j - 9. Factor k(z).
-4*(z - 2)*(z + 2)*(z + 21)
Let u(l) be the first derivative of -l**6/3 - 18*l**5/5 - 13*l**4/2 + 6*l**3 + 14*l**2 - 917. Suppose u(q) = 0. What is q?
-7, -2, -1, 0, 1
Let d = -631 - -665. Suppose d*r = 32*r. Factor -1/3*c + r - 2/3*c**2 - 1/3*c**3.
-c*(c + 1)**2/3
Let z = 235 + -230. Find l such that 5*l**4 + 4*l**4 + 0*l**3 - 6*l**4 - z*l**2 - 2*l**4 - 4*l**3 = 0.
-1, 0, 5
Let c = -55002/907 + 48736707/739205. Let x = c - -18/163. What is b in x*b**5 - 3/5*b - 36/5*b**4 + 42/5*b**2 - 24/5*b**3 - 6/5 = 0?
-1, -1/3, 2/3, 1
Let j(i) be the third derivative of i**8/80640 - i**7/2880 - 11*i**6/720 + 199*i**5/60 - 228*i**2 + 2*i. Let g(h) be the third derivative of j(h). Factor g(n).
(n - 11)*(n + 4)/4
Factor -1332 + 23314/5*t - 14/5*t**2.
-2*(t - 1665)*(7*t - 2)/5
Suppose 439*w - 666 = 421*w. Let p(x) be the second derivative of -33/20*x**5 - w*x - 1/14*x**7 + 5/4*x**4 + 0 + 0*x**2 + 0*x**3 + 7/10*x**6. Factor p(u).
-3*u**2*(u - 5)*(u - 1)**2
Suppose 2/7*a**2 + 243602/7 + 1396/7*a = 0. What is a?
-349
Let m(r) be the second derivative of r**7/273 - r**6/13 + 83*r**5/130 - 67*r**4/26 + 60*r**3/13 - 666*r. Let m(j) = 0. Calculate j.
0, 3, 4, 5
Suppose -5*k = -3*h + 2391, 0 = -3*h - 3*k - 85 + 2452. What is s in -8*s - 795 + 2*s - 3*s**2 + h = 0?
-1
Suppose -5*h = 4*q - 3, 2*h + 5 = 2*q - 1. Factor -8 + 10*a**3 + 14 + 42*a**q + 144*a - 106*a.
2*(a + 1)*(a + 3)*(5*a + 1)
Let f be 8 + (50/(-18) - (-8)/(-36)). Factor 4*h**3 + 14*h + h**4 + 17*h - 2*h**4 - f*h**2 - 29*h.
-h*(h - 2)*(h - 1)**2
Let n(b) be the third derivative of -b**5/30 + 15*b**4/2 - 176*b**3/3 + 489*b**2. Suppose n(l) = 0. What is l?
2, 88
Let v(l) be the third derivative of l**6/360 + 73*l**5/36 + 32375*l**4/72 - 171125*l**3/18 - 2*l**2 + 1152*l + 2. Determine g, given that v(g) = 0.
-185, 5
Let u = 1209 + -1249. Let q be 4/(u/(-77)) + 13/(-65). Determine m so that -7/2*m**2 + 1/2*m**3 + q*m - 9/2 = 0.
1, 3
Let k(j) be the second derivative of j**4/6 - 55*j**3/3 + 574*j**2 - 372*j. Suppose k(b) = 0. What is b?
14, 41
Determine x so that -9*x**4 - 9285*x**2 - 23838*x + 1919 - 1408*x**3 + 856*x**3 + 18265 = 0.
-29, -4, 2/3
Let h be -34*(-47 - -39 - ((-38)/(-627))/((-2)/213)). Factor -2/11*c**2 - h + 68/11*c.
-2*(c - 17)**2/11
Let q(l) = -160*l**3 + 20*l - 4*l - 27*l - 65*l**2. Let w(a) = -81*a**3 - 33*a**2 - 6*a. Let m(c) = -3*q(c) + 5*w(c). Determine u, given that m(u) = 0.
-1/5, 0
Let z = 12259/20 - 3061/5. Suppose 42*a = 38*a + 12. Find x such that -z + 3*x - a*x**3 + 3/4*x**2 = 0.
-1, 1/4, 1
Let h = 149 - 109. Factor 6*z**2 + 5015*z - 2*z**2 - h - 5027*z.
4*(z - 5)*(z + 2)
Suppose 10 = -33*n + 38*n. Suppose 5*d - 25 = n*r - 6*r, d = 5. Factor 0 + r*b**4 - 1/2*b**2 + 1/4*b**5 - 3/4*b**3 + 0*b.
b**2*(b - 2)*(b + 1)**2/4
Let r(w) be the first derivative of -w**3/3 + 89*w**2 - 177*w + 980. Factor r(j).
