 17913*h**2 - 74423 = 0. Calculate h.
-3, -1, 118
Let n(w) be the second derivative of -1 + 4/3*w**3 - 1/6*w**4 - 3*w**2 - 4*w. Factor n(o).
-2*(o - 3)*(o - 1)
Let p(d) be the third derivative of 0*d**3 + 0 - 1/32*d**4 + 0*d**6 + 0*d - 3/160*d**5 - 97*d**2 + 1/560*d**7. Factor p(c).
3*c*(c - 2)*(c + 1)**2/8
Solve -183/4*o**2 + 0 - 3/4*o**3 - 45*o = 0 for o.
-60, -1, 0
Let t be 322/8 + (-4)/16. Let o be 1/(-1) + -4*(-14)/4. Factor -19 + t*x + 104*x - 162*x**2 - o.
-2*(9*x - 4)**2
Let n(m) be the second derivative of 2*m**2 + 0*m**3 - 32*m + 0 + 3/16*m**4 + 1/40*m**5. Let x(d) be the first derivative of n(d). What is v in x(v) = 0?
-3, 0
Let y(v) be the first derivative of -v**4/5 - 248*v**3/15 - 512*v**2 - 7040*v - 11038. Factor y(w).
-4*(w + 20)**2*(w + 22)/5
Factor -2/3*v - 1/3*v**4 + 0 + 4/3*v**2 + 1/6*v**5 - 1/2*v**3.
v*(v - 2)*(v - 1)**2*(v + 2)/6
Factor 0 + 2/5*p**3 - 26/5*p - 24/5*p**2.
2*p*(p - 13)*(p + 1)/5
Solve -4416/7*z + 2304/7 - 652/7*z**3 + 62/7*z**4 + 2704/7*z**2 - 2/7*z**5 = 0 for z.
1, 2, 4, 12
Factor -4/5*b**3 + 4/5*b - 476/5*b**2 + 476/5.
-4*(b - 1)*(b + 1)*(b + 119)/5
Factor -6*a**3 + 3/2*a**4 + 15/2 - 9*a**2 + 6*a.
3*(a - 5)*(a - 1)*(a + 1)**2/2
Let l(j) be the third derivative of -1/30*j**6 + 26/3*j**3 - 52*j**2 + 0 + 0*j + 25/6*j**4 + 11/15*j**5. Factor l(o).
-4*(o - 13)*(o + 1)**2
Let k be (168/224)/(51/136). Factor -2/13*n**3 + 4/13*n**k + 10/13*n - 12/13.
-2*(n - 3)*(n - 1)*(n + 2)/13
Let i(w) be the third derivative of w**6/600 + 7*w**5/20 + 13*w**4/15 - 162*w**2 - 3. Determine n, given that i(n) = 0.
-104, -1, 0
Let i(l) be the first derivative of 116*l**3/3 - 86*l**2 - 120*l + 3391. Solve i(t) = 0 for t.
-15/29, 2
Suppose 33/4 - 27/4*p**2 - 3/2*p = 0. Calculate p.
-11/9, 1
Suppose 5*q = f - 108, 10*q + f = 6*q - 81. Let v(b) = b**2 - 7*b + 2. Let w(j) = 3*j**2 - 22*j + 7. Let i(g) = q*v(g) + 6*w(g). Suppose i(o) = 0. Calculate o.
0, 5
Suppose z - 3249 = -3248. Factor z - j + 1/4*j**2.
(j - 2)**2/4
Let t(v) be the first derivative of v**4/34 - 280*v**3/51 + 304*v**2 - 2176*v - 2492. Factor t(j).
2*(j - 68)**2*(j - 4)/17
Suppose 3/5*f**4 - 1476/5*f**3 + 242064/5*f**2 + 0 - 13232832/5*f = 0. What is f?
0, 164
Let o(f) be the second derivative of -f**7/840 + f**6/120 + f**4/12 + f**2/2 + 28*f. Let k(s) be the third derivative of o(s). Factor k(d).
-3*d*(d - 2)
Let n(d) be the second derivative of d**6/6 + 3*d**5/4 - 15*d**4/4 + 25*d**3/6 - 702*d + 2. Solve n(m) = 0 for m.
-5, 0, 1
Let n(q) be the third derivative of 5880*q**3 + 35*q**4 - 7*q**2 + 1/12*q**5 + 0*q + 13. Find u, given that n(u) = 0.
-84
Let s(q) be the second derivative of -q**5/540 - 29*q**4/108 - 841*q**3/54 - 22*q**2 + 32*q. Let n(y) be the first derivative of s(y). Factor n(u).
-(u + 29)**2/9
Find t such that 2187/7*t + 48/7*t**3 + 810/7 + 216*t**2 = 0.
