 the first derivative of -9*k**5/5 + 3*k**4/4 + 9*k**3 - 27*k**2/2 + 6*k - 2. Suppose a(h) = 0. Calculate h.
-2, 1/3, 1
Suppose 8*b - 55 = -31. Let c(k) be the first derivative of 2 + 0*k - 2/3*k**b - k**2. What is h in c(h) = 0?
-1, 0
Factor 0*q - 5/3*q**2 + 0 + 65/3*q**3 + 55/3*q**5 - 115/3*q**4.
5*q**2*(q - 1)**2*(11*q - 1)/3
Suppose 0 = -2*o - 0*o. Let x be (2/(-4))/(0 - 1). Let x*t - 1/2*t**4 - 3/2*t**2 + o + 3/2*t**3 = 0. What is t?
0, 1
Let u(r) be the third derivative of -r**6/480 + r**5/120 + 25*r**2. Let u(a) = 0. What is a?
0, 2
Factor -10*f**2 + 6 - f - 5 + 9*f**2 + f**3.
(f - 1)**2*(f + 1)
Suppose 0 = -16*l + 14*l. Let b(f) be the third derivative of f**2 + 0 - 1/120*f**6 + l*f + 0*f**4 + 0*f**3 + 1/120*f**5 + 1/420*f**7. Solve b(q) = 0 for q.
0, 1
Solve -8/5 - 32/15*t - 2/15*t**3 - 14/15*t**2 = 0 for t.
-3, -2
Suppose -3*y = 4*j - 27, 2*j + 3*y - 20 = 1. Suppose 0 = -2*w + 1 + j. Factor 2*x**4 + w*x - 2*x.
2*x**4
Suppose -3*t + 16 = -14. Let k = -10 + t. Determine v, given that -1/4*v + 1/4*v**3 + 0*v**2 + k = 0.
-1, 0, 1
Let b be (-4)/(0 + 8/(-6)). What is v in -3*v**2 - 2*v + 0 + b + 2*v = 0?
-1, 1
Let c be -4*(-9)/24*2. Let a be (22/(-33))/((-5)/c). Factor -2/5*u + a*u**3 + 0*u**2 + 0.
2*u*(u - 1)*(u + 1)/5
Factor 14*g**4 - 27*g**2 + 9*g**3 + 15*g - 4*g**4 - 7*g**4.
3*g*(g - 1)**2*(g + 5)
Let l(x) be the third derivative of x**9/52920 - x**8/11760 - x**7/8820 + x**6/1260 + 5*x**4/24 - x**2. Let p(y) be the second derivative of l(y). Factor p(s).
2*s*(s - 2)*(s - 1)*(s + 1)/7
Let i(h) be the second derivative of h**6/180 + h**5/60 - h**3/3 - 3*h. Let d(y) be the second derivative of i(y). Factor d(n).
2*n*(n + 1)
Let f(a) = -a**3 - 5*a**2 + 5*a + 3. Let u be f(-6). Factor -3*z**3 - u + 2*z**3 + z + 9.
-z*(z - 1)*(z + 1)
Let g(h) be the first derivative of 5*h**4 + 32*h**3/3 - 8*h**2 - 47. Find s, given that g(s) = 0.
-2, 0, 2/5
Let x(y) = -y + 1. Let c(m) = -2*m**2 - 55*m - 393. Let g(n) = -c(n) - x(n). Factor g(q).
2*(q + 14)**2
Let a = 247 + -427. Let u be 2/(-9) + (-112)/a. Determine q, given that -2/5*q**4 + 0*q + u*q**3 + 2/5*q**2 - 2/5*q**5 + 0 = 0.
-1, 0, 1
Let j be -4 + 372/368 - -3. Let u = 191/644 - j. Factor 4/7*x + u*x**2 + 0 - 2/7*x**3.
-2*x*(x - 2)*(x + 1)/7
Let s = -29/7 - -33/7. Suppose -3*g - 4 = -0*k + 4*k, 0 = -3*k - 4*g - 10. Suppose 0*y + 0*y**3 - 2/7 + s*y**k - 2/7*y**4 = 0. Calculate y.
-1, 1
Solve 17/10*a**3 - 3/5*a**2 - 2*a + 7/5*a**4 - 4/5 + 3/10*a**5 = 0 for a.
-2, -1, -2/3, 1
Let o = 4 + 0. Let n = -1 + o. Find h such that -2*h**2 - 3*h**2 - h**4 + 3*h**2 - n*h**3 = 0.
-2, -1, 0
Let t(h) be the first derivative of 35*h**3/3 + 11*h**2/2 - 6*h - 10. Let c(i) = 70*i**2 + 22*i - 12. Let b(r) = 3*c(r) - 7*t(r). Solve b(a) = 0.