-(j - 177)*(j - 1)
Solve -1058089859/4 - 3057/4*g**2 - 1/4*g**3 - 3115083/4*g = 0 for g.
-1019
Let o(w) be the second derivative of w**7/168 + w**6/60 + w**5/80 - 1139*w. Let o(z) = 0. Calculate z.
-1, 0
Let j(r) be the second derivative of r**7/294 - r**6/30 - 11*r**5/140 + 19*r**4/84 + 19*r**3/21 + 8*r**2/7 + 915*r. Factor j(s).
(s - 8)*(s - 2)*(s + 1)**3/7
Let y = -343 + 3737/11. Let b = y - -340/77. Find r, given that -2/7*r**2 - 10/7*r - b = 0.
-4, -1
Factor -15/2*s**3 - 39/4*s**2 - 3/4*s**4 - 27 + 45*s.
-3*(s - 1)**2*(s + 6)**2/4
Suppose -60 = -20*m - 5*q, -5*q - 387 = 4*m - 319. Determine n, given that -3/2*n**5 + m*n**4 - 12*n**3 + 8*n + 0*n**2 + 0 = 0.
-2/3, 0, 2
Let x be (-1)/11 - (-21)/231. Factor m**2 + 45*m - 17*m**3 + 14*m**3 - 7*m**2 + 0*m**2 + x*m**2.
-3*m*(m - 3)*(m + 5)
Let n(v) = -4*v**2 - 16*v + 84. Let m be n(-7). Let t be (-2)/(-13) + 40/78. Determine d, given that 0 + t*d**2 + m*d + 4/3*d**3 + 2/3*d**4 = 0.
-1, 0
Let j(k) be the second derivative of k**6/3 - 239*k**5/60 + 101*k**4/18 + 7*k**3/18 - 1461*k. Find i, given that j(i) = 0.
-1/30, 0, 1, 7
Let j be (8 - 11)/((-3)/2). Suppose 15 = 3*t + j*t. Factor 4*q**4 - 6 + 9*q**3 + 3*q**3 + 1 - 12*q + 4*q**2 - t.
4*(q - 1)*(q + 1)**2*(q + 2)
Let w(b) be the first derivative of -10/3*b**3 + 25/6*b**2 + 5/12*b**4 + 0*b - 65. Factor w(m).
5*m*(m - 5)*(m - 1)/3
Let q be 8/(-20) - 2410/(-25). Factor -3*f**2 - 3849 + q*f + 1923 + 1926.
-3*f*(f - 32)
Let d(o) be the first derivative of -8*o**5/45 - 761*o**4/18 + 2684*o**3/27 - 385*o**2/9 - 128*o/3 + 1137. Let d(t) = 0. What is t?
-192, -1/4, 1
Suppose -t - 3 + 49 = 5*x, 1 = t. Suppose -3*p**3 + 3*p**3 + 9*p**3 - x*p**2 - 3*p**4 + 3*p = 0. What is p?
0, 1
Suppose -22 = -k - 2*d, -4*d + 68 = k + 2*k. Suppose 2*u + 3 = -o, 2*u + k = 4*o - 2*o. Let -8*c**2 + o*c**2 + 4*c**3 - 9*c**2 + c**3 = 0. What is c?
0, 2
Find r such that 0 + 38/15*r**2 + 28/3*r + 2/15*r**3 = 0.
-14, -5, 0
Factor 199/6*r**2 + 202/3 + 302/3*r - 1/6*r**3.
-(r - 202)*(r + 1)*(r + 2)/6
What is n in -1/3*n**2 + 61*n + 0 = 0?
0, 183
Let c(s) be the third derivative of s**5/630 - 395*s**4/252 + 56*s**3/3 + s**2 - 3*s - 164. Determine u so that c(u) = 0.
3, 392
Let x(b) be the second derivative of b**7/252 + b**6/15 + 3*b**5/8 + 25*b**4/36 + 1501*b. Factor x(v).
v**2*(v + 2)*(v + 5)**2/6
Let k be 116 + -122 + ((-624)/(-21))/4. Let f(j) be the second derivative of 0 + 1/21*j**4 + 10*j + k*j**2 + 4/7*j**3. Factor f(x).
4*(x + 1)*(x + 5)/7
Let k(c) = 3*c**3 - 3*c**2 - 3*c - 1. Let t be k(3). Suppose -2*o + t = -72. Factor 6*l**3 + o*l**4 - 54*l**4 + 3*l - 5*l.
