 1
Factor -17424/19*d**2 + 116/19*d**4 - 2/19*d**5 - 1122/19*d**3 + 0*d + 0.
-2*d**2*(d - 33)**2*(d + 8)/19
Suppose -9 = -2*c + m, -22*c - 3*m - 7 = -23*c. Factor 15/2*b - 15/2*b**3 - 5/2*b**2 + 0 + 5/2*b**c.
5*b*(b - 3)*(b - 1)*(b + 1)/2
Let p(q) be the third derivative of q**6/48 - 317*q**5/24 + 395*q**4/12 + 26*q**2 - 21*q + 3. Factor p(t).
5*t*(t - 316)*(t - 1)/2
Let z(g) be the third derivative of g**6/1260 - g**5/14 - 71*g**4/126 - 32*g**3/21 - 1979*g**2. Suppose z(s) = 0. Calculate s.
-2, -1, 48
Let d(u) be the first derivative of 0*u**3 + 2/35*u**5 + 0*u + 3/14*u**4 - 4/7*u**2 + 53. Let d(g) = 0. What is g?
-2, 0, 1
Suppose 17*i + 182 = 43*i. Let m be (-1*(-1 + i)/(-6))/5. Factor 0*c + 0 + m*c**3 + 0*c**2 - 3/5*c**4.
-c**3*(3*c - 1)/5
Let h(w) be the first derivative of -1/36*w**4 + 0*w - 9 - 1/6*w**3 - 23/2*w**2 + 1/180*w**5. Let s(l) be the second derivative of h(l). Factor s(p).
(p - 3)*(p + 1)/3
Let s(g) be the third derivative of -g**5/50 - 4*g**4/15 + 4*g**3/5 + 408*g**2. Factor s(p).
-2*(p + 6)*(3*p - 2)/5
Suppose -29*k + 20*k + 18 = 0. Let 37*r + 39*r - 155*r**3 + 84*r**2 + 0*r**4 - k*r**4 - 80 + 79*r**3 - 2*r**4 = 0. Calculate r.
-20, -1, 1
Let 27/7 + 3/7*b**2 + 30/7*b = 0. Calculate b.
-9, -1
Let n = 10 + 30. Suppose -14*q + 9*q = -n. Factor 10*v - 9*v - q*v + 6 + v**3.
(v - 2)*(v - 1)*(v + 3)
Let d(y) be the first derivative of y**7/126 + y**6/36 - y**5/12 + 29*y**2 + 46. Let i(z) be the second derivative of d(z). Factor i(n).
5*n**2*(n - 1)*(n + 3)/3
Let i = 504 - 499. What is s in -i*s**2 + 5*s**2 + 479 - 2*s**2 - 7*s**3 - 509 - 46*s + 21*s**3 = 0?
-1, 15/7
Let s(h) be the first derivative of -2*h**6/3 - 4*h**5 + 51*h**4 + 20*h**3/3 - 100*h**2 + 2728. Suppose s(n) = 0. What is n?
-10, -1, 0, 1, 5
Let w(c) be the third derivative of -c**8/13440 - c**7/3360 - 13*c**5/20 - c**2 - 27*c. Let t(o) be the third derivative of w(o). Factor t(p).
-3*p*(p + 1)/2
Let m(c) be the first derivative of 0*c - 3/5*c**5 + 1/4*c**4 + 1/6*c**6 - c**2 + c**3 + 167. Factor m(f).
f*(f - 2)*(f - 1)**2*(f + 1)
Let n(y) = y**3 + y. Let h(w) = -w**4 - 2*w**3 + 21*w**2 - 4*w. Let k = -249 - -277. Let r(t) = k*n(t) - 4*h(t). Solve r(z) = 0 for z.
-11, 0, 1
Let z(d) be the third derivative of -1/48*d**4 + 0*d + 7/240*d**5 - 1/96*d**6 + 0*d**3 - 39*d**2 + 0. Factor z(v).
-v*(v - 1)*(5*v - 2)/4
Let u(m) be the second derivative of 0 + 5/144*m**4 + 1/360*m**5 + 27*m - 7/18*m**3 - 3/2*m**2. Let y(t) be the first derivative of u(t). Solve y(c) = 0 for c.
-7, 2
Let w(x) be the first derivative of x**7/140 - 3*x**6/40 + 9*x**5/40 - x**4/4 - 41*x**2/2 - 60. Let y(n) be the second derivative of w(n). Factor y(p).
3*p*(p - 4)*(p - 1)**2/2
Let v(m) be the first derivative of -2*m**3/33 - 22*m**2 + 1677. Factor v(o).