-30, -3/4
Let o = -97315 + 13040137/134. Let h = -3/67 - o. Suppose 1/2*q + h*q**4 + 0 + 3/2*q**3 + 3/2*q**2 = 0. Calculate q.
-1, 0
Let 444 + 2294*s - 9*s**3 - 1286*s - s**3 - 396*s**2 - 1958*s = 0. Calculate s.
-37, -3, 2/5
Let t(n) = -20933*n - 125598. Let m be t(-6). Determine v, given that m*v + 2 - 1/2*v**2 = 0.
-2, 2
Let h(z) be the first derivative of z**2 + 1/105*z**5 + 0*z + 1/84*z**4 + 0*z**3 - 3. Let n(d) be the second derivative of h(d). Determine o so that n(o) = 0.
-1/2, 0
Let h(i) be the first derivative of i**4/6 - 2*i**3 + 29*i - 53. Let u(y) be the first derivative of h(y). Find b such that u(b) = 0.
0, 6
Let z(k) be the first derivative of -k**8/6720 - k**7/420 - k**6/96 - 7*k**3/3 - 2*k**2 + 328. Let l(t) be the third derivative of z(t). Factor l(h).
-h**2*(h + 3)*(h + 5)/4
Let g(f) = -3*f**3 - 69*f**2 - 223*f - 160. Let m(v) = -3*v**3 - 67*v**2 - 222*v - 152. Let b(l) = 4*g(l) - 5*m(l). Factor b(j).
(j + 4)*(j + 15)*(3*j + 2)
Suppose 57/5*p**4 + 135*p**2 - 319/5*p**3 + 204/5 - 616/5*p - 1/5*p**5 = 0. Calculate p.
1, 2, 51
Let t(o) = -o**2 + 7*o - 10. Let q be t(4). Let -18*y**3 + 144*y**q - 28*y**3 + 1728*y - 21*y**3 + 70*y**3 = 0. Calculate y.
-24, 0
Let r(b) = 5*b**3 - 6*b**2 - 8. Suppose 11 = -6*u - 13. Let g(y) = -4*y**3 + 6*y**2 + 6. Let z(l) = u*g(l) - 3*r(l). Find i such that z(i) = 0.
0, 6
Let d(j) be the second derivative of 1/75*j**6 + 0*j**3 + 0*j**2 + 867/10*j**4 + 51/25*j**5 + 1 + 29*j. Solve d(u) = 0 for u.
-51, 0
Let f = -70 + 89. Let i = f + -11. Let o(n) = -64*n**2 + 35*n - 4. Let t(s) = 192*s**2 - 104*s + 12. Let a(c) = i*o(c) + 3*t(c). Solve a(m) = 0 for m.
1/4
Let q(l) = 36*l**2 + 76*l - 32. Let h(n) = -11*n**2 - 25*n + 11. Let a be (68/(-8) + 6)*(-2 + 4). Let m(p) = a*q(p) - 16*h(p). Suppose m(i) = 0. What is i?
1, 4
Solve -7969329/2 + 7966506*i - 3979019*i**2 - 2822*i**3 - 1/2*i**4 = 0 for i.
-2823, 1
Let k(z) be the third derivative of 1/4*z**4 + z**2 + 2/45*z**5 - 6 + 2/9*z**3 + 0*z. Factor k(l).
2*(l + 2)*(4*l + 1)/3
Factor -6384*q - 6299*q**4 - 2544*q**2 - q**5 - 4704 - 120*q**3 - 2*q**5 - 6327*q**4 + 12692*q**4.
-3*(q - 14)**2*(q + 2)**3
Let a(i) be the third derivative of i**6/840 + 4*i**5/105 - 37*i**4/56 - 3*i**3 - 78*i**2 + 9*i. Let a(h) = 0. What is h?
-21, -1, 6
Let m = 1433/6 - -1131/2. Let b = m - 803. Factor -1/6*d**3 - b*d - 2/3 - 5/6*d**2.
-(d + 1)*(d + 2)**2/6
Let h(n) = n**4 + n**3 - n - 1. Let i(s) = -5*s**4 + 29*s**2 + 28*s + 4. Let b(w) = 20*h(w) + 5*i(w). Factor b(x).
-5*x*(x - 8)*(x + 1)*(x + 3)
Let r(g) = -g**2 - 7*g + 3*g**3 - 6 + 3*g**3 - g**2 - 7*g**3. Let j be r(-1). Factor j - 6/7*v**2 - 3/7*v - 3/7*v**3.
-3*v*(v + 1)**2/7
Let h(i) = -5*i**3 + 18*i**2 - 4*i - 13. Let d be h(3). Let k(y) be the second derivative of 1/4*y**4 + 0*y**d + 0 + 12*y + 4*y**3. Factor k(q).
