 2*z + 4*z.
3*z**3*(z + 1)*(2*z - 1)
Let u(f) be the first derivative of -f**3/6 - 39*f**2/4 + 289. Factor u(a).
-a*(a + 39)/2
Let p(h) = -4*h**3 + 2*h - 1. Let s be p(1). Let a be (s/(-2))/(-1)*(-8)/6. Solve 3*d - 3 + 9/4*d**a + 3/4*d**4 - 3*d**3 = 0 for d.
-1, 1, 2
Let s = 86991/7 - 12417. Solve -s*i + 6/7*i**2 + 216/7 = 0.
6
Let j(v) be the second derivative of v**6/45 + v**5/5 + 13*v**4/18 + 4*v**3/3 + 4*v**2/3 - 6*v - 9. Factor j(c).
2*(c + 1)**2*(c + 2)**2/3
Let o(k) be the second derivative of k**6/45 - 19*k**5/30 + 35*k**4/6 - 49*k**3/9 - 686*k**2/3 - 44*k. Factor o(c).
2*(c - 7)**3*(c + 2)/3
Factor 792*p**2 + 48 - 367*p + 16*p + 48*p**3 + 738*p.
3*(p + 16)*(4*p + 1)**2
Let n(i) be the first derivative of -i**3/2 + 15*i**2/4 + 21*i - 173. Factor n(b).
-3*(b - 7)*(b + 2)/2
Factor 2400/7 + 80/7*q + 2/21*q**2.
2*(q + 60)**2/21
Factor 2*g**2 + 264*g + 6778 + 1415 - 511 + 1030.
2*(g + 66)**2
Suppose 7*w = 31 + 95. Let q be (12/w)/(3/(-2) + 2). Solve -q*i**3 - 2 - 4/3*i + 14/3*i**2 = 0.
-1/2, 1, 3
Solve 3 - 1/2*l - 1/2*l**2 = 0 for l.
-3, 2
Let n(k) = -k**2 + 583*k - 4030. Let z be n(7). Find f, given that 1/4*f**z + 0*f - 1/4 = 0.
-1, 1
Factor 1/8*d**2 + 200 + 10*d.
(d + 40)**2/8
Factor 6*l**2 + 2*l**5 + 82 - 10*l**3 - 42 - 40 + 2*l**4.
2*l**2*(l - 1)**2*(l + 3)
Let s(g) = -13*g**2 - 1179*g - 43803. Let x(q) = -7*q**2 - 589*q - 21901. Let k(d) = -3*s(d) + 5*x(d). Factor k(z).
4*(z + 74)**2
Let q = -2/22537 - -270458/157759. Factor 0*k - q*k**4 - 4/7*k**5 + 0*k**2 + 0 - 8/7*k**3.
-4*k**3*(k + 1)*(k + 2)/7
Determine g, given that 4/7*g**2 + 0 - 4/7*g + 4/7*g**3 - 4/7*g**4 = 0.
-1, 0, 1
Let f(y) be the second derivative of y**8/1344 - y**7/252 + y**6/144 - y**4/4 - 15*y. Let s(b) be the third derivative of f(b). Solve s(g) = 0 for g.
0, 1
Solve 20404 - 12*h - 20404 + 9*h**2 = 0 for h.
0, 4/3
Let a be 5/(-10)*508/(-635). Find v, given that 2/5*v**4 - 6/5*v**2 + a*v - 2/5*v**3 + 4/5 = 0.
-1, 1, 2
Let n = 343/417 - -3/278. Let d(t) be the second derivative of -8*t + 0 + n*t**3 - 1/2*t**2 - 1/3*t**4. Factor d(c).
-(c - 1)*(4*c - 1)
Suppose -5*w = -4*f + 29, -3*w - f + 4*f = 15. Let g = w + 14. What is m in -29*m**4 + 33*m**4 + 6*m**3 + m**g + m + m**2 + 3*m**2 = 0?
-1, 0
Let x(b) be the first derivative of 5/4*b**4 - 5/6*b**6 - 22 + 0*b + 0*b**3 + 0*b**5 + 0*b**2. Factor x(y).
-5*y**3*(y - 1)*(y + 1)
Let a(d) = -d**3 - 3*d**2 + 2. Let y(q) = q**3 - 6*q**2 + 6*q - 2. Let i be y(4). Let b(p) = -p**2 - p + 1. Let n(f) = i*b(f) + 5*a(f). Factor n(g).
-5*g*(g - 1)*(g + 2)
What is z in -2/7*z**2 + 236/7*z - 6962/7 = 0?
59
Factor 1/6 + 5/6*c**2 - 2/3*c - 1/3*c**3.
-(c - 1)**2*(2*c - 1)/6
Let q = 12756 + -12752. Solve -82/13*i**q + 56/13*i**5 + 56/13*i + 8/13 - 112/13*i**3 + 74/13*i**2 = 0.
