
Let f(n) = 191*n**2 + 468*n - 11. Let g(d) = 52*d**2 + 117*d - 3. Let x(k) = 9*f(k) - 33*g(k). Determine r so that x(r) = 0.
-117, 0
Let p(h) be the first derivative of 2*h**5/25 - h**4/5 - 2*h**3/15 + 2*h**2/5 + 13261. Factor p(z).
2*z*(z - 2)*(z - 1)*(z + 1)/5
Suppose -57/5*g**3 + 541/5*g**2 + 1/5*g**4 - 327*g + 230 = 0. Calculate g.
1, 5, 46
Let t(f) be the first derivative of f**4 - 104*f**3/3 - 112*f**2 - 1429. Factor t(o).
4*o*(o - 28)*(o + 2)
Let p = -39959 - -39964. Factor 2/3*i**3 + 0*i - 4/5*i**4 + 0 + 2/15*i**p + 0*i**2.
2*i**3*(i - 5)*(i - 1)/15
Let h(j) be the first derivative of j**4/12 + 79*j**3/9 - 40*j**2/3 - 24. Suppose h(t) = 0. What is t?
-80, 0, 1
Suppose 200/3*b + 85/6*b**2 - 5/6*b**3 + 70 = 0. Calculate b.
-2, 21
Suppose -726 + 7*x**2 - 20*x**2 + 4*x**2 + 33*x + 11*x**2 + x**2 = 0. What is x?
-22, 11
Let j(a) be the first derivative of 610*a**3/11 - a**2/11 - 540. Solve j(k) = 0.
0, 1/915
Let s(l) be the second derivative of l**7/84 + 53*l**6/30 - 273*l**5/20 + 124*l**4/3 - 775*l**3/12 + 111*l**2/2 - 84*l + 8. Factor s(p).
(p - 2)*(p - 1)**3*(p + 111)/2
Suppose -80*h - 13 = -85*h - p, h = -p - 3. Let q(m) be the first derivative of 22 - 17*m**2 + 12*m - 56/3*m**3 - 28/5*m**5 + 53/2*m**h. Solve q(o) = 0 for o.
-1/2, 2/7, 1, 3
Suppose 21 = 4*k - 3*u, -45*k - 35 = -40*k + 5*u. Let t(x) be the third derivative of 0 + k*x**5 - 1/360*x**6 - 34*x**2 + 1/72*x**4 + 0*x**3 + 0*x. Factor t(v).
-v*(v - 1)*(v + 1)/3
Let q(v) be the second derivative of v**6/6 - v**5/2 - 5*v**4/4 + 20*v**3/3 - 10*v**2 + 7*v + 129. Factor q(u).
5*(u - 2)*(u - 1)**2*(u + 2)
Let h(p) be the first derivative of -p**4/2 + 190*p**3/3 - 2303*p**2 + 4418*p - 3771. Determine a so that h(a) = 0.
1, 47
Let t be (-98)/((-4018)/1845) + -45. Factor t - 6/7*h - 8/7*h**2 - 2/7*h**3.
-2*h*(h + 1)*(h + 3)/7
Let v = -2 + 10. Let s = 18 - 14. Let -5*j - 10 + 10*j**3 + 20*j**2 - 10*j**s - 8*j**3 + v*j**3 - 5*j**5 = 0. What is j?
-2, -1, 1
Let c = 18/4879 - -82835/29274. Factor -27/2 + c*b**2 + 21/2*b + 1/6*b**3.
(b - 1)*(b + 9)**2/6
Suppose 0 = 58*m + 530724 - 530840. Factor -28*n + 392 + 1/2*n**m.
(n - 28)**2/2
Let c(j) be the third derivative of -j**8/2520 + 4*j**7/525 - 13*j**6/450 - 2*j**5/75 + 3*j**4/20 + 1737*j**2. What is l in c(l) = 0?
-1, 0, 1, 3, 9
Let i(s) = -102*s + 14384. Let x be i(141). Factor -2 + 1/4*o + 2*o**x - 1/4*o**3.
-(o - 8)*(o - 1)*(o + 1)/4
Let r(o) = o**2 - 7*o - 228. Suppose 0 = 4*k - 5*b + 73, 4*k = k - 5*b - 11. Let p be r(k). Solve 0*l + 2/5*l**2 + p - 2/5*l**3 - 4/5*l**4 = 0.
-1, 0, 1/2
Let x(t) be the second derivative of t**7/210 - t**6/30 + t**5/20 + 130*t**2 - 92*t. Let k(p) be the first derivative of x(p). Factor k(y).
y**2*(y - 3)*(y - 1)
Suppose -155*o + 670*o = -16926 + 37011. Factor -1/3*p**3 + 54 - o*p + 8*p**2.
