f -17*o**2/2 + 7*o - 27. Let g be p(-1). Suppose 6 + 15/2*j**3 + 51/2*j**2 + g*j = 0. What is j?
-2, -1, -2/5
Let q(c) be the second derivative of 0*c**2 + 35/12*c**3 + 19*c + 0 + 5/24*c**4. Find u such that q(u) = 0.
-7, 0
Let q be (-18 - 1 - -16)/(3/(-4)). Let 19/3*x + 10/3*x**q + 2 - 4/3*x**2 - 31/3*x**3 = 0. What is x?
-1/2, -2/5, 1, 3
Let o(t) be the third derivative of -t**8/336 - t**7/105 + 13*t**6/120 - t**5/6 + 69*t**2. Factor o(n).
-n**2*(n - 2)*(n - 1)*(n + 5)
Let v(k) be the third derivative of -k**8/224 + 3*k**7/140 - k**6/40 - k**5/20 + 3*k**4/16 - k**3/4 - 41*k**2. Factor v(x).
-3*(x - 1)**4*(x + 1)/2
Suppose -5*c - 124 = -q, 6*c - 3*c + 576 = 5*q. Let i = q + -568/5. Factor -i*f**2 + 0 - 1/5*f**3 - 1/5*f.
-f*(f + 1)**2/5
Let r(k) be the third derivative of -k**7/16380 + k**5/195 + k**4/24 - 2*k**2. Let w(s) be the second derivative of r(s). Factor w(f).
-2*(f - 2)*(f + 2)/13
Let 23328 + 23339*y**4 - 23555*y**4 - 23112*y**2 - 3888*y + 1753*y**3 + 2131*y**3 + 4*y**5 = 0. What is y?
-1, 1, 18
Let n(o) be the second derivative of -o**9/7560 + o**7/1260 - 17*o**4/6 + 22*o. Let q(k) be the third derivative of n(k). Suppose q(g) = 0. Calculate g.
-1, 0, 1
Let j(d) be the second derivative of d**4/3 + 8*d**3/3 - 10*d**2 + 261*d. Factor j(u).
4*(u - 1)*(u + 5)
Determine m so that 4*m**4 - 24/5*m**3 + 0*m - 4/5*m**5 + 0*m**2 + 0 = 0.
0, 2, 3
Let h(d) be the first derivative of d**6/720 - d**5/240 + d**3 - 11. Let g(x) be the third derivative of h(x). Solve g(z) = 0.
0, 1
Factor -2/7*d**2 - 4608/7 - 192/7*d.
-2*(d + 48)**2/7
Let g(k) be the second derivative of -k**4/28 + 90*k**3/7 - 12150*k**2/7 - 92*k. Factor g(p).
-3*(p - 90)**2/7
Let x be (23 - 22) + 7 + 0. Let d(q) be the third derivative of 1/60*q**5 + x*q**2 + 0 - 1/4*q**4 + 3/2*q**3 + 0*q. Suppose d(z) = 0. Calculate z.
3
Let x(h) be the third derivative of -1/12*h**4 + 0 + 1/18*h**5 + 0*h + 2*h**2 + 0*h**3. Factor x(r).
2*r*(5*r - 3)/3
Find f such that -2/5*f**2 - 22/5 - 24/5*f = 0.
-11, -1
Let k(z) be the second derivative of z**6/720 - z**5/120 - z**4/16 - 29*z**3/6 - 18*z. Let g(l) be the second derivative of k(l). Factor g(n).
(n - 3)*(n + 1)/2
Suppose -9*h + 3*h + 144 = 0. Factor -h*r**2 + 12*r + 3*r**3 - 48*r - 2*r**3 - 5*r**3.
-4*r*(r + 3)**2
Let q be 4 + -1 - (-103)/114*-3. Let p = 641/114 - q. Solve -p*f**2 + 0 - 7/3*f**3 - 4/3*f = 0 for f.
-2, -2/7, 0
Let y(m) be the first derivative of -7/2*m**2 - 4 - 1/80*m**5 + 1/8*m**3 + 0*m - 1/480*m**6 + 1/96*m**4. Let g(t) be the second derivative of y(t). Factor g(r).
-(r - 1)*(r + 1)*(r + 3)/4
Let t = 1/294 - -571/4998. Let c be 17139/3349 - (-2)/(2/(-5)). Determine i, given that -c*i**2 + 0 + t*i = 0.
0, 1
Let k be 1/((-6)/(-108)*6). Let c be ((-20)/13 - 1) + k. Find h, given that -2/13*h**2 - 4/13*h + c = 0.
