 48. Let q(y) = 0. What is y?
-2, 1
Let l(x) be the first derivative of 20 - x**2 + x + 1/3*x**3. Factor l(c).
(c - 1)**2
Let z(f) = f**3 + 5 - 7*f - 8 - 2*f**2 + 7*f**2. Let m be z(-6). Factor m*n - n + n**2 + n**2.
2*n*(n + 1)
Factor -10*t**2 + 20*t - 24 - 11*t**2 + 25*t**2.
4*(t - 1)*(t + 6)
Let x(d) = d**5 + 28*d**4 - 138*d**3 + 285*d**2 - 207*d. Let n(u) = -u**5 - 56*u**4 + 276*u**3 - 571*u**2 + 417*u. Let r(c) = 3*n(c) + 5*x(c). Solve r(k) = 0.
0, 2, 3, 6
Let t be 10/15 + (40/(-6))/(-2). Suppose 18 = d - 4*w + w, -t*d + 3*w + 27 = 0. Factor 2/7*m**4 + 4/7*m + 0 + 8/7*m**d + 10/7*m**2.
2*m*(m + 1)**2*(m + 2)/7
Let d be (-1)/(-3) - (-4)/(-24). Let q(v) be the second derivative of 1/15*v**6 - 1/42*v**7 - 1/6*v**4 + 0*v**2 - 3*v + d*v**3 + 0*v**5 + 0. Factor q(n).
-n*(n - 1)**3*(n + 1)
Let a be ((104/(-90))/13)/(8/(-20)). Let l(b) be the first derivative of -2/3*b**2 - a*b**3 - 2/3*b - 8. Determine s, given that l(s) = 0.
-1
Let c(p) = p**3 - 33*p**2 + p - 33. Let g be c(33). Find n such that -2/3*n**5 + g + 2/3*n**3 + 2/3*n**2 - 2/3*n**4 + 0*n = 0.
-1, 0, 1
Let g(t) be the third derivative of -t**8/2240 + t**7/210 - t**6/80 - t**4/8 + 22*t**2. Let h(r) be the second derivative of g(r). What is i in h(i) = 0?
0, 1, 3
Let t(b) = b**3 - 2*b**2 - 7*b - 2. Let g be t(4). Suppose g = -5*o + 7, -3*m + 2 = -4*o. Find u such that -1/2*u + 1/2*u**4 + u**3 + 1/2 - u**m - 1/2*u**5 = 0.
-1, 1
Let l(n) = 5*n + 17. Let j(m) = -6*m - 18. Let o(p) = 6*j(p) + 7*l(p). Let c be o(5). Let 0*x**3 + x + 8*x**4 - 5*x**4 - c*x**3 - 3 + 5*x = 0. What is x?
-1, 1
Let h = -5120/679 + 53/7. Let x = h + 179/485. Solve 0*v - 8/5 + x*v**2 = 0 for v.
-2, 2
Let h(p) be the second derivative of 3/2*p**2 - 1/90*p**5 - 1/18*p**4 + 1/360*p**6 - 5*p + 4/9*p**3 + 0. Let n(z) be the first derivative of h(z). Factor n(i).
(i - 2)**2*(i + 2)/3
Let c(q) be the third derivative of q**5/180 - 2*q**4/9 + 8*q**3/3 + 537*q**2. Factor c(p).
(p - 12)*(p - 4)/3
Find g, given that 65*g**3 + 9*g**5 + 130*g**2 - 24*g**4 + 45 + 34*g**4 + 115 - 4*g**5 - 50*g**4 - 320*g = 0.
-2, 1, 4
Suppose 4*w = -5*m - 8 - 2, -5*w - 2*m = 4. Factor w*o + 3*o**2 + 2*o + o - o**3 - 5*o**3.
-3*o*(o - 1)*(2*o + 1)
Let u(i) be the second derivative of -i**4/4 + 52*i**3 - 4056*i**2 - 88*i. What is a in u(a) = 0?
