 2/7 + 8/7*j**3 = 0.
-1, 1/2
Let s(g) = 5*g**3 + 17*g**2 + 5*g - 15. Let y(r) = -19*r + 135. Let x be y(7). Let h(w) = -w**3 - w**2 + w - 3. Let c(j) = x*s(j) + 6*h(j). Factor c(t).
4*(t - 1)*(t + 2)*(t + 6)
Let p(n) be the first derivative of -9*n - 65 - 3/4*n**2 + 1/2*n**3. Suppose p(t) = 0. What is t?
-2, 3
Let o(w) be the first derivative of 22/9*w**3 + 8/3*w**4 + 0*w + 40 + 2/3*w**2 + 14/15*w**5. Factor o(q).
2*q*(q + 1)**2*(7*q + 2)/3
Let p be (15/240*0)/4. Let g(r) be the second derivative of -1/45*r**6 + 0*r**2 + 0*r**5 + 0 + 18*r + 2/9*r**4 + p*r**3. Factor g(v).
-2*v**2*(v - 2)*(v + 2)/3
Let s(i) be the third derivative of -i**8/112 + 97*i**7/35 + 147*i**6/10 + 59*i**5/2 + 197*i**4/8 + 8*i**2 + 3. Factor s(h).
-3*h*(h - 197)*(h + 1)**3
Let z(m) be the first derivative of -2*m**3/3 - 795*m**2 - 1529. Let z(g) = 0. What is g?
-795, 0
Let r(s) be the third derivative of s**8/1008 + 4*s**7/105 + 1006*s**2. Factor r(x).
x**4*(x + 24)/3
Factor 137*t**2 + 447730*t - 449950*t + 5*t**3 - 1237*t**2.
5*t*(t - 222)*(t + 2)
Let a(v) be the first derivative of 32*v**2 + 4*v**5 + 2*v**3 - 1 - 22*v**3 - 16*v + 29 - 2*v**4 + 45. Determine s, given that a(s) = 0.
-2, 2/5, 1
Factor -1/8*c**4 + 28*c + 3*c**3 - 39/2*c**2 + 0.
-c*(c - 14)*(c - 8)*(c - 2)/8
Suppose 5*o - 1 = -l + 3*l, -4*l + 2*o = -22. Let z be 2/((-10)/4 + l). Let -10/9*i + z*i**2 + 4/9 = 0. What is i?
1/2, 2
Factor -2554/5*o**3 - 117026/5*o**2 - 14/5*o**4 - 49686/5*o + 0.
-2*o*(o + 91)**2*(7*o + 3)/5
Let b be (1 - 0) + 4/(-4). Suppose 0*o + 2*o - 8 = b. Factor -5*y**3 - o*y**4 - 10*y**2 + 3 - 3 + 9*y**4.
5*y**2*(y - 2)*(y + 1)
Let i = -374834 + 1874938/5. Determine d so that 177/5*d**4 - i + 1068/5*d**3 + 6/5*d**5 - 3459/5*d**2 + 2976/5*d = 0.
-16, 1/2, 1
Let t(y) be the first derivative of -y**5/20 + 25*y**4/16 + 18*y**3 + 34*y**2 - 128*y - 4. Suppose t(z) = 0. Calculate z.
-4, 1, 32
Let t(b) = -9*b**3 + 263*b**2 - 776*b + 480. Let x(d) = 40*d**3 - 1053*d**2 + 3104*d - 1902. Let o(c) = -9*t(c) - 2*x(c). Factor o(y).
(y - 258)*(y - 2)*(y - 1)
Find z such that 204*z**2 - 209*z**2 - 170*z - 411 - 392 + 203 = 0.
-30, -4
Let n(a) be the second derivative of 0 + 2/75*a**5 + 2/3*a**2 + 7/18*a**4 - 49/45*a**3 - 63*a. Find p, given that n(p) = 0.
-10, 1/4, 1
Let x(j) be the second derivative of -3*j + 0*j**2 - 19/4*j**3 + 2 + 1/8*j**4. Factor x(m).
3*m*(m - 19)/2
Let a(w) be the second derivative of w**7/42 + w**6/3 - 3*w**5/20 - 8*w**4/3 - 10*w**3/3 + 5325*w. Factor a(u).
u*(u - 2)*(u + 1)**2*(u + 10)
Suppose 0 = 5*s + 4*v - 503, -v - 6 + 8 = 0. Let -5*j**2 - 174*j + s + 96 - 16*j = 0. Calculate j.
-39, 1
Let g(v) be the first derivative of -v**8/1680 - v**7/525 - 55*v**2/2 + 81. Let z(x) be the second derivative of g(x). Find y such that z(y) = 0.