3*q*(q + 8)
Let d(h) = -h**3 - 2*h**2 - 5*h - 20. Let l be d(-5). Let f be 5/3 + l/60. Factor -40*c - 2*c**3 + 13*c**f - 4*c**4 - 5*c**2 + 38*c.
-c*(c - 2)*(c - 1)*(4*c + 1)
Factor 9474*s - s**2 - 6154*s + 1181591 - 3937191.
-(s - 1660)**2
Let q(c) be the first derivative of c**4/5 + 52*c**3/5 - 164*c**2/5 - 2816. Let q(u) = 0. What is u?
-41, 0, 2
Factor 0 + 8*r + 5/2*r**4 + 9*r**3 + 1/4*r**5 + 14*r**2.
r*(r + 2)**3*(r + 4)/4
Let m(i) = -80*i**2 - 13*i - 26. Let x be m(-3). Let r = -2116/3 - x. Factor -r*y**2 - y + 2/3.
-(y + 1)*(5*y - 2)/3
Factor -84*g + 17*g**2 - 1/2*g**3 + 0.
-g*(g - 28)*(g - 6)/2
Factor -510/7*g + 21675/7 + 3/7*g**2.
3*(g - 85)**2/7
Let q(z) be the third derivative of 0*z**3 - 31/42*z**7 + 3*z + 1/3*z**5 - 91*z**2 + 0*z**4 + 0 + 55/336*z**8 + 2/3*z**6. Determine n so that q(n) = 0.
-2/11, 0, 1, 2
Let u(f) be the third derivative of f**5/630 + 23*f**4/252 - 10*f**3/3 + 16*f**2 + 2*f. Factor u(m).
2*(m - 7)*(m + 30)/21
Let v(k) = -6*k + 55. Let c = -2 + 11. Let h be v(c). Factor h - a**2 + 6*a**2 - 3*a**2 - 5*a**2 + 2*a.
-(a - 1)*(3*a + 1)
Factor -1/5*s**2 + 1898/5*s - 900601/5.
-(s - 949)**2/5
Let a be 3/1 + (-4462)/23. Let y = -947/5 - a. What is q in 0 + 4/5*q**2 + y*q = 0?
-2, 0
Let o(i) be the first derivative of i**6/24 - 37*i**5/10 + 495*i**4/4 - 5566*i**3/3 + 10648*i**2 - 6673. Factor o(n).
n*(n - 22)**3*(n - 8)/4
Solve -86/19*w**3 - 30/19*w**5 + 232/19*w**4 + 0 - 1540/19*w**2 - 400/19*w = 0 for w.
-2, -4/15, 0, 5
Let q(h) be the first derivative of -h**4/34 - 8*h**3/51 + 67*h**2/17 + 140*h/17 + 1270. Factor q(u).
-2*(u - 7)*(u + 1)*(u + 10)/17
Let m(j) be the second derivative of -4*j**7/189 - 4*j**6/9 - 17*j**5/10 + 289*j**4/27 - 1226*j. Suppose m(h) = 0. Calculate h.
-17/2, 0, 2
Factor 2/11*c**4 - 78/11*c**2 + 82/11*c + 2*c**3 - 28/11.
2*(c - 1)**3*(c + 14)/11
Let x(v) = v**3 - 10*v**2 + 9*v + 3. Suppose -2*u + 38 = 4*l, 32 = -0*u + 3*u + l. Let n be x(u). Find c, given that -13*c**2 + n*c + 5*c**2 + 5*c**2 = 0.
0, 1
Suppose 3*i - 71*i = 277*i. Let k = -15/2 + 8. Solve i*h**3 + k - h**2 + 0*h + 1/2*h**4 = 0.
-1, 1
Let l(m) be the second derivative of -85*m**4/12 + 395*m**3 + 140*m**2 - 68*m - 22. Factor l(g).
-5*(g - 28)*(17*g + 2)
Suppose 1461 = 26*r - 23*r. Factor r*j + 52 + 15*j**4 + j**5 + 12 - 535*j - 79*j**2 + 68*j**3 - 21*j**3.
(j - 1)**2*(j + 1)*(j + 8)**2
Suppose 81*a = 385*a - 1216. Let p(z) be the second derivative of 81/11*z**2 + 0 + 6/11*z**3 + 1/66*z**a + 14*z. Factor p(v).
2*(v + 9)**2/11
Let w be (54 + -6)/(14/5 - 3). Let l be ((-4)/(-3))/(w/(-54) - 4). Factor -4/11*s**2 - 10/11*s**l + 0 + 0*s.
-2*s**2*(5*s + 2)/11
Let