- 15*n**2 - 16*n + 30. Let j be i(16). Let u be ((-31)/12 + 2)*j/(-105). Factor -11/6*s + u*s**2 + 5/3.
(s - 10)*(s - 1)/6
Let a(n) be the third derivative of -n**7/1575 - 241*n**6/450 - 19199*n**5/150 + 29161*n**4/45 - 58564*n**3/45 + 2807*n**2. Factor a(m).
-2*(m - 1)**2*(m + 242)**2/15
Let g(w) be the second derivative of 21*w - 4/33*w**3 - 1/660*w**6 + 1/330*w**5 + 0 + 1/33*w**4 - w**2. Let r(i) be the first derivative of g(i). Factor r(v).
-2*(v - 2)*(v - 1)*(v + 2)/11
Let g(k) be the second derivative of -k**4/12 - 47*k**3 + 284*k**2 + 14*k - 44. Factor g(i).
-(i - 2)*(i + 284)
Let a be (-70)/(-15)*(48/(-7))/(-2). Suppose -4 = -2*i - x, -13*i + a*i + 4*x = 11. Suppose 1/2*o + i - o**2 - 1/2*o**3 = 0. Calculate o.
-2, -1, 1
Let l(t) be the third derivative of t**6/72 + t**5/8 - 5*t**4/6 - 44*t**3/3 + 3*t**2 - 6. Let u(y) be the first derivative of l(y). Factor u(z).
5*(z - 1)*(z + 4)
Let v = -542 - -547. Suppose -o + v*l = -2, -5*o - l + 7 = -3. Factor 0 + 0*w + 1/5*w**3 - 1/5*w**o - 1/5*w**5 + 1/5*w**4.
-w**2*(w - 1)**2*(w + 1)/5
Let g be 8 - 33 - (-32)/(256/214). Factor 1/4*w**3 + 3/4 + 5/4*w**2 + g*w.
(w + 1)**2*(w + 3)/4
Let c(a) = 5*a**2 - 14*a - 13. Suppose -9 = -94*m + 91*m. Let b(d) = 2*d - 6*d**2 + 8*d + 10 + 5*d + 2. Let y(i) = m*c(i) + 2*b(i). Factor y(h).
3*(h - 5)*(h + 1)
Let v(t) be the second derivative of t**6/72 + 5*t**5/24 - 5*t**4 - 163*t**3/6 + t + 127. Let m(n) be the second derivative of v(n). Factor m(d).
5*(d - 3)*(d + 8)
Let h be (-2)/6 - -1 - (-140)/(-21). Let c be ((-7)/(5 - -2))/(8/h). Let c*v**5 - 9/4*v**4 + 3/4*v**3 + 0 - 3/2*v + 9/4*v**2 = 0. Calculate v.
-1, 0, 1, 2
Let d(z) be the third derivative of z**7/105 - z**6/60 - 13*z**5/15 + 7*z**4 - 24*z**3 + z**2 - 337. Factor d(h).
2*(h - 3)*(h - 2)**2*(h + 6)
Let s(u) be the third derivative of -u**7/1050 - u**6/120 - u**5/100 + 3*u**4/40 - 28*u**2 + 2. Find k such that s(k) = 0.
-3, 0, 1
Solve 1 - 32*l**3 - l**4 + 82 + 136*l**2 + 61 - 208*l + l**5 - 32 = 0 for l.
-7, 2
Let s(y) = -4784*y - 95676. Let n be s(-20). Factor 0 - 1/5*b**n + 9/5*b**2 + 1/5*b**3 - 9/5*b.
-b*(b - 3)*(b - 1)*(b + 3)/5
Let q = -7691 - -7691. Let a(b) be the third derivative of q*b - 1/280*b**6 + 0*b**3 - 1/42*b**5 + 0 + 21*b**2 + 1/21*b**4. Suppose a(w) = 0. What is w?
-4, 0, 2/3
Let l(a) be the third derivative of 0*a - 56*a**2 - 4913/2*a**3 + 0 + 867/8*a**4 + 1/40*a**6 - 51/20*a**5. Factor l(d).
3*(d - 17)**3
Let g(n) be the third derivative of -n**8/448 + 3*n**7/140 + 9*n**6/80 - 17*n**5/20 - 81*n**4/32 + 63*n**3/4 - 5545*n**2. Find v, given that g(v) = 0.
-3, -2, 1, 3, 7
Let w(f) be the first derivative of f**4/26 - 8*f**3/3 - 982. Factor w(z).
2*z**2*(z - 52)/13
Let t = -68488 + 273961/4. Suppose 0 + t*v - 3/8*v**2 = 0. Calculate v.