-2, 0
Let k(f) be the first derivative of 4/3*f**6 + 0*f + 4/3*f**3 - 21 + 2*f**2 - 3*f**4 - 4/5*f**5. Suppose k(h) = 0. Calculate h.
-1, -1/2, 0, 1
Let m(s) be the second derivative of s**7/42 - 4*s**6/3 + 553*s**5/20 - 1475*s**4/6 + 2198*s**3/3 - 980*s**2 - 1440*s. Solve m(g) = 0 for g.
1, 10, 14
Let w(t) be the first derivative of 11*t**6/5 + 32*t**5/5 + 29*t**4/6 - 2*t**3/3 - 114*t + 6. Let f(p) be the first derivative of w(p). Factor f(k).
2*k*(k + 1)**2*(33*k - 2)
Let d(r) = 5*r**3 - 364*r**2 + 300*r + 627. Let g(k) = 3*k**3 - 186*k**2 + 149*k + 314. Let h(a) = -8*d(a) + 14*g(a). Factor h(n).
2*(n - 2)*(n + 1)*(n + 155)
Let a(d) be the first derivative of d**4/4 - 58*d**3 + 345*d**2/2 - 172*d + 1893. Let a(x) = 0. What is x?
1, 172
Let r(y) = -2*y**2 - 8*y + 3. Let c be r(-6). Let m be 16/(-56) - (2421/c + -2). Factor -117 + f**2 + 3*f**3 + f - f**4 - 4*f + m.
-f*(f - 3)*(f - 1)*(f + 1)
Factor 2*s**2 + 1/3*s**3 + 0 - 7/3*s.
s*(s - 1)*(s + 7)/3
Suppose -4*n + 133 = 49. Suppose h + 5 - 2 = 2*i, 0 = 2*h + 5*i - n. Let 0 + h*k**2 - 18*k + 8 - 2 + 27*k = 0. What is k?
-2, -1
Let z(k) be the third derivative of -k**5/120 + 310*k**4/3 - 1537600*k**3/3 - 7930*k**2. Let z(r) = 0. Calculate r.
2480
Suppose 0 = -38*q + 266 - 38. Let p(u) be the third derivative of 0 + 0*u**4 + 0*u - 9*u**2 + 0*u**3 + 1/42*u**7 + 0*u**5 + 1/24*u**q. Factor p(b).
5*b**3*(b + 1)
Suppose 8*m - 7*m + 345 = -5*q, 2*q = 4*m - 116. Let s be q/(-60) - 0 - (-6)/30. Factor 0*j + 0 - s*j**2.
-4*j**2/3
Let m(p) be the first derivative of -50*p**3/21 + 136*p**2 - 152*p/7 + 11085. Factor m(x).
-2*(x - 38)*(25*x - 2)/7
Let i = 139 - 1166. Let a = -7173/7 - i. Factor -12/7*m + 0 + a*m**2.
4*m*(4*m - 3)/7
Let p be -1 - 1 - 14/(126/(-153)). Suppose -5*i = -2*k + 15, 0*k + 5*i + p = 4*k. Solve -2*b**2 + k - 4/3*b - 2/3*b**3 = 0.
-2, -1, 0
Let d(z) be the second derivative of -z**4/12 + 6*z**2 + 27*z. Let w(j) = -2*j**2 + j + 26. Let m(l) = -10*d(l) + 4*w(l). Solve m(a) = 0 for a.
-4, 2
Let v(x) be the first derivative of 141 + 0*x + 1/4*x**4 - 2/3*x**2 + 1/15*x**5 + 0*x**3. Let v(a) = 0. What is a?
-2, 0, 1
Let 68/9*x**2 + 14*x - 2/3*x**3 + 52/9 = 0. What is x?
-1, -2/3, 13
Let h(p) = 167 - 4307*p**3 - 160*p**2 + 0*p + 17*p + 4290*p**3. Let l(d) = 8*d**3 + 80*d**2 - 8*d - 83. Let k(q) = -3*h(q) - 7*l(q). Factor k(j).
-5*(j - 1)*(j + 1)*(j + 16)
Let g(t) be the third derivative of t**5/15 - 40*t**4 - 482*t**3/3 - 1563*t**2. Determine u, given that g(u) = 0.
-1, 241
Let p(n) = -3*n**2 - 1603*n + 41952. Let d be p(25). Let 6*w + 1/2*w**d - 13/2 = 0. What is w?
-13, 1
Suppose 0 = 5*c - u + 46, -16*c - 54 = -11*c + u. Let k be (9/(-12 - -3))/(c/12). Find z such that 3/5*z**4 + 0 - k*z**2 - 3/5*z**3 + 0*z = 0.