-(p - 18)*(p - 3)**2/3
Let s be (-2 - -6)/(1/(-12)). Let a = 50 + s. Suppose 4 + 11 - 7 - 4*i**a - i - 3*i = 0. What is i?
-2, 1
Let a(q) be the second derivative of -2/3*q**3 - 1/12*q**4 + 0 + 3*q**2 - 10*q + 1/30*q**5. Let g(t) be the first derivative of a(t). Factor g(k).
2*(k - 2)*(k + 1)
Let a(t) = -2*t**3 - 39*t**2 + 66*t + 94. Let y(c) = 4*c**3 + 77*c**2 - 138*c - 190. Let b(v) = 7*a(v) + 3*y(v). Solve b(g) = 0.
-22, -1, 2
Let l(u) be the first derivative of -10*u**5 + u**4/6 + 50*u**3/3 - u**2/3 + 1390. Let l(o) = 0. Calculate o.
-1, 0, 1/75, 1
Let b(t) = -2*t**4 - 28*t**3 - 87*t**2 - 95*t - 31. Let s(j) = 5*j**4 + 56*j**3 + 173*j**2 + 191*j + 62. Let q(i) = 7*b(i) + 3*s(i). Factor q(h).
(h - 31)*(h + 1)**3
Let x(t) be the third derivative of -1/840*t**8 + 0*t**3 + 0*t**5 + 0*t + 0*t**4 - 59*t**2 + 1/75*t**6 + 1/175*t**7 + 0. Find w such that x(w) = 0.
-1, 0, 4
Let v(c) be the first derivative of -27*c - 27/2*c**2 + 7/4*c**3 - 189. Factor v(q).
3*(q - 6)*(7*q + 6)/4
Find p such that -944*p - 154 + 211 + 242*p**2 + 45 + 834 + 10*p**3 - 12*p**3 = 0.
2, 117
Let g = -54761 + 164287/3. Factor -g*v + 4/3*v**2 + 0 - 1/3*v**3.
-v*(v - 2)**2/3
What is w in -31/7*w + 34 + 1/7*w**2 = 0?
14, 17
Factor 44 + 4*k**2 + 2*k - 2*k - 2*k**2 - 32 - 10*k.
2*(k - 3)*(k - 2)
Let a(u) be the first derivative of -90*u**2 - 118*u**3 - 99/5*u**5 - 72*u**4 - 21 - 2*u**6 - 27*u. Solve a(y) = 0 for y.
-3, -1, -1/4
Let v(u) = u**3 + u**2 - 2*u - 1. Let q(s) = -16*s**3 + 120*s**2 - 1040*s + 12. Let m(h) = q(h) + 12*v(h). What is a in m(a) = 0?
0, 14, 19
Let x(k) = 1. Let d = 558 - 557. Let c(l) = -2*l**2 - 20*l + 32. Let u(s) = d*c(s) - 10*x(s). Let u(a) = 0. What is a?
-11, 1
Let g(w) be the first derivative of 10/3*w - 18 - 35/9*w**3 - 25/6*w**2. Factor g(y).
-5*(y + 1)*(7*y - 2)/3
Suppose 5*o - 20 = m, -o + m + 4 = -m. Let u be o/10 + (16 - 12672/780). Factor 0 + 2/13*f**2 - u*f**4 + 0*f**3 + 0*f.
-2*f**2*(f - 1)*(f + 1)/13
Factor 3626 + 2271 - 2068*u - 608 + 4*u**2 - 1169.
4*(u - 515)*(u - 2)
Let d = 552 - 550. Factor 2187 + 2*r**2 - 852*r + 690*r + 0*r**d + r**2.
3*(r - 27)**2
Suppose 540 = -0*p - 20*p. Let b = p - -193/7. Factor b*l**3 - 4/7*l + 0*l**2 + 0.
4*l*(l - 1)*(l + 1)/7
Suppose 52*w + 9 = 49*w. Let r be 4 + (78/(-10) - w) + 1. Suppose f - 4/5*f**2 - 2/5 + r*f**3 = 0. What is f?
1, 2
Let g(p) be the first derivative of 6*p**6 - 1164*p**5/5 + 2395*p**4 - 812*p**3 - 2496*p**2 - 1024*p - 1807. Find z, given that g(z) = 0.
-1/3, 1, 16
Let x(t) = 8*t**5 - 55*t**4 + 114*t**3 + 51*t**2 + 9*t + 3. Let f(v) = v**5 + v**4 + v**3 - v**2 + 3*v + 1. Let k(r) = -3*f(r) + x(r). Factor k(c).
c**2*(c - 9)*(c - 3)*(5*c + 2)
Suppose 19*l - 472 = 364. Suppose -23*q**2 - l*q**3 - 29*q**2 + 75*q**2 + 12*q**4 - 39*q**2 = 0. What is q?