-2*o*(o + 242)/11
Suppose 3*q = 28*q - 100. Let j be q/38 - (-116)/342. Determine y so that 2/9*y + j - 2/9*y**2 = 0.
-1, 2
Suppose -4*k - i = 7, -5*k + 15*i - 17*i = 8. Let d be 0 + k/5 + (-528)/(-45). Find f, given that -d*f - 289/6*f**2 - 2/3 = 0.
-2/17
Let b = -7/401 - -429/1604. Let r(c) = c**3 + 3*c**2 + c + 2. Let m be r(-2). Factor 1/8*j**m + 0*j + 0 - b*j**2 + 1/8*j**3.
j**2*(j - 1)*(j + 2)/8
Let k be (1/77)/((-51)/(-42) + (-256)/224). Factor 798/11*d + 78/11*d**2 + k*d**3 + 722/11.
2*(d + 1)*(d + 19)**2/11
Suppose 3*i**3 - 15*i**2 + 5*i + 4*i + 38*i**4 - 35*i**4 = 0. Calculate i.
-3, 0, 1
Let q be 2 + 40 - (8 - 6). Let c = q - 30. Factor 8*l**2 + 4*l**2 - 2*l**3 + l**3 - c*l**2.
-l**2*(l - 2)
Suppose 245*d - 50*d - 683 + 98 = 0. Let p(m) be the second derivative of -1/120*m**4 + 1/30*m**d + 0 + 0*m**2 + 5*m. Factor p(u).
-u*(u - 2)/10
Solve -2/15*h**2 + 932/15*h - 108578/15 = 0 for h.
233
Let 92*s**2 + 94*s**2 + 100*s**2 - 369*s**2 + 86*s**2 - 93*s = 0. Calculate s.
0, 31
Let d(v) be the third derivative of -v**7/560 - v**6/80 - v**5/40 - 31*v**3 + v**2 + 262*v. Let s(t) be the first derivative of d(t). Factor s(o).
-3*o*(o + 1)*(o + 2)/2
Factor 165*q**4 + 265*q**3 - 1225*q**3 - 1904*q**2 - 169*q**4.
-4*q**2*(q + 2)*(q + 238)
Suppose 4*b - 12 = -0. Suppose 2*l - 14 = -3*d, b*l = -0*d - 2*d + 16. Factor -i**d - 3*i**2 - 11*i**3 - 3*i**4 + i + 2*i - i**2.
-i*(i + 1)*(i + 3)*(3*i - 1)
Suppose -1/3*p**2 + 0 - 308*p = 0. What is p?
-924, 0
Let w(q) be the first derivative of -420 - 428 - 5*q**2 - 3*q**3 - q + 813. Factor w(y).
-(y + 1)*(9*y + 1)
Let r(k) be the first derivative of k**6/1080 + k**5/90 + k**4/18 + 7*k**3 - k - 58. Let i(c) be the third derivative of r(c). Solve i(x) = 0.
-2
Let m(x) be the third derivative of -x**6/30 + 8*x**5/5 - 37*x**4/2 - 272*x**3/3 - 2237*x**2. Factor m(k).
-4*(k - 17)*(k - 8)*(k + 1)
Let f(n) be the first derivative of 1/60*n**4 + 14*n + 15 - 2/5*n**2 + 1/10*n**3. Let a(u) be the first derivative of f(u). Factor a(t).
(t - 1)*(t + 4)/5
Suppose -2*k - 1 = -g, 5*k - 6 = 3*g - 14. Suppose 14*d - 6 = g*d. Factor -6*i**d + 8*i + 5 + 7 - 2*i**3 - 4 - 6*i**3 - 2*i**4.
-2*(i - 1)*(i + 1)*(i + 2)**2
Let x(k) be the first derivative of 2*k**5/15 - 55*k**4/6 + 766*k**3/9 - 329*k**2/3 + 193. Determine d, given that x(d) = 0.
0, 1, 7, 47
Let u(y) = -y**3. Let l be ((-2)/6)/(13/(-117)). Let d(k) = 4*k**3 + 2320*k**2 - 3*k**l - 160 - 2290*k**2. Let r(i) = d(i) - 4*u(i). Factor r(j).
5*(j - 2)*(j + 4)**2
Let a(t) be the second derivative of -t**4/42 + 37*t**3/21 + 258*t**2/7 + 3624*t. Find u such that a(u) = 0.
-6, 43
Let b = -560 - -1573. Suppose 28*j**2 - 8*j**2 - b*j + 25*j**3 + 504*j + 504*j = 0. What is j?
-1, 0, 1/5
Let 4163*y - 2187*y - 3*y**2 - 2135*y + 162 = 0. Calculate y.
