/2*g**4 - 4*g**3 - 12*g**2 - 16*g. Factor r(x).
-2*(x + 2)**3
Factor -13/4*f - 4*f**2 + 15/2 - 1/4*f**3.
-(f - 1)*(f + 2)*(f + 15)/4
Let u(o) be the third derivative of o**5/12 + 85*o**4/12 + 55*o**3/2 + 44*o**2. Solve u(n) = 0.
-33, -1
Let l = 97/8 + -91/8. What is j in l*j**5 - 3/2*j**4 + 0*j**2 + 0*j + 0 + 3/4*j**3 = 0?
0, 1
Let j be 2/(4/2162)*(1 + -2). Let u = j + 5423/5. Factor -u - 2/5*d**2 + 12/5*d.
-2*(d - 3)**2/5
Let s(b) = b**3 - 9*b**2 + 18*b + 5. Let f be s(6). Factor 32*g**3 + 15*g**4 - 7*g**3 - f*g**2 - 20*g - 15*g**2.
5*g*(g - 1)*(g + 2)*(3*g + 2)
Let u(n) = -3*n**2 + 6*n - 3. Let o be u(1). Let q(z) be the third derivative of o + 1/21*z**3 - 2*z**2 - 1/168*z**4 - 1/420*z**5 + 0*z. Factor q(t).
-(t - 1)*(t + 2)/7
Let n be 13/(52/(-4) + 7 + 11). Find o such that -28/5*o - 2/5*o**4 - 6*o**2 - 8/5 - n*o**3 = 0.
-2, -1/2
Let n be (-2461)/(-966) - (75/(-18))/(-5). Let o(k) be the first derivative of -2 - n*k**2 + 10/21*k**3 + 8/7*k. Factor o(j).
2*(j - 2)*(5*j - 2)/7
Let t(q) be the second derivative of 7*q**5/100 - 73*q**4/20 + 136*q**3/15 - 6*q**2 + 85*q. What is r in t(r) = 0?
2/7, 1, 30
Let a(j) = -j**3 - 10*j**2 + 9*j + 4. Let c(n) = 6*n**3 + 52*n**2 - 45*n - 22. Let u(o) = 11*a(o) + 2*c(o). Factor u(h).
h*(h - 3)**2
Find p, given that -3/4*p - 1/4*p**2 - 1/2 = 0.
-2, -1
Let h(m) be the first derivative of 29 + 2/13*m + 0*m**2 - 2/39*m**3. Determine c, given that h(c) = 0.
-1, 1
Let w = 1613 + -1611. Factor -3*j - 3/2*j**w + 9/2.
-3*(j - 1)*(j + 3)/2
Let g(t) be the third derivative of -t**3 + 0*t + 1/40*t**5 + 0 + 3/16*t**4 + 26*t**2. Factor g(n).
3*(n - 1)*(n + 4)/2
Let c(s) be the second derivative of 2*s**4/3 - 74*s**3/3 - 38*s**2 - 4*s + 86. Let c(o) = 0. Calculate o.
-1/2, 19
Solve -248832/7 + 1728/7*l - 3/7*l**2 = 0.
288
Let f(v) = -2*v**2 + 2*v - 4. Let s = 15 + -13. Let y(j) = 5*j - s*j - 8 - 2*j**2 - 2*j**2 + 0*j. Let c(p) = -9*f(p) + 4*y(p). Factor c(g).
2*(g - 2)*(g - 1)
Solve 2/11*k**4 + 94/11*k + 26/11*k**3 + 36/11 + 82/11*k**2 = 0 for k.
-9, -2, -1
Let t = -10 - -14. Suppose -j + t = 2. Solve 5*n**4 + 2*n**5 - 2*n**3 + 2*n + 12*n**2 + 14*n**3 + 3*n**4 - 4*n**j = 0 for n.
-1, 0
Let w(f) be the third derivative of -f**9/4032 - 3*f**8/8960 + f**7/1680 + 13*f**4/24 - 2*f**2. Let a(k) be the second derivative of w(k). Factor a(m).
-3*m**2*(m + 1)*(5*m - 2)/4
Suppose 0 = -5*u + 4*l + 2, -2*l + 8 = 2*u - 0. Suppose u*v - 1 = 3. Let o(n) = n**2 + 3. Let i(b) = 2*b**2 + 4. Let j(s) = v*i(s) - 3*o(s). Solve j(d) = 0.
-1, 1
Let o be 0 - (-4)/(-2 - -4). Let m(f) = -f**o - 4 + 0*f + 6*f**2 + 23*f + 1. Let i(u) = -2*u**2 - 12*u + 2. Let l(c) = -7*i(c) - 4*m(c). Factor l(z).