-3, 1
Let t = -17 - -15. Let q be (2 + -3)*2*t. Suppose 9*y**2 - 6 - 3*y**q - 9*y**3 + 3*y + 7*y**3 - y**3 + 0*y**3 = 0. What is y?
-2, -1, 1
Let f(k) be the third derivative of k**6/3060 - k**5/1020 - 7*k**3/6 - 17*k**2. Let i(a) be the first derivative of f(a). Factor i(g).
2*g*(g - 1)/17
Let r(f) = -23*f**4 - 70*f**3 + 93*f**2 - 13*f - 13. Let k(b) = 11*b**4 + 35*b**3 - 46*b**2 + 6*b + 6. Let n(v) = 13*k(v) + 6*r(v). Factor n(j).
5*j**2*(j - 1)*(j + 8)
Suppose -2*s**3 + s - 19705*s**2 + s - 2*s**4 + 19707*s**2 = 0. What is s?
-1, 0, 1
Factor -g**3 + 43/3*g**2 - 161/3*g + 49/3.
-(g - 7)**2*(3*g - 1)/3
Let q(w) = -w**3 - 7*w**2 + 7*w + 2. Let g be q(-8). Suppose -58 = -2*f - g. Let 8*y**2 + 4*y**2 - f*y + 9*y + 3 = 0. Calculate y.
1/4, 1
Suppose 23*z - 116 + 24 = 0. Let w be (-6)/z*((-56)/(-3))/(-7). Factor -1/9 - 4/9*g - 4/9*g**3 - 2/3*g**2 - 1/9*g**w.
-(g + 1)**4/9
Let p be 57 + -52 + 118/(-24). Let b(x) be the third derivative of p*x**4 - 1/60*x**5 - 8*x**2 + 0*x - 1/6*x**3 + 0. Solve b(m) = 0 for m.
1
Factor -24/5*h - 74/5*h**2 + 0 - 6*h**4 - 78/5*h**3 - 2/5*h**5.
-2*h*(h + 1)**3*(h + 12)/5
Let x = -612 + 616. Let i(t) be the first derivative of 4*t**2 + 0*t + 8/3*t**3 - 15/2*t**x - 1. Solve i(z) = 0.
-2/5, 0, 2/3
Let f(a) be the third derivative of -1/60*a**5 + 0*a + 0 + 0*a**3 - 1/48*a**4 + 19*a**2 - 1/240*a**6. Factor f(l).
-l*(l + 1)**2/2
Let w(t) = -86*t**2 - 164*t - 32. Let a(i) = 57*i**2 + 110*i + 22. Let j(q) = -8*a(q) - 5*w(q). Factor j(f).
-2*(f + 2)*(13*f + 4)
Let n = -4/35419 + 3329806/3718995. Let x = -8/35 + n. Factor 10/3*q**2 - 2/3*q**4 + 2*q**3 - x*q**5 + 4/3*q + 0.
-2*q*(q - 2)*(q + 1)**3/3
Let w = 72 + -93. Let y be (3 + 259/w)*3/(-22). Determine s, given that 18/11*s - 46/11*s**2 + y*s**3 - 2/11 + 48/11*s**4 - 32/11*s**5 = 0.
-1, 1/4, 1
Suppose 0 = -3*j - 4*m + 20, 9 = 4*j - 4*m + 29. Factor -4/3*t**4 + j + 2/3*t**3 + 0*t**2 + 2/3*t**5 + 0*t.
2*t**3*(t - 1)**2/3
Find s such that -2*s**4 - 4*s**5 + 3202*s**3 - 3*s**4 - 3*s**4 + 33*s**2 - 9*s**2 - 3182*s**3 = 0.
-3, -1, 0, 2
Let r(f) be the first derivative of 49/4*f + f**4 + 13/2*f**3 + 14*f**2 + 22 + 1/20*f**5. Let r(c) = 0. Calculate c.
-7, -1
Factor 16/9*f**3 - 2/9*f**4 + 0 + 0*f - 14/9*f**2.
-2*f**2*(f - 7)*(f - 1)/9
Let f(y) be the first derivative of -y**5/10 + 9*y**4/8 - 25*y**3/6 + 27*y**2/4 - 5*y + 82. Factor f(w).
-(w - 5)*(w - 2)*(w - 1)**2/2
Solve 1/2*x**2 - 15/2 + 7*x = 0.
-15, 1
Factor -4*z + 6/13*z**2 + 32/13.
2*(z - 8)*(3*z - 2)/13
Let n be 4059/7980*310/30. Let f = n - 4/665. Let f*r - 9/4*r**2 - 3/2 = 0. Calculate r.
1/3, 2
Let q(c) be the third derivative of -c**5/3 + 5*c**3/2 - 3*c**2. Let h(g) = -g**4 + g**3 - g**2 - g + 1. Let w(b) = 5*h(b) - q(b). Find k, given that w(k) = 0.