-1, -2/7, -1/4, 1, 2
Let p(y) = -y**2 + 7*y + 10. Let c be p(8). Let i = 2 + 1. Suppose 6*r**3 - r**c + r - 5*r**3 - 2*r**i + 1 = 0. What is r?
-1, 1
Let o be ((5/(-3))/(-5))/6. Let g(h) be the second derivative of 0 + 1/3*h**2 + 0*h**3 - o*h**4 - 3*h. Factor g(j).
-2*(j - 1)*(j + 1)/3
Let w(h) be the third derivative of -h**9/302400 + h**8/33600 - 7*h**5/20 + 27*h**2. Let k(t) be the third derivative of w(t). Factor k(j).
-j**2*(j - 3)/5
Let w = 27 + -27. Let o = 87/190 + 29443/2090. Suppose 24/11*q + 8*q**2 - o*q**4 + 50/11*q**5 + w - 2/11*q**3 = 0. What is q?
-2/5, 0, 1, 3
Suppose 3*u + 5 - 1 = 4*s, 0 = 5*u - s + 1. Suppose -2*n - 3*g + 19 = u, 4*g - 9 = 3*n + 5. Factor 0 + 2/9*y**n + 2/9*y.
2*y*(y + 1)/9
Let t(f) = -6*f**2 + f. Let k(a) = 29*a**2 + 20*a - 46. Let d(x) = k(x) + 5*t(x). Factor d(h).
-(h - 23)*(h - 2)
Let h(l) be the second derivative of 1/30*l**5 + 0*l**2 + 0 + 1/6*l**4 - 4/9*l**3 - 10*l. Determine s, given that h(s) = 0.
-4, 0, 1
Let r(z) be the first derivative of z**4/16 + 5*z**3/6 - 7*z**2/8 - 49*z - 169. Suppose r(o) = 0. What is o?
-7, 4
Let x(t) = t + 14. Let p be x(8). Let -8*s**4 + 22*s + p*s**4 + 49*s**4 + 50*s - 12 + 147*s**5 - 219*s**3 - 51*s**2 = 0. Calculate s.
-1, 2/7, 1
Factor 2/3*m**2 + 0 - 2/3*m.
2*m*(m - 1)/3
Let i(r) be the first derivative of r**3/15 + 21*r**2/10 - 22. Factor i(u).
u*(u + 21)/5
Let l(u) be the third derivative of -u**7/1470 - u**6/840 + u**5/70 + u**4/42 - 4*u**3/21 + 2*u**2 - 22*u. Let l(z) = 0. What is z?
-2, 1, 2
Let w(c) be the first derivative of c**8/840 - c**7/420 - c**6/180 + c**5/60 + c**3/3 + 10. Let n(j) be the third derivative of w(j). Factor n(y).
2*y*(y - 1)**2*(y + 1)
Suppose 10*f = 3*f + 28. Factor 3*v**3 - 20 - 3*v**3 - 5*v**f + 20*v - 10*v**3 + 15*v**2.
-5*(v - 1)**2*(v + 2)**2
Let y(z) be the first derivative of z**3/3 + z**2/2 - 2*z - 152. Factor y(u).
(u - 1)*(u + 2)
Suppose 0 = -9*a + 11*a + 10. Let b be (a/80*4)/(2/(-8)). Determine l, given that 13/2*l + 2*l**4 + b + 12*l**2 + 17/2*l**3 = 0.
-2, -1, -1/4
Let b = 24917 - 125196/5. Let c = b - -124. Let c*o - 9/5*o**3 - 3/5*o**4 - 3/5*o**2 + 6/5 = 0. Calculate o.
-2, -1, 1
Let i(o) be the first derivative of -o**6/1980 + o**5/165 - o**4/44 - 22*o**3/3 - 18. Let v(r) be the third derivative of i(r). Factor v(q).
-2*(q - 3)*(q - 1)/11
Let g(m) = -2*m**3 - 10*m**2 + 28*m - 14. Let b(h) = -6*h**3 - 30*h**2 + 85*h - 42. Let r be -7*((-2)/(-6) - (-2)/3). Let o(y) = r*g(y) + 2*b(y). Factor o(j).
2*(j - 1)**2*(j + 7)
Let c(g) be the third derivative of 0 + 12*g**2 + 0*g - 1/8*g**5 + 5/4*g**3 + 1/48*g**6 - 5/48*g**4. Find v such that c(v) = 0.
-1, 1, 3
Let p(q) = -q**2 - q + 17. Let h be p(-5). Let l be (h - 132/(-35)) + 2/(-10). Factor -2/7*n**2 + l*n + 6/7.
-2*(n - 3)*(n + 1)/7
Let g(n) be the first derivative of -n**4/7 - 8*n**3/7 - 18*n**2/7 + 15. Factor g(x).