2*l*(l + 1)**2*(2*l - 1)
Solve -2*j**4 - 132*j - 17*j**2 - 3327 + 3255 - 53*j**2 - 27*j**3 - j**4 - 20*j**2 = 0 for j.
-3, -2
Let j(s) be the third derivative of -s**5/12 + 85*s**4/24 + 115*s**3 + 20*s**2 + s. What is w in j(w) = 0?
-6, 23
Let y(i) = -i**2 + 30*i - 222. Let a be y(16). Solve -37*s**3 + 2*s + 155*s**2 - 19*s**3 - 186*s - 2*s**4 + 0*s**4 + 25*s**a + 62 = 0 for s.
-31, 1
Let c be ((-2)/4)/(1/(-10)). Let r = 2053628/810645 + 2/270215. What is o in 4/15 - 112/15*o**4 + 32/5*o**c - r*o - 58/15*o**3 + 36/5*o**2 = 0?
-1, 1/4, 2/3, 1
Let b(i) be the second derivative of -2*i**7/147 - 16*i**6/15 - 726*i**5/35 + 232*i**4/3 - 1682*i**3/21 + 1303*i - 4. Factor b(t).
-4*t*(t - 1)**2*(t + 29)**2/7
Let y(v) be the third derivative of v**6/120 + 103*v**5/60 + 203*v**4/24 + 101*v**3/6 + 8*v**2 - 73*v. Factor y(d).
(d + 1)**2*(d + 101)
Let w(k) be the second derivative of k**6/45 + 59*k**5/30 + 133*k**4/2 + 9025*k**3/9 + 13718*k**2/3 + 1098*k. Factor w(o).
2*(o + 2)*(o + 19)**3/3
Let h(d) be the first derivative of -d**6/12 - 88*d**5/5 - 212*d**4 - 3016*d**3/3 - 2332*d**2 - 2656*d - 2085. Suppose h(i) = 0. What is i?
-166, -4, -2
Let f = -266 + 256. Let z(x) = -36*x**3 + 106*x**2 - 86*x + 16. Let t(b) = b - 7. Let c be t(6). Let h(w) = w**2 - w. Let j(m) = c*z(m) + f*h(m). Factor j(s).
4*(s - 2)*(s - 1)*(9*s - 2)
Let t(g) = g**4 + 5*g**3 + 4*g**2. Let f(h) be the first derivative of h**5/5 + h**4 + h**3 - 234. Let z(q) = 3*f(q) - 2*t(q). Find v such that z(v) = 0.
-1, 0
Let u(s) be the first derivative of -s**6/1080 - s**5/360 + 29*s**3/3 + s**2 + 103. Let v(y) be the third derivative of u(y). Factor v(z).
-z*(z + 1)/3
Let o(n) be the first derivative of n**3 + 495*n**2/2 - 2028*n + 5152. Determine i so that o(i) = 0.
-169, 4
Let z(l) be the first derivative of -7*l**3 - 60*l**2 - 371*l + 3. Let s(o) = 341 + 11*o**2 - 40*o + 100*o - 155. Let d(x) = -11*s(x) - 6*z(x). Factor d(m).
5*(m + 6)**2
Solve 0*m - 1040/11*m**3 + 0 + 266/11*m**4 - 2/11*m**5 + 1032/11*m**2 = 0.
0, 2, 129
Suppose -4*l = -w - 5154, -5*l + 5*w = -7*l + 2566. Let o = -1285 + l. Suppose 2/17*v**4 + 0 - 6/17*v**2 + 0*v**o + 4/17*v = 0. Calculate v.
-2, 0, 1
Factor -9*p - p**3 - 2 + 65*p**2 + 6 + 3*p**2 - 57*p**2 - 5*p**2.
-(p - 4)*(p - 1)**2
Suppose 34/3*k**3 - 2/9*k**5 - 136/9*k + 28/9*k**4 + 0 + 8/9*k**2 = 0. What is k?
-2, 0, 1, 17
Let n be -3 - ((-3060)/(-238) + -16). Factor 11/7*x**2 + 10/7*x + n*x**3 + 0.
x*(x + 1)*(x + 10)/7
Let x(m) be the first derivative of 3*m**4/8 - m**3 - 9*m**2/4 - 887. Let x(a) = 0. Calculate a.
-1, 0, 3
Let x(f) be the third derivative of -f**6/540 - 3*f**5/5 + 356*f**2. Find w, given that x(w) = 0.
-162, 0
Let r(b) be the first derivative of b**6/60 + 281*b**5/25 + 78961*b**4/40 + 253. Suppose r(z) = 0. What is z?
-281, 0
Let t be 267/89*40/(