-1, 0, 2
Let i(b) be the second derivative of -1/42*b**4 - 39*b + 0 + 0*b**2 + 5/21*b**3. Find z, given that i(z) = 0.
0, 5
Suppose 10*k - 5*k = 25. Let h(s) = 3*s**2 - 3*s + 2. Let d be h(2). Factor 2*t**4 - 8 + t**2 - 2*t**3 + 2*t**k - 3*t**2 + d.
2*t**2*(t - 1)*(t + 1)**2
Let g(b) be the first derivative of -b**5/80 + b**4/32 + 21*b**3/4 + 25*b**2 + 232. Let p(d) be the second derivative of g(d). Factor p(y).
-3*(y - 7)*(y + 6)/4
Let p(t) be the second derivative of -3*t**5/5 - 30*t**4 + 387*t**3/2 - 891*t**2/2 - 2308*t. Determine g so that p(g) = 0.
-33, 3/2
Solve -2/5*x**4 - 648/5 - 54*x**2 - 42/5*x**3 - 702/5*x = 0.
-12, -3
Let s be (4564/8)/7 - 3/2. Let l = s + -159/2. What is x in 1/2*x**2 + 0 + 0*x - l*x**3 = 0?
0, 1
Suppose 4*l + 1 = -5*o + 75, 3*l = -3*o + 45. Factor o*c**4 - 16*c**5 - 9*c**4 - 9*c**4.
-4*c**4*(4*c + 1)
Let i(j) be the second derivative of 9/40*j**6 - j**3 + 0 + 1/8*j**4 + 2*j + 3/5*j**5 + 15*j**2. Let m(v) be the first derivative of i(v). Solve m(h) = 0 for h.
-1, -2/3, 1/3
Let v(d) be the third derivative of d**8/30240 - d**7/540 + d**5/30 - 5*d**3/6 - 7*d**2 + 6. Let n(p) be the third derivative of v(p). Factor n(m).
2*m*(m - 14)/3
Let x(w) be the first derivative of -2*w**5/55 + 37*w**4/22 - 240*w**3/11 + 324*w**2/11 - 1076. Determine z so that x(z) = 0.
0, 1, 18
Let g(t) be the first derivative of -2*t**3/15 - 756*t**2/5 - 302*t - 8355. Factor g(k).
-2*(k + 1)*(k + 755)/5
Factor 12817467/2 - 6201*d + 3/2*d**2.
3*(d - 2067)**2/2
Let j(p) = -15*p**3 - 168*p + 132. Let x(y) = y**3 + 4*y**2 + y + 1. Let v(b) = -j(b) - 12*x(b). Factor v(s).
3*(s - 12)*(s - 2)**2
Let a(k) be the second derivative of k**7/1680 - k**6/36 + k**3/6 + 67*k**2/2 - 346*k. Let g(j) be the second derivative of a(j). Suppose g(d) = 0. What is d?
0, 20
Let f be 148/(-333) - (-28)/36. Let r(c) be the first derivative of 2*c + 6 - 1/2*c**2 - f*c**3. Suppose r(m) = 0. Calculate m.
-2, 1
Let g(q) = 9*q**2 + 1180*q - 389. Let j(o) = 18*o**2 + 2361*o - 777. Let v(t) = 9*g(t) - 4*j(t). Factor v(h).
3*(h + 131)*(3*h - 1)
Suppose -d + 3*k = -2*k + 5, d = -5*k + 15. Factor d*f**2 + f**2 + 6 + 0*f + 12*f + 6 - 3*f**2.
3*(f + 2)**2
Let i(b) be the third derivative of -b**9/5040 + b**8/2240 - 47*b**4/8 + 285*b**2. Let t(n) be the second derivative of i(n). Let t(q) = 0. Calculate q.
0, 1
Let b(h) be the first derivative of -h**4/14 - 2*h**3/3 - 4*h**2/7 + 24*h/7 + 835. Factor b(g).
-2*(g - 1)*(g + 2)*(g + 6)/7
Let f = 1172971/7 - 167567. Find b, given that f*b**3 + 0*b - 2/7*b**5 - 8/7 + 2*b**2 - 6/7*b**4 = 0.
-2, -1, 1
Let i be (1/3)/((-8)/(-36)). Suppose 930 = 3*p - 4*c, 4*p - 39*c + 37*c = 1200. Let 42*h + p + i*h**2 = 0. What is h?
-14
What is s in 272/3*s + 88 + 74/3*s**2 + 2/3*s**3 = 0?
-33, -2