-1, 1, 2
Let v(n) be the second derivative of -n**4/48 - 7*n**3/12 + 51*n**2/8 - 651*n. What is l in v(l) = 0?
-17, 3
Let o(a) be the second derivative of 1/30*a**5 + 1/45*a**6 + 2*a**2 - 1/9*a**3 - 7/18*a**4 + 37*a + 0. Suppose o(n) = 0. What is n?
-3, -1, 1, 2
Let o(b) be the third derivative of -b**9/10584 + b**7/2940 + 2*b**3 + 14*b**2. Let l(q) be the first derivative of o(q). Let l(t) = 0. What is t?
-1, 0, 1
Let q(s) = s**5 + s**4 - 4*s**3 - s**2 - 3. Let w(b) = -b**5 - b**4 + 4*b**3 + 2*b**2 + 2. Let t(n) = 2*q(n) + 3*w(n). Factor t(u).
-u**2*(u - 2)*(u + 1)*(u + 2)
Let o(m) = -6*m**3 + 8*m**2 + 72*m + 104. Let w(l) = 2*l**3 - 3*l**2 - 24*l - 35. Let z(r) = -3*o(r) - 8*w(r). Factor z(q).
2*(q - 4)*(q + 2)**2
What is m in -125*m**3 - 76381 - 475*m**2 - 119*m - 201*m + 76321 = 0?
-3, -2/5
Let s(g) be the third derivative of -5*g**8/2352 + g**7/70 + 31*g**6/840 - 19*g**5/140 + 5*g**4/84 + 811*g**2. Let s(f) = 0. Calculate f.
-2, 0, 1/5, 1, 5
Factor 16/5 - 2224/5*d + 77284/5*d**2.
4*(139*d - 2)**2/5
Let d = 12688 - 12685. Factor 1/2*k**d - 2*k + 1/2*k**2 - 2.
(k - 2)*(k + 1)*(k + 2)/2
Let y(r) = 9*r**3 + 119*r**2 + 232*r + 94. Let w(u) = 6*u**3 + 79*u**2 + 155*u + 62. Let l(f) = -7*w(f) + 5*y(f). Let l(m) = 0. What is m?
-12, -1
Let l be -7 + (-186)/(-24) + (-305)/(-4). Find t, given that 55*t**3 + 110*t**4 + 20*t**4 - 8*t + l*t**5 - 27*t**5 + 86*t**2 - 313*t**3 = 0.
-4, 0, 1/5, 1
Let q(v) be the first derivative of 2994750*v**6 + 7056720*v**5 + 4167405*v**4 - 637592*v**3/3 + 3928*v**2 - 32*v + 368. Determine o so that q(o) = 0.
-1, 2/165
Let -1/3*f**2 - 1444/3 + 76/3*f = 0. What is f?
38
Suppose -5*q = -0*q - 20. Factor 4*g**3 - 4 + 9*g - 44*g**3 - 4*g**5 - 20*g**q - 40*g**2 - 29*g.
-4*(g + 1)**5
Let n(b) be the third derivative of b**7/840 + b**6/240 + 23*b**4/24 - 7*b**2. Let t(q) be the second derivative of n(q). Factor t(l).
3*l*(l + 1)
What is z in -9/5*z**2 - 7/5*z**3 + 8*z + 12/5 = 0?
-3, -2/7, 2
Factor 6*i + 1/4*i**2 + 36.
(i + 12)**2/4
Let j(q) be the third derivative of q**7/105 - q**6/30 + q**5/30 + 91*q**2. Factor j(g).
2*g**2*(g - 1)**2
Determine u, given that -6*u - 24*u - 32 - 13 - 5*u**2 = 0.
-3
Factor -3*o**4 + 4*o**4 - 25*o**3 - 4*o**4 - 2*o**4 + 0*o**4 - 20*o**2.
-5*o**2*(o + 1)*(o + 4)
Let i = 609/4 - 151. Let r(d) be the second derivative of 3/5*d**5 + i*d**4 + 0*d**2 + d**3 + 1/10*d**6 - 3*d + 0. Determine h so that r(h) = 0.
-2, -1, 0
Let q(x) = -4*x**3 + 612*x**2 - 23702*x + 23094. Let y(g) = g - 1. Let w(z) = q(z) - 10*y(z). Factor w(b).
-4*(b - 76)**2*(b - 1)
Let n = -452 - -455. Let t(a) be the first derivative of 6 + 0*a**2 - 1/14*a**4 + 0*a**n + 0*a. Suppose t(x) = 0. What is x?
0
Let r(b) = 2*b**2 - 13*b - 3. Let l