-2*(z + 1)*(3*z + 1)
Suppose -q + 15 = 4*d, 2*q + 0*q = -d + 9. Let x be (4 - (0 + 4 + -1)) + 23. Factor -4*h**2 + 2*h**4 - x*h**3 - 2*h + 26*h**q + 2*h**2.
2*h*(h - 1)*(h + 1)**2
Let h(i) = 17*i**4 + 20*i**3 - 291*i**2 + 513*i - 273. Let m(z) = -8*z**4 - 10*z**3 + 144*z**2 - 257*z + 137. Let y(r) = -3*h(r) - 7*m(r). Factor y(b).
5*(b - 2)**2*(b - 1)*(b + 7)
Factor -60*b**3 + 9*b**2 - 36 - 64*b**3 + 121*b**3 + 12*b.
-3*(b - 3)*(b - 2)*(b + 2)
Let i(m) be the second derivative of -m**4/12 + 49*m**3/6 - 24*m**2 - m - 30. Factor i(a).
-(a - 48)*(a - 1)
Suppose -w = -5*w + 3*t + 24, -4*w - 4*t - 4 = 0. Let p = 2791/6965 + -1/1393. Factor 4/5*s - 4/5*s**w + 2/5*s**4 + 0 - p*s**2.
2*s*(s - 2)*(s - 1)*(s + 1)/5
Let w(y) be the third derivative of 0 + 2/525*y**7 + 3/100*y**5 - 1/30*y**3 + 0*y + 9*y**2 - 1/120*y**4 - 11/600*y**6. Factor w(g).
(g - 1)**3*(4*g + 1)/5
Let u(k) be the second derivative of k**6/160 + k**5/20 + 3*k**4/32 + 25*k**2/2 - 8*k. Let h(d) be the first derivative of u(d). Factor h(i).
3*i*(i + 1)*(i + 3)/4
Factor -30*w**2 - 8771 - 71*w + 8693 + 3*w**3 - 40*w.
3*(w - 13)*(w + 1)*(w + 2)
Let p = -3 + 7. Let t(d) be the third derivative of 0*d + 0 + 2/15*d**5 + 1/3*d**3 + 5/12*d**p - 11*d**2. Factor t(c).
2*(c + 1)*(4*c + 1)
Let w(v) be the second derivative of v**4/20 - 17*v**3/5 + 96*v**2/5 - 642*v. Factor w(h).
3*(h - 32)*(h - 2)/5
Suppose 5*f - 3*q = 0, 3*f + 5*q - 22 = 4*f. Let n be (-9)/(-27) - (-5)/f. Factor 3*s**2 - s - 5*s**n + 10*s**4 - 8*s**4 + 2*s - s**3.
s*(s - 1)*(s + 1)*(2*s - 1)
Suppose 0*z - z = -5. Suppose -z*w = -2*n - 7, w - 5*w + 65 = 5*n. What is y in 3*y**3 - n - 10 - 27*y**2 + 81*y - 62 = 0?
3
Let -22/5*w**3 + 88/5*w + 4/5*w**2 - 16/5 = 0. Calculate w.
-2, 2/11, 2
Let l be ((-15)/(-2))/((-33)/(-88)). Solve -2*x**4 + 5*x**4 + 40*x**3 - 3*x**4 + 15*x**4 + l*x**2 = 0 for x.
-2, -2/3, 0
Let b be ((-3)/(-110)*16)/((-15)/(-50)). Suppose 2/11*o**2 + 32/11 + b*o = 0. Calculate o.
-4
Let g = -344/7 - -50. Let y(z) = 2*z**2 + 4*z - 13. Let d be y(-4). Suppose 2/7*u + 0 + 2/7*u**4 + g*u**2 + 6/7*u**d = 0. Calculate u.
-1, 0
Let m(k) be the first derivative of -k**5/80 + 5*k**4/48 - k**3/3 + k**2/2 + 13*k - 13. Let o(f) be the first derivative of m(f). Factor o(g).
-(g - 2)**2*(g - 1)/4
Let f be (-2)/(484/33)*12*(-6)/9. What is k in 2/11*k**2 + f*k + 18/11 = 0?
-3
Let k(t) be the second derivative of -t**7/378 + 7*t**6/270 - t**5/90 - 10*t**4/27 - 208*t. Find h, given that k(h) = 0.
-2, 0, 4, 5
Let k(q) = 12*q + 51. Let r be k(-4). Let t(w) be the first derivative of 3 + 2/9*w + 2/9*w**2 + 2/27*w**r. Factor t(c).
2*(c + 1)**2/9
Let r(s) be the second derivative of -s**7/945 - s**6/270 + s**4/54 + s**3/27 - 4*s**2 + 19*s. Let l(q) be the first derivative of r(q). Factor l(h).