52
Let y(a) = -2 - 5*a + 4*a - 6*a - 9*a**2 - 2. Let x(r) = -r - 1. Let s(g) = -4*x(g) + y(g). Find i, given that s(i) = 0.
-1/3, 0
Let l(n) be the third derivative of -n**6/80 - n**5/4 - n**4 - 2*n**2 + 15. Suppose l(i) = 0. Calculate i.
-8, -2, 0
Let p(l) be the second derivative of -7*l**6/6 - 10*l**5 + 305*l**4/12 - 35*l**3/3 + 156*l + 2. Determine z, given that p(z) = 0.
-7, 0, 2/7, 1
Let h(k) be the third derivative of -k**8/312 + 23*k**7/1365 - k**6/60 - 19*k**5/390 + 5*k**4/39 - 4*k**3/39 + k**2 - 7. Find g such that h(g) = 0.
-1, 2/7, 1, 2
Let w(d) be the first derivative of -5*d**3/3 - 110*d**2 - 2420*d + 37. Factor w(r).
-5*(r + 22)**2
Suppose -7 = -2*j - 2*j + i, 15 = 3*i. Factor 2*x**4 + 2*x**4 + 0*x**4 + 2*x**4 - 3*x**j - 3*x**5.
-3*x**3*(x - 1)**2
Determine g so that 38/5*g + 4/5*g**2 - 2/5*g**3 - 8 = 0.
-4, 1, 5
Let j(b) be the second derivative of b**6/1980 - b**5/220 + 5*b**3/3 + 4*b. Let f(t) be the second derivative of j(t). Find h such that f(h) = 0.
0, 3
Let k(a) be the third derivative of a**5/20 - 61*a**4/8 + 30*a**3 + 123*a**2. Solve k(z) = 0.
1, 60
Find c such that 3*c**3 + 15 + c - 45/4*c**2 + 1/4*c**4 = 0.
-15, -1, 2
Suppose 8*c**4 - 36*c**3 + 26*c**4 - 13*c**2 + 42*c - 163 - 6*c**5 - 39*c**2 + 90 + 91 = 0. What is c?
-1, -1/3, 1, 3
Let o(s) be the second derivative of s**9/30240 + s**8/13440 - s**7/5040 - s**6/1440 - 4*s**4/3 - 8*s. Let f(i) be the third derivative of o(i). Factor f(l).
l*(l - 1)*(l + 1)**2/2
Let r(n) = -7*n + 6 + 0*n**2 + 8*n**2 - 7*n**2. Let u be r(6). Factor -3/4*p**2 + 3/4 + u*p.
-3*(p - 1)*(p + 1)/4
Suppose 19*p - 73 = 3. Let g(y) be the third derivative of -1/20*y**p + 0 - 1/350*y**7 - 1/50*y**6 + 5*y**2 + 0*y**3 - 1/20*y**5 + 0*y. Factor g(z).
-3*z*(z + 1)**2*(z + 2)/5
Let s(l) be the third derivative of -l**6/660 - l**5/10 + 23*l**4/44 - 35*l**3/33 + 144*l**2. Determine g so that s(g) = 0.
-35, 1
Find t, given that 0 - 3/4*t**2 - 21*t = 0.
-28, 0
Factor 10/11 - 8/11*q - 2/11*q**2.
-2*(q - 1)*(q + 5)/11
Suppose -8/7*z**4 - 74/7*z - 12/7 - 120/7*z**2 - 66/7*z**3 = 0. What is z?
-6, -1, -1/4
Let k be 4/7 + 660/70. Let l be (k/10)/(5/1). Let -2/5*d + l*d**2 - 3/5 = 0. Calculate d.
-1, 3
Let a(i) be the second derivative of 5*i**7/42 + 5*i**6/3 - i**5/2 - 25*i**4/3 + 5*i**3/6 + 25*i**2 + 575*i. Let a(k) = 0. Calculate k.
-10, -1, 1
Let w(