-3/5, 2/7
Factor -10 + 49 + 27*y - 3*y**2 - 9.
-3*(y - 10)*(y + 1)
Let q(n) = 3*n**3 + 11*n**2 - 29*n + 15. Let o(c) = 14*c**3 + 56*c**2 - 146*c + 76. Let l(g) = 3*o(g) - 16*q(g). Factor l(u).
-2*(u - 1)*(u + 3)*(3*u - 2)
Factor -1/3*c**2 + 0*c - c**4 + 0 - c**3 - 1/3*c**5.
-c**2*(c + 1)**3/3
Let o(t) = -t**2 + 7*t - 6. Let i(c) = -3*c**2 + 24*c - 21. Let f(u) = 5*i(u) - 18*o(u). Factor f(h).
3*(h - 1)**2
Let q(h) be the first derivative of h**8/9240 + h**7/2310 + h**6/1980 + 4*h**3/3 + 1. Let v(s) be the third derivative of q(s). Factor v(g).
2*g**2*(g + 1)**2/11
Suppose 13 = 5*z - 7. Let m**4 + 6*m - z*m + 0 + 0 + 5*m**2 + 4*m**3 = 0. What is m?
-2, -1, 0
Let y(f) be the first derivative of f**4/8 - f**3/3 + 2. Factor y(t).
t**2*(t - 2)/2
Let b(i) = 2*i**2 - 23*i + 53. Let j(s) = -22*s**2 + 254*s - 584. Let l(p) = -68*b(p) - 6*j(p). What is y in l(y) = 0?
5
Let t = -30 + 121/4. Let p = 105/4 + -26. What is l in t*l**3 + 0 + 1/4*l**4 - 1/4*l**2 - p*l = 0?
-1, 0, 1
Let f(i) be the second derivative of -i**5/30 - 11*i**4/45 - 8*i**3/45 - 7*i. Suppose f(h) = 0. What is h?
-4, -2/5, 0
Suppose j - 7*j - 11*j**2 + 18*j**2 + 17*j**2 - 4 - 14*j**3 = 0. What is j?
-2/7, 1
Let g(h) = 12*h**4 + 32*h**3 - 88*h**2 + 44. Let c(t) = -t**4 - 3*t**3 + 8*t**2 - 4. Let z(s) = 32*c(s) + 3*g(s). Factor z(j).
4*(j - 1)**2*(j + 1)**2
Suppose -4*g + 2*r + 0*r - 70 = 0, 0 = -5*g + r - 89. Let d be ((-8)/g)/((-24)/(-36)). Let 0*l**2 + d*l**4 + 0 - 2/3*l**3 + 0*l = 0. Calculate l.
0, 1
Suppose -y + 8 = 20. Let w be (54/y)/(-2 - 4). Factor -w*c**2 + 0 + 3/4*c**3 - 1/4*c**4 + 1/4*c.
-c*(c - 1)**3/4
Let p(c) be the third derivative of c**7/630 - c**6/180 + c**4/36 - c**3/3 - c**2. Let m(x) be the first derivative of p(x). Factor m(n).
2*(n - 1)**2*(2*n + 1)/3
Solve 0 - 1/4*r - 1/2*r**2 - 1/4*r**3 = 0 for r.
-1, 0
Let l(y) be the third derivative of -y**8/112 - y**7/10 - 3*y**6/8 - 9*y**5/20 - 36*y**2. Factor l(u).
-3*u**2*(u + 1)*(u + 3)**2
Let g(c) be the first derivative of c**9/7560 - c**8/4200 + 2*c**3/3 - 5. Let i(y) be the third derivative of g(y). Factor i(f).
2*f**4*(f - 1)/5
What is b in 4/5*b**3 - 144/5 + 96/5*b + 44/5*b**2 = 0?
-6, 1
Let o = 720 + -720. Solve m**5 - 7/3*m**4 + 0 + 5/3*m**3 - 1/3*m**2 + o*m = 0 for m.
0, 1/3, 1
Suppose -51 + 1 = -5*d. Let 10*t - d*t + 2*t**2 = 0. What is t?
0
Let c(z) = 2*z**5 + 3*z**4 - 3*z**2 + 3. Let o(x) = -3*x**5 - 4*x**4 + 4*x**2 - 4. Let w(f) = -4*c(f) - 3*o(f). Factor w(y).
y**5
Let q(d) be the third derivative of -1/840*d**7 + 1/480*d**6 - 3*d**2 + 1/80*d**5 - 1/12*d**3 + 0 - 1/96*d**4 + 0*d. Solve q(k) = 0.
-1, 1, 2
Let l(x) = -x**3 + x**2 + 3*x - 3. Let i be l(1). Factor 0*z**2 + 2/7*z**3 + 0*z + i + 0*z**4 - 2/7*z**5.
-2*z**3*(z - 1)*(z + 1)/7
Suppose 6*k - k = 0. Let s(j) be the second derivative of 7/4*j**4 - 3*j + k + 1/6*j**3 - j**2. Find u such that s(u) = 0.
-1/3, 2/7
Let m be 1/(2 + (1 - 0)). Let c(u) be the first derivative of -m*u + 1/18*u**6 + 1/5*u**5 - 1/2*u**2 - 3 + 1/6*u**4 - 2/9*u**3. Factor c(j).
(j - 1)*(j + 1)**4/3
Let o(u) = 3*u**3 - 8*u**2 + 6*u + 36. Let t(c) = c**3 - 4*c**2 + 3*c + 18. Let q(m) = -4*o(m) + 10*t(m). Factor q(x).
-2*(x - 2)*(x + 3)**2
Factor -3/4*f**2 - f**3 + 0 + 1/4*f.
-f*(f + 1)*(4*f - 1)/4
Let p(g) be the third derivative of -g**9/90720 + g**8/10080 - g**7/3780 - g**4/4 - 5*g**2. Let a(y) be the second derivative of p(y). Factor a(z).
-z**2*(z - 2)**2/6
What is d in -4/7*d + 0 - 2/7*d**2 + 2/7*d**3 = 0?
-1, 0, 2
Let b(x) = 32*x**4 + 27*x**3 - 29*x**2 - 11*x + 13. Let p(a) = -16*a**4 - 14*a**3 + 14*a**2 + 6*a - 6. Let z(f) = -2*b(f) - 5*p(f). Solve z(m) = 0 for m.
-1, 1/2
Let i = -1748/7 - -250. Factor 4/7*z**3 + 0 - 2/7*z**2 + 0*z - i*z**4.
-2*z**2*(z - 1)**2/7
Let k = -56666 + 13430152/237. Let b = k + 2/79. Factor 0 - 2/3*w - 2/3*w**3 + b*w**2.
-2*w*(w - 1)**2/3
Factor 0*s - 1/3*s**4 - 4/3*s**3 - s**2 + 0.
-s**2*(s + 1)*(s + 3)/3
Let o = 40/129 + 1/43. Find k, given that o*k**2 + 0*k - 1/3 = 0.
-1, 1
Let h(o) be the second derivative of o**4/4 - o**3 + 3*o**2/2 - 4*o. Find d such that h(d) = 0.
1
Let f(d) be the third derivative of d**8/84 - d**6/10 - 2*d**5/15 - 12*d**2. Determine p so that f(p) = 0.
-1, 0, 2
Let w(q) be the third derivative of -q**6/280 + q**5/70 - q**4/56 - 33*q**2. Factor w(l).
-3*l*(l - 1)**2/7
Let a(i) be the first derivative of i**4/16 + 4*i**3/3 + 77*i**2/8 + 49*i/2 + 32. Factor a(z).
(z + 2)*(z + 7)**2/4
Suppose -d - 59 = 4*d - 3*j, 2*j = d + 16. Let b be 4/d + 51/15. Solve 4*a**4 - 6*a**4 - 2*a - 2*a + 2 + 4*a**b = 0 for a.
-1, 1
Suppose f - 2*g - 13 = 0, -f - 3*g = -8 + 20. Factor 6*k + 1/2*k**f + 3*k**2 + 4.
(k + 2)**3/2
Find i such that 0*i**2 + 2/9*i**3 + 0*i + 0 = 0.
0
Let f be -3*2/(-4)*4. Let r = 8 - f. Factor -d + r*d + 0*d - d**3.
-d*(d - 1)*(d + 1)
Let o(l) = l**3 + 4*l + 9. Let v(c) = c + 1. Let s(q) = -3*o(q) + 21*v(q). Let s(p) = 0. Calculate p.
-2, 1
Let k(a) be the second derivative of -a**9/6048 + a**8/1344 - a**7/840 + a**6/1440 + a**3/6 - a. Let q(l) be the second derivative of k(l). Factor q(s).
-s**2*(s - 1)**2*(2*s - 1)/4
Let x(n) = -n**3 - 2*n**2 + 3*n + 3. Let t be x(-3). Suppose 12*o**2 - 16 + 8*o**2 + 8*o + 6*o**3 + 0*o**t = 0. Calculate o.
-2, 2/3
Let r(i) be the first derivative of -i**7/28 + i**6/10 + 3*i**5/40 - i**4/4 - 2*i + 1. Let a(m) be the first derivative of r(m). Find w such that a(w) = 0.
-1, 0, 1, 2
Let y be 15/(-25)*(-2)/18. Let i(f) be the second derivative of 0*f**2 + 1/63*f**7 + 0*f**6 + 0 - f + 1/9*f**3 - y*f**5 + 0*f**4. Factor i(a).
2*a*