-1/3, 0, 4
Suppose 36 = -3*z - 2*s - 78, 177 = -5*z + s. Let l be (-4)/18 + (-152)/z. Find p such that p**2 + 2*p**4 - 2*p**l - p**4 - p**4 + p**3 = 0.
-1/2, 0, 1
Suppose -33*a = -14*a - 95. Suppose 16 = 3*r - 5*w, w = -a*r + 9*r - 10. Factor 2/7*h**5 + 12/7*h**3 + 2/7*h - 8/7*h**4 + 0 - 8/7*h**r.
2*h*(h - 1)**4/7
Suppose -d + 3*h = -2*h - 23, -3*h - 21 = -3*d. Suppose -v = -d - 0. What is t in -t**v + 9 - 3*t - 2*t**2 - 8 + 5*t**2 = 0?
1
Factor -2*c**4 + 36*c + 349*c + 2410*c**2 + 15*c**3 - 2005*c**2 - 3*c**4.
-5*c*(c - 11)*(c + 1)*(c + 7)
Let a(y) be the first derivative of -14 - 63/2*y**2 + 5*y**3 + 49*y - 1/4*y**4. Factor a(k).
-(k - 7)**2*(k - 1)
Let s(b) = 35*b**2 - 2610*b + 1522. Let q(x) = -665*x**2 + 49590*x - 28925. Let f(h) = 6*q(h) + 115*s(h). Determine j, given that f(j) = 0.
4/7, 74
Let k be 5 + (4/14)/((-22)/154). Let r(j) be the first derivative of -2/7*j**2 + 4/21*j**3 - k - 4/35*j**5 + 1/7*j**4 + 0*j. What is z in r(z) = 0?
-1, 0, 1
Let q(g) be the first derivative of 99 - 2*g**2 + 1/3*g**3 + 0*g. Factor q(l).
l*(l - 4)
Factor 3600*j - 3480*j**2 + 0*j**3 - j**4 - 4 + 4 - 111*j**3 - 8*j**3.
-j*(j - 1)*(j + 60)**2
Let y(m) be the third derivative of -7*m**5/90 + 205*m**4/36 + 212*m**3/9 - 1207*m**2. Factor y(q).
-2*(q + 1)*(7*q - 212)/3
Determine h so that 0*h**3 - 320/3*h - 2/3*h**4 + 56*h**2 + 0 = 0.
-10, 0, 2, 8
Let i = -120/937 - 2746684/4685. Let f = i - -590. Factor -f + 3/5*b**2 - 3/5*b.
3*(b - 3)*(b + 2)/5
Let c(k) be the first derivative of 144/7*k + 32*k**2 + 76/7*k**3 + 5/7*k**4 - 64. Let c(x) = 0. What is x?
-9, -2, -2/5
Let r(l) = -14*l - 780. Let j be r(-56). Let w(u) = u**2 + 2*u - 5. Let t be w(-4). Factor 29*n + j*n**t - 8*n**2 - 66*n + 25*n.
4*n*(n - 3)*(n + 1)
Let a(s) be the third derivative of s**5/150 + 168*s**4/5 + 338688*s**3/5 + s**2 + s + 1320. Let a(r) = 0. Calculate r.
-1008
Factor -135*b - 5*b**2 - 242*b - 54*b + 240 + 196*b.
-5*(b - 1)*(b + 48)
Suppose u + 9*u - 190 = 0. Suppose -3*x - u = -25. Suppose 9*p**4 - 2*p**3 - 6*p**x + 8*p**3 + 3*p**5 - 17 + 14 + 0*p**3 - 9*p = 0. Calculate p.
-1, 1
Let p = -632/549 + 754/549. Let p*i**3 + 4232/9 + 4048/9*i - 182/9*i**2 = 0. What is i?
-1, 46
Let b(h) be the third derivative of -1/2184*h**8 + 0 - 1/455*h**7 + 0*h**4 + 0*h + 0*h**5 - 1/390*h**6 + 0*h**3 + 55*h**2. Factor b(k).
-2*k**3*(k + 1)*(k + 2)/13
Let g = 565 + -573. Let h = 13 + g. Find i, given that -1/2*i**3 + 0 - 1/4*i**h - 3/4*i**4 + 0*i**2 + 0*i = 0.
-2, -1, 0
Suppose -731*s = -726*s - 65. Let f be 4 - s/(13/2). Factor 34/3*w - 4 - 10/3*w**f.
-2*(w - 3)*(5*w - 2)/3
Suppose 334*t = 336*t - 24. Let b be 26/130*10/t. Factor -7/6*k**4 + b*k**5 - 1/2 + 3*k**3 - 11/3*k**2 + 1