0, 6
Let n(a) be the first derivative of a**2/2 + 137. Let s(h) = 11*h + 6*h + 9*h - 2*h**2 - 72 + 0*h**2. Let c(i) = -4*n(i) + 2*s(i). Solve c(k) = 0.
6
Let y be (-12)/(-52)*(-416)/(-128). Factor 117/4*t + y*t**2 + 57/2.
3*(t + 1)*(t + 38)/4
Suppose -2863 - 5417 = -15*n. Let -552*g + n*g - 15*g**4 - 25*g**2 - 45*g**3 + 5*g**5 = 0. What is g?
-1, 0, 5
Let h(w) = 7*w**2 - 361*w + 208. Let o be h(51). Let x(y) be the first derivative of -5/2*y**4 + 16 - o*y**2 + 2/5*y**5 + 0*y + 16/3*y**3. Solve x(u) = 0 for u.
0, 1, 2
Suppose -7 - 5 = -6*b. Determine y, given that -158*y**b + 163*y**2 + 18 + 22 - 30*y = 0.
2, 4
Determine i, given that -1/5*i**2 - 257/5*i + 258/5 = 0.
-258, 1
Let c(n) be the first derivative of 5*n**4/2 + 155*n**3/3 - 85*n**2/2 - 80*n - 755. What is h in c(h) = 0?
-16, -1/2, 1
Let b(v) = v**3 + 39*v**2 - 4*v - 152. Let j(g) = g**3 + 8*g**2 - 2*g + 24. Let y be j(-9). Let w be b(y). Factor -8/7*u + 6/7*u**2 + 0*u**3 + 3/7 - 1/7*u**w.
-(u - 1)**3*(u + 3)/7
Let d(o) be the first derivative of o**4/30 + 46*o**3/15 - 96*o**2/5 + 584*o/15 - 4521. Let d(m) = 0. What is m?
-73, 2
Let p(i) be the first derivative of -5*i**4/4 - 145*i**3 - 10455*i**2/2 - 42025*i - 8876. Find x, given that p(x) = 0.
-41, -5
Let p = 435 - 395. Let k(b) = b**2 - 6*b - 2. Let v be k(7). Factor 10*x**2 + 15 - 4*x**5 - 30*x**3 - 5*x - 25*x**4 - 3*x**5 + p*x + 2*x**v.
-5*(x - 1)*(x + 1)**3*(x + 3)
Suppose -5*u = -28*o + 522, -184 = 3*u + 3*o - 247. Factor d + 1/2*d**u - 4.
(d - 2)*(d + 4)/2
Suppose 0 = 3*q + 3*w, -2*q + 16 = -3*q - 5*w. Find u such that -20*u + 35*u**5 - 92*u**3 + 95*u**4 + 227*u**3 + 24*u**q + 20*u**2 + 11*u**4 = 0.
-2, -1, 0, 2/7
Let r(g) = 12*g**4 + 45*g**2 + 30*g. Let t(o) = -o**4 + 2*o**3 - o**2 + 1. Suppose -5*q = 3*w - 32, w - 5*q - 2 = 2. Let x(y) = w*t(y) + r(y). Factor x(k).
3*(k + 1)**3*(k + 3)
Let y(g) = g**3 + 13*g**2 + 41*g + 112. Let u be y(-10). Let k(b) be the first derivative of 1/6*b**4 + 2/9*b**3 - 2/15*b**5 - 1/3*b**u + 11 + 0*b. Factor k(i).
-2*i*(i - 1)**2*(i + 1)/3
Let c(h) = 98*h**2 - 540*h + 4. Let u(m) = -396*m**2 + 2159*m - 12. Let k(r) = 9*c(r) + 2*u(r). Determine o, given that k(o) = 0.
1/45, 6
Factor -300/7*z**2 - 18/7*z**3 + 424/7*z - 144/7.
-2*(z + 18)*(3*z - 2)**2/7
Let r be ((-3)/5)/(-1)*5. Let u(o) be the first derivative of 2*o**r + 4*o + 10*o**3 - 9 + 3 - 3 - 12*o**2. Determine j so that u(j) = 0.
1/3
Let k(s) be the first derivative of -2/7*s**2 - 1/21*s**6 + 2/7*s**5 + 2/3*s**3 + 0*s - 60 - 9/14*s**4. Find x such that k(x) = 0.
0, 1, 2
Factor -17/6*m**2 + 0 - 1/6*m**4 + 5/3*m + 4/3*m**3.
-m*(m - 5)*(m - 2)*(m - 1)/6
Let q = 761551/72 - 94772/9. Factor 45/8*h**2 - 3/8*h**3 - 225/8*h + q.