-2*(h - 1)*(h + 1)**3/9
Let n(b) be the third derivative of b**5/20 + 15*b**4/8 + 7*b**3 + 226*b**2. Find q, given that n(q) = 0.
-14, -1
Let i(y) be the first derivative of -4*y**5/5 + 40*y**4/3 + 112*y**3/9 + 19. Solve i(v) = 0 for v.
-2/3, 0, 14
Let l(d) be the first derivative of d**8/2800 - d**7/1400 - d**6/300 - 5*d**3/3 - 3. Let o(r) be the third derivative of l(r). Suppose o(i) = 0. What is i?
-1, 0, 2
Let w(s) be the third derivative of -11*s**8/98 - 2*s**7/735 + 34*s**6/105 + s**5/105 - s**4/21 + 2*s**2 - 270*s. Determine y so that w(y) = 0.
-1, -2/11, 0, 1/6, 1
Let z be 1*((-2 - -1) + -1) - 268. Let w = 1356/5 + z. What is x in -3/5*x**3 - 12/5*x**2 - w - 3*x = 0?
-2, -1
Let d be 7 + (-1 - (3 + 0)). Factor -12 - 17 + 35*i**2 + 3 + 15*i**d + 6.
5*(i + 1)*(i + 2)*(3*i - 2)
Factor 3*d**4 - 3*d**2 + 27*d**2 - 2053*d**5 + 11*d**4 + 32*d**3 + 2055*d**5.
2*d**2*(d + 2)**2*(d + 3)
Let q be 1/(2592/868 - 3). Let k = q - -73. Factor 32/3*s**5 + 0 - k*s**2 + 0*s + 6*s**3 - 16*s**4.
2*s**2*(s - 1)*(4*s - 1)**2/3
Let l(x) be the third derivative of -x**6/300 + 8*x**5/75 - x**4/4 - 144*x**2. Factor l(v).
-2*v*(v - 15)*(v - 1)/5
Let h be 9/45*25 - 838/168. Let z(x) be the second derivative of 1/12*x**4 - h*x**7 + 0*x**3 + 0*x**6 + 0*x**2 + 0 + 2*x + 3/40*x**5. Factor z(y).
-y**2*(y - 2)*(y + 1)**2/2
Let i(g) be the third derivative of -g**8/672 - 23*g**7/1260 - 5*g**6/72 - g**5/15 - 231*g**2. Suppose i(k) = 0. What is k?
-4, -3, -2/3, 0
Let i = -5697/2 - -2784. Let k = i - -65. Suppose -k*s**3 + 4 + 2*s - s**2 = 0. What is s?
-2, 2
Let y be 1/4 + 35/20. Suppose 3*z - 68 = -4*c, 4*z - 92 = -c - 3*c. Solve 1 + y*s**3 + 11 - 6*s**3 + 15*s**2 + s**3 - z*s = 0.
1, 2
Let c(b) be the first derivative of -7*b**6/600 - b**5/60 + b**4/60 + 4*b**2 + 4. Let o(y) be the second derivative of c(y). Solve o(a) = 0.
-1, 0, 2/7
Let h(n) = n**2 + 187*n + 1536. Let g(s) = -3*s**2 - 468*s - 3840. Let j(d) = -5*g(d) - 12*h(d). Factor j(o).
3*(o + 16)**2
Let y(u) = 20*u**3 - 11*u**2. Let p = -31 + 33. Let b(t) = 4*t**3 - 2*t**2. Let r(g) = p*y(g) - 11*b(g). Factor r(j).
-4*j**3
Let p(z) = -z**3 + 2*z**2 + z. Let g(u) = -508088*u**3 + 172858*u**2 - 1168*u + 2. Let s(n) = 2*g(n) - 4*p(n). Solve s(j) = 0.
1/291, 1/3
Let g(z) be the first derivative of -z**4/20 - 4*z**3/15 - z**2/2 - 2*z/5 + 120. Let g(y) = 0. Calculate y.
-2, -1
Let p(b) = -b**3 - 2*b**2 - 3*b - 1. Let r be p(-2). Let -8*d**5 + 15*d**4 + 18*d**r - 7*d**5 + 8*d**3 + 10*d**3 = 0. What is d?
-3, -2, 0
Let x(a) be the first derivative of a**6/10 + 6*a**5/25 - 2*a**3/5 - 3*a**2/10 + 195. Let x(j) = 0. What is j?
-1, 0, 1
Let h(b) be the third derivative of 2*b**7/315 + b**6/18 + 4*b**5/45 - 160*b**2. What is l in h(l) = 0?
-4, -1, 0
Let w = -215/7 + 31. Let p(i) be the first derivative of -w*i + 0*i**3 + 2/35*i**5 - 2/7*i**2 - 3 