2
Let t(r) be the second derivative of -r**4/6 + 19*r**3/3 - 34*r**2 - 471*r. Find x such that t(x) = 0.
2, 17
Let w(q) be the third derivative of q**8/6720 - q**7/840 - q**6/180 - q**4/8 - 11*q**2. Let k(u) be the second derivative of w(u). Let k(p) = 0. Calculate p.
-1, 0, 4
Let w(i) be the second derivative of -i**5/5 + 4*i**4/3 + 32*i**3/3 - 128*i**2 + 540*i. Suppose w(s) = 0. Calculate s.
-4, 4
Let k(l) be the third derivative of l**5/240 + l**4/12 - 3*l**3/8 - 3*l**2 + 10*l. Factor k(y).
(y - 1)*(y + 9)/4
Let a(d) be the second derivative of -d**7/504 + d**5/24 - d**4/12 + 22*d. Let y(z) be the third derivative of a(z). Factor y(o).
-5*(o - 1)*(o + 1)
Let x(i) be the third derivative of i**6/225 + i**5/300 - i**4/20 - 25*i**3/6 + 32*i**2. Let m(d) be the first derivative of x(d). Find c such that m(c) = 0.
-1, 3/4
Let h(q) = q**2 - 5*q - 8. Let w = -17 + 24. Let t be h(w). Determine i, given that -t*i**2 + 0*i**5 + 6*i**3 + 3 - 6*i**5 - 3*i + 3*i**4 + 3*i**5 = 0.
-1, 1
Let n = 15 - 12. Suppose 2*a + 4*m + 12 = -a, -n*m - 9 = 3*a. What is i in -i**3 + 5*i**3 + 8*i**2 + 4*i + 0*i**3 + a*i**3 = 0?
-1, 0
Let i be 1190/(-51) + 21 + (5 - 2)/1. Find h such that -4/3*h**2 - i*h**3 + 0 - 2/3*h = 0.
-1, 0
Let z be -2 - ((4 - 3) + -3). Suppose z = -v + 3*v - 26. Factor -14*k**2 + 3*k + v*k**2 + 2 - 2*k.
-(k - 2)*(k + 1)
Let v be -1 - 0 - -5 - 240/80. Let z be (-5 - (-85)/15)/(1/v). Factor 0*k + z*k**2 + 0.
2*k**2/3
Let d(o) be the second derivative of o**4/48 + 5*o**3/8 - o + 8. Let d(x) = 0. What is x?
-15, 0
Let f be (-1 - -1) + 16 - 4. Suppose 0 = 5*g - 2*g - f. Factor -2 - 9*l + 5 - 1 + 3*l**2 + g.
3*(l - 2)*(l - 1)
Let s be 309/28 - 6 - 5. Let y(o) be the second derivative of -s*o**4 + 0 - 5*o + 3/14*o**2 + 1/14*o**3 - 3/140*o**5. Solve y(i) = 0 for i.
-1, 1
Let c(g) = -7*g**2 - 14*g + 25. Let h be 4*(2/(-8) - (-21)/(-28)). Let i(j) = -j**2 + j + 1. Let f(m) = h*i(m) + c(m). Factor f(v).
-3*(v - 1)*(v + 7)
Factor 3/2*x**2 + 2/3*x - 5/6.
(x + 1)*(9*x - 5)/6
Let -5/11*c**2 + 0*c + 0 + 6/11*c**3 - 1/11*c**4 = 0. Calculate c.
0, 1, 5
Let z be (10 - 3 - 2) + -2. Let v be 1 - -2 - (-11 + -2). Suppose -v*l + z + 4*l + l**2 + 9 + 2*l**2 = 0. What is l?
2
Let q(t) be the first derivative of 1/2*t**3 + 9/2*t + 3*t**2 - 5. Determine d so that q(d) = 0.
-3, -1
Find k, given that -k - 55*k**3 + 6*k**2 + 56*k**3 - 8 + 2 = 0.
-6, -1, 1
Let d(x) be the second derivative of -x**6/90 - x**5/4 - 17*x**4/9 - 10*x**3/3 + 24*x**2 + 14*x + 14. Factor d(k).
-(k - 1)*(k + 4)*(k + 6)**2/3
Suppose -3*u = 4*r + 4 + 4, 0 = -3*u - 3*r - 6. Factor -5/2*i**2 + 0 + u*i**3 + 5/2*i**4 + 0*i.
5*i**2*(i - 1)*(i + 1)/2
Find i such that 4*i**5 + 14 + 48*i**4 - 5 + 84*i**3 + 40*i**2 - 9 = 0.
-10, -1, 0
Let p(b) be the first derivative of 6 + 0*b**2 + 5/18*b**6 + 8/15*b**5 + 1/12*b**4 - 2/9*b**3 + 0*b. Factor p(w).
w**2*(w + 1)**2*(5*w - 2)/3
Let r be (-3)/(-5) + (-1414)/(-1010). Solve 15/2*u - 3/4*u**r - 75/4 = 0.