-54, 1
Let o(h) = -h**3 + 72*h**2 + 500*h - 2493. Let q be o(78). Determine p so that 2/5 + 4/5*p**2 + p + 1/5*p**q = 0.
-2, -1
Let i = -11834/3 + 3945. Let g(f) be the first derivative of i*f**3 - f**2 + 0*f - 3. Factor g(c).
c*(c - 2)
Let x be 7 + 2265/(-171) + 5. Let q = 49/19 + x. Factor -8/3*u**2 + q*u - 4*u**3 + 0.
-4*u*(u + 1)*(3*u - 1)/3
Let f = -1/115650 - -92521/115650. Let 12*w**3 - 2/5*w**5 - f*w**2 - 58/5*w + 6 - 26/5*w**4 = 0. Calculate w.
-15, -1, 1
Let a(g) be the third derivative of -g**7/105 - g**6/12 + g**5/15 + 2*g**4 + 1222*g**2. Let a(b) = 0. Calculate b.
-4, -3, 0, 2
Let a(d) be the third derivative of -d**7/630 + 3*d**6/40 - 37*d**5/90 + 2*d**4/3 - 47*d**2 + 22*d. Factor a(o).
-o*(o - 24)*(o - 2)*(o - 1)/3
Suppose -o + 21 = 3*j, -2*o - 2*j + 26 = -4*j. Factor 6 - 2*g**2 + o*g - 18 - g**2.
-3*(g - 4)*(g - 1)
Let o be (276/(-69) - 1156/6)*6/(-25). Let -48*h - o - 4/5*h**2 = 0. Calculate h.
-59, -1
Let i(r) be the first derivative of -3 + 38/15*r**3 - 48/5*r + 22/5*r**2 + 3/10*r**4. Factor i(y).
2*(y + 3)*(y + 4)*(3*y - 2)/5
Let a(v) be the third derivative of -v**5/15 + v**4 - 16*v**3/3 + 141*v**2 + v. Let a(r) = 0. Calculate r.
2, 4
Solve -22*h**4 + 325*h**4 - 21*h**5 + 24*h**5 + 1849*h**2 + 5184*h + 791*h**2 - 2244*h**3 = 0.
-108, -1, 0, 4
Let d(i) be the third derivative of -i**6/660 - 4*i**5/55 - 95*i**4/132 + 5284*i**2. Factor d(v).
-2*v*(v + 5)*(v + 19)/11
Let v = 7 + -73/11. Suppose 1051*o = 1046*o - 2*c + 12, 3*o + 2*c - 12 = 0. Suppose 2/11 + 0*u - v*u**2 + o*u**3 + 2/11*u**4 = 0. What is u?
-1, 1
Let g(v) be the third derivative of -2*v**7/21 - 127*v**6/15 - 1023*v**5/5 + 2002*v**4/3 - 1352*v**3/3 - 757*v**2. Find l, given that g(l) = 0.
-26, 1/5, 1
Let m(p) = -2*p**3 + 28*p**2 + 30*p + 7. Let a be m(15). What is c in 33*c - a*c - 6 - 6*c**2 - 15*c + 3*c**2 = 0?
2/3, 3
Let a be -1*(2258/(-14) + 4). Let u = a + -157. Factor u*p**5 + 0*p**2 + 4/7*p**4 + 0*p + 2/7*p**3 + 0.
2*p**3*(p + 1)**2/7
Let b be -3 + (-35 + (-9 - -57) - (-138)/(-14)). Solve 0 + b*y**3 + 51/7*y**2 + 0*y = 0 for y.
-51, 0
Suppose 7*f = 6*f + 292. Let z = 473 - f. Solve 9*g + 16 + 31*g + z*g**2 + 14*g**3 - 145*g**2 + 2*g**4 = 0.
-2, -1
Let j be -7 + 4 + (0 - (-17)/5). Let z = 1567 + -1565. Factor 0 - j*c**z - 1/5*c**3 + 0*c.
-c**2*(c + 2)/5
Let a(q) be the first derivative of q**6/2 - 9*q**5 + 111*q**4/2 - 132*q**3 + 108*q**2 + 1704. Factor a(w).
3*w*(w - 6)**2*(w - 2)*(w - 1)
Find y such that 15*y**4 - 2*y**2 + 4*y**3 - 13*y**2 - 5*y**5 + y**3 - 4*y**3 + 4*y**3 = 0.
-1, 0, 1, 3
Let y(b) = 2*b**3 - 6*b**2 + 20*b - 59. Let o be y(4). Suppose o*u - 17*u = 180. Let 14/3*v**2 - 2/3*v**u - 2*v**4 + 2/3*v**3 - 8/3 + 0*v = 0. What is v?
-2, -1, 1
Let