-3*(h - 5)**3/8
Let i(l) = -14070*l + 15. Let g be i(-2). Suppose -g + 12*k + 28151 + 2*k**3 - 8*k**2 - 2*k = 0. What is k?
1, 2
Let j(z) be the first derivative of z**8/10920 - z**7/1820 + z**6/1170 + 60*z**3 - 57. Let k(n) be the third derivative of j(n). Find l, given that k(l) = 0.
0, 1, 2
Let y(a) = -10*a - 48. Let u be y(-5). Factor 170*c**2 - c - 2 - 89*c**2 - 80*c**u.
(c - 2)*(c + 1)
Let a = -32 + 34. Find f, given that -151*f**2 - 784 - 107*f - 5*f + 147*f**a = 0.
-14
Suppose 0 = -74*o + 72*o + 2, -2016 = -t - 2*o. Let i = 2017 - t. Factor -192/7 + 20/7*p**2 - 4/7*p**i + 32/7*p.
-4*(p - 4)**2*(p + 3)/7
Let m = 39241 - 39237. Factor -2/13*v**5 + 6/13*v**3 + 0*v + 0 - 4/13*v**2 + 0*v**m.
-2*v**2*(v - 1)**2*(v + 2)/13
Let v(x) be the second derivative of 23*x**4/3 - 181*x**3/6 - 3*x**2 + 29*x + 7. Factor v(t).
(t - 2)*(92*t + 3)
Let i(d) be the third derivative of 0 + 8*d**2 - 1/5*d**5 + 3*d**3 + 1/105*d**7 - 3/8*d**4 - 3*d + 1/180*d**6 + 1/1008*d**8. Factor i(b).
(b - 2)*(b - 1)*(b + 3)**3/3
Let c be (0 - 1/3)/((154/(-30))/77). Factor 0 + 0*m + 0*m**3 + 4/7*m**c + 4/7*m**4 + 0*m**2.
4*m**4*(m + 1)/7
Let f = 141378 + -141376. Factor 1/4*u**5 - 23*u**f - 11/4*u**4 + 22*u + 23/2*u**3 - 8.
(u - 4)*(u - 2)**3*(u - 1)/4
Let v(b) be the second derivative of 5*b**4/36 - 6845*b**3/9 + 9370805*b**2/6 - 5465*b. Factor v(t).
5*(t - 1369)**2/3
Let u(b) = 3*b**2. Let d be u(-4). Factor 27*a**5 + 16*a**3 + 8 - d*a**4 + 40*a**2 + 215*a - 7*a**5 - 251*a.
4*(a - 1)**3*(a + 1)*(5*a - 2)
Let x(u) be the first derivative of -u**4/10 - 10*u**3/3 - 143*u**2/5 + 338*u/5 + 997. Factor x(k).
-2*(k - 1)*(k + 13)**2/5
Let o(h) = h**3 - h. Let n(k) = k**3 - k**2. Let x(c) = c**3 - 6*c**2 + 19*c - 18. Let u(f) = 2*n(f) + x(f). Let w(q) = -2*o(q) + u(q). Factor w(a).
(a - 3)**2*(a - 2)
Let m(t) be the second derivative of -2*t**6/15 + 68*t**5 - 12882*t**4 + 2962408*t**3/3 - 2885794*t**2 - 1830*t. Factor m(u).
-4*(u - 113)**3*(u - 1)
Let n = 17802 + -17776. Let r(h) be the second derivative of -1/24*h**6 + 0*h**3 + 0*h**2 + n*h + 0 - 5/12*h**4 - 1/4*h**5. Factor r(k).
-5*k**2*(k + 2)**2/4
Let v(h) be the second derivative of -h**6/720 - h**5/240 - 32*h**3/3 + h**2 + h + 18. Let s(b) be the second derivative of v(b). Factor s(r).
-r*(r + 1)/2
Suppose 58*n - 115*n + 4*n**2 + 71*n + 8 - 2*n**3 = 0. What is n?
-1, 4
Let i(b) be the second derivative of 8*b**6/9 + 74*b**5/3 - 1345*b**4/12 + 190*b**3 - 315*b**2/2 - 836*b. Solve i(j) = 0.
-21, 3/4, 1
Let y(r) = -r**2 - 6*r - 6. Let a be y(-4). Let d = 22668/5 + -90667/20. Factor -d*s + 1/2 - 1/4*s**a.
-(s - 1)*(s + 2)/4
Suppose -29*m = 7*m - 26460. Let x = m + -8077/11. Suppose x*r - 2/11*r**2 - 8/11 = 0. What is r?
2
What is f in -2/11*f**2 + 3028/11 - 3026/11*f = 0?
-1514, 1
Let d(n) be the third derivative 