5
Let z(o) be the second derivative of o**4/78 + 20*o**3/39 + 84*o**2/13 + 164*o. Factor z(g).
2*(g + 6)*(g + 14)/13
Let r(w) be the second derivative of 0*w**3 + 0 - 3*w - 9/40*w**5 - 1/6*w**4 - 1/84*w**7 - 1/10*w**6 + 0*w**2. Factor r(k).
-k**2*(k + 1)**2*(k + 4)/2
Let m(p) = 5*p**4 + 96*p**3 - 1927*p**2 - 4128*p - 2122. Let b(y) = -6*y**4 - 97*y**3 + 1926*y**2 + 4126*y + 2123. Let l(v) = 6*b(v) + 7*m(v). Solve l(w) = 0.
-1, 46
Factor 53*v**4 - 66*v**4 + 3*v**5 + 39*v**3 + 36*v**2 + 31*v**4 + 12*v.
3*v*(v + 1)**2*(v + 2)**2
Factor 0 + 20/3*u**2 - 4*u**5 - 4/3*u**4 + 0*u + 28/3*u**3.
-4*u**2*(u + 1)**2*(3*u - 5)/3
Factor 10/19*h**4 - 8/19*h**2 + 0 - 2/19*h**5 + 16/19*h - 12/19*h**3.
-2*h*(h - 2)**3*(h + 1)/19
Let k(p) be the first derivative of -p**3/12 + 7*p**2/8 + 57. Find s, given that k(s) = 0.
0, 7
Solve -76/3*p**4 + 8/3*p + 0 + 8*p**5 - 44/3*p**2 + 88/3*p**3 = 0.
0, 1/2, 2/3, 1
Let t be ((-40)/25)/(6/(-15)). Factor v**3 + 3*v - 51*v**2 - v - 3*v**3 - 2*v**t + 53*v**2.
-2*v*(v - 1)*(v + 1)**2
What is n in -6*n**2 + 3 - 95*n + 6 + 98*n = 0?
-1, 3/2
Let a(i) be the second derivative of -i**6/10 - 3*i**5/20 + 3*i**4/4 + i**3/2 - 3*i**2 + 144*i. Find h, given that a(h) = 0.
-2, -1, 1
Suppose 4*y - 5*a - 26 = 0, 2*y - 3*a + 2 = 4*y. Solve -15*o**3 + 12*o**5 - 6*o**2 + 77*o**4 + 48*o**3 - 116*o**y = 0.
0, 1/4, 1, 2
Suppose -y - 4 = 0, 2*t - 6*y = -4*y + 14. Let o be 0 - (4/4 - t). Suppose -24*j - 60*j**3 - 2 - 68*j**3 - 7*j**2 - 44*j**2 - 45*j**o = 0. What is j?
-1/4
Let n(s) = -s**2 + 14*s - 47. Let f be n(7). Let o be 9/((-36)/(-16)) - f. Suppose 3/8 - 9/8*t - 3/8*t**3 + 9/8*t**o = 0. What is t?
1
Suppose 0 = g - 0*g - 1. Let u be (g - -1) + (7 - 6). Factor m**u + m**3 + 2 - 3*m + m + 2*m**2 - 4.
2*(m - 1)*(m + 1)**2
Let n(l) be the first derivative of 0*l**2 - 1/120*l**6 - 6 + 0*l**4 + 0*l**5 + 0*l + l**3. Let y(s) be the third derivative of n(s). What is u in y(u) = 0?
0
Suppose -5*i - 5 = 4*s - 20, 5*s = -4*i + 12. Suppose -i*l - 3*d = 3, 3*l = 7*l + 5*d + 7. Determine u so that -l*u + 4/3 - 10/3*u**2 = 0.
-1, 2/5
Factor -36/5 + 12/5*j + 3/5*j**2.
3*(j - 2)*(j + 6)/5
Let a(t) = t**2 + 11*t + 8. Let c be a(-12). Let -5*h**2 - 13 - 3 - c*h + 1 = 0. What is h?
-3, -1
Let f(m) = 3*m**4 + m**3 + 16*m**2 - 20*m + 6. Let c(j) = -j**4 - 4*j**3 + j**2 + 1. Let s(w) = -4*c(w) - 2*f(w). Factor s(x).
-2*(x - 2)**3*(x - 1)
Let i(z) be the second derivative of 0*z**2 + 5/6*z**4 - 1/4*z**5 + 0*z**3 + 0 + 54*z. Factor i(q).
-5*q**2*(q - 2)
Determine w, given that -701494*w**2 + 701489*w**2 - 2*w**3 - 3*w**3 = 0.
