t s = r - -2/227. Find a, given that 0*a + 2/7*a**2 - s = 0.
-2, 2
Let n(r) = r**2 - 16. Let d be n(-6). Let v be 4/14*(-16 + d). Find w such that -2/7*w**3 + 0 - v*w + 8/7*w**2 = 0.
0, 2
Let o(s) be the first derivative of 3/35*s**5 - 2 - 3/28*s**4 + 0*s + 1/21*s**3 - 1/42*s**6 + 0*s**2. Determine t so that o(t) = 0.
0, 1
Let x(w) be the first derivative of -2*w**3/9 - 13*w**2/3 + 20*w - 3. Factor x(b).
-2*(b - 2)*(b + 15)/3
Let u(k) = -2*k**5 + 70*k**4 - 106*k**3 + 52*k**2 + 7. Let z(c) = -c**5 + 23*c**4 - 35*c**3 + 17*c**2 + 2. Let p(h) = -2*u(h) + 7*z(h). Solve p(r) = 0 for r.
0, 1, 5
Let b(t) be the third derivative of t**5/180 + 5*t**4/24 + 7*t**3/9 + 122*t**2. Factor b(m).
(m + 1)*(m + 14)/3
Suppose 9*w = 11 + 7. Let -6*a - 20*a**3 - 14*a + 8 + 32