-4*x*(x + 3)**2/7
Let i(p) be the third derivative of -p**8/112 - p**7/70 + p**6/40 + p**5/20 - 162*p**2. Find u, given that i(u) = 0.
-1, 0, 1
Let c(p) be the second derivative of 0*p**5 + 5/12*p**4 + 0*p**3 + 7*p - 1/6*p**6 + 3 + 0*p**2. Factor c(q).
-5*q**2*(q - 1)*(q + 1)
Let 0 + 0*g + 0*g**2 + 1/4*g**3 + 1/4*g**5 - 1/2*g**4 = 0. What is g?
0, 1
Let v = -21 - -41. Factor 2*z**3 + 4*z - 23*z**4 - v*z**4 - 7*z**2 + 44*z**4.
z*(z - 1)**2*(z + 4)
Let n be 18/63 - 19/(-7). Suppose 21*j**2 + 4*j - 17*j**2 - 4*j**n - 4 + 0*j**3 = 0. What is j?
-1, 1
Suppose l + 2 = -0*l, -w + 5*l = -55. Solve 15 + 12 - w*i**2 - 43*i**4 + 11 + 4*i - 34 + 9*i**5 + 71*i**3 = 0.
-2/9, 1, 2
Let z = 2471 - 2471. Factor 2/7*f**2 - 2/7 + z*f.
2*(f - 1)*(f + 1)/7
Factor -24/7*c**2 + 44/7*c - 24/7 + 4/7*c**3.
4*(c - 3)*(c - 2)*(c - 1)/7
Determine d so that 20*d**2 + 60*d**3 - 10*d - 32 - 64*d**3 + 2*d = 0.
-1, 2, 4
Let o be (-5)/56*-6 + 3/(-12). Let j(q) be the first derivative of -1/2*q**4 - 5/7*q**2 - 6/7*q**3 + 3 - 4/35*q**5 - o*q. Suppose j(v) = 0. What is v?
-1, -1/2
Find y such that -6*y**2 + y**4 + 7 + 16*y**2 - 5*y**4 + 14*y**2 + 32*y + 5 = 0.
-1, 3
Let m be 56/21*(-2)/(640/(-24)). Factor -7/5*t**3 + 0*t - m*t**5 - t**4 + 0 - 3/5*t**2.
-t**2*(t + 1)**2*(t + 3)/5
Let b(s) be the second derivative of -s**9/3024 - s**8/840 - s**7/840 + 5*s**3/6 - 7*s. Let i(t) be the second derivative of b(t). Solve i(n) = 0.
-1, 0
Let k(f) be the third derivative of -12*f**2 - 1/24*f**6 - 1/3*f**5 + 5/24*f**4 + 0 + 10/3*f**3 + 0*f. Factor k(w).
-5*(w - 1)*(w + 1)*(w + 4)
Let b(x) be the third derivative of -x**6/96 + 13*x**5/48 - 5*x**4/2 + 15*x**3/2 + 535*x**2. Factor b(c).
-5*(c - 6)**2*(c - 1)/4
Find a, given that 117/4*a + 119/2 - 1/4*a**2 = 0.
-2, 119
Let g = 99 + -96. Let f = 5 - g. Solve 0*b + b**f + 0*b**4 - 1/2*b**5 + 0 + 3/2*b**3 = 0 for b.
-1, 0, 2
Let n(x) be the first derivative of 3*x**5/4 - x**4/4 - 5*x**3/2 + 3*x**2/2 + 14*x - 24. Let l(a) be the first derivative of n(a). Factor l(s).
3*(s - 1)*(s + 1)*(5*s - 1)
Solve 3*s**4 + 3*s**4 - 4*s**4 - 10*s**3 + 6*s**2 + 22*s - 4*s = 0 for s.
-1, 0, 3
Suppose -15 = -3*h - 3. Let z = h + -3. Factor z + 3 + 5*v**2 + 5 - 21*v + v**2.
3*(v - 3)*(2*v - 1)
Let d(a) be the first derivative of -a**4/4 - a**3 - 3*a**2/2 - 7*a - 9. Let y be d(-3). Factor -3*s**2 - 8*s - 25*s**y + 20*s**3 + 0*s**2 - 4*s**3.
4*s*(s - 2)*(4*s + 1)
Let x be (19/6 - 2)/(45 + 13494/(-312)). Let s = 3/19 + 29/57. Factor 0 + 2/3*a**2 - 2/3*a**3 + x*a - s*a**4.
-2*a*(a - 1)*(a + 1)**2/3
Let a be 2/(-7) + 182/(-49). Let h be (8 + -5)*a/(-3). Factor 0*r**h - 4*r + r**4 + 4*r**3 + r**4 - 2.
2*(r - 1)*(r + 1