-1, 0
Factor 1/3*n**2 + 0 + 1/6*n**3 - 1/2*n.
n*(n - 1)*(n + 3)/6
Suppose 5*y = -u - 19, 4*u + 12 = -y - 3*y. Let z be (-4 + (u - -4))/3. Factor -o**2 + 1/3*o**3 + o - z.
(o - 1)**3/3
Let s = 473/122 + -206/61. Factor 0*m**4 + 0*m**2 + 0 + s*m**5 + 1/2*m - m**3.
m*(m - 1)**2*(m + 1)**2/2
Factor -35 - 126*s - 15*s**2 + 5*s**2 - 112 - 14*s**2 - 3*s**2.
-3*(3*s + 7)**2
Solve 96/7 + 32/7*h**3 + 4/7*h**4 + 20/7*h**2 - 152/7*h = 0 for h.
-6, -4, 1
Suppose 1564*w - 12 = 1560*w. Let a(c) be the second derivative of 68/9*c**w + 9*c - 5/27*c**6 + 17/9*c**5 + 0 - 4*c**2 - 349/54*c**4. Factor a(y).
-2*(y - 3)**2*(5*y - 2)**2/9
Let u(s) = -s**2 + s. Let q(f) = 4*f**2 - 24*f - 12. Let y(t) = -q(t) - 8*u(t). Factor y(z).
4*(z + 1)*(z + 3)
Suppose 3*n + 71 = 71. Factor 4/5*d + n - 2/5*d**2.
-2*d*(d - 2)/5
Let u(t) be the third derivative of -t**5/40 - 7*t**4/48 - t**3/3 + 132*t**2. Factor u(f).
-(f + 1)*(3*f + 4)/2
Determine a so that 2/13*a**2 - 402/13 + 400/13*a = 0.
-201, 1
Let m(k) be the first derivative of k**6/3 + 22*k**5/5 + 16*k**4 + 56*k**3/3 + 43. Factor m(p).
2*p**2*(p + 2)**2*(p + 7)
Let g(q) be the second derivative of -1/17*q**2 + 0 - 4*q - 1/102*q**4 - 2/51*q**3. Factor g(r).
-2*(r + 1)**2/17
Let -4/11*s**3 + 0 - 2/11*s**4 - 2/11*s**2 + 0*s = 0. Calculate s.
-1, 0
Let l be (8/(-840)*-7)/(2/5). Let y(r) be the first derivative of -1/9*r**3 + 1/15*r**5 - 1/12*r**4 + 0*r + 4 + l*r**2. Find j, given that y(j) = 0.
-1, 0, 1
Suppose 5*c + 25 = 5*a, -a - 3*c - 2*c = -5. Factor d - 5*d**2 + a*d**2 + d**2.
d*(d + 1)
Let z(x) be the second derivative of x**6/10 - 9*x**5/20 + x**4/4 + 3*x**3/2 - 3*x**2 + 2*x - 5. Solve z(l) = 0.
-1, 1, 2
Factor -2/7*b**3 + 0 + 0*b + 8/7*b**2.
-2*b**2*(b - 4)/7
Let k be 16/104 - (-204)/26. Determine j, given that 11*j**3 - j**5 - 6*j**5 - 3*j**2 + 4*j**5 - k*j**3 + 3*j**4 = 0.
-1, 0, 1
Let h be 120/80*(-4)/(-3). Let f(d) be the second derivative of 0*d**4 - 3*d - 1/30*d**3 + 0 + 1/100*d**5 + 0*d**h. Find v, given that f(v) = 0.
-1, 0, 1
Let z(g) be the second derivative of g**6/30 - 3*g**5/50 - 13*g**4/60 + g**3/5 + 4*g**2/5 - 68*g. Determine i so that z(i) = 0.
-1, -4/5, 1, 2
Suppose -k + 5 = 10, -5 = 4*b + 5*k. Let l be (-2)/(-8) - 57/(-12). Factor -9*y**2 + 2*y**l - 8*y - 4 + 8*y**3 + 8*y**4 - 2*y + b*y**2.
2*(y - 1)*(y + 1)**3*(y + 2)
Suppose -9*t = 6*t - t. Factor 3/7*r + t + 3/7*r**2.
3*r*(r + 1)/7
Suppose -10/13*a + 2/13*a**2 + 12/13 = 0. Calculate a.
2, 3
Let t(u) be the first derivative of 5*u**9/144 + 13*u**8/336 + u**7/84 - 2*u**3/3 + 8. Let i(p) be the third derivative of t(p). Factor i(c).
5*c**3*(3*c + 1)*(7*c + 2)
Let u be 1 + (1/1 - -3). Let b be (-5)/((-250)/380) + -6. Factor 8/5*a**4 - 2/5*a**u + 0 + b*a**2 - 2/5*a - 12/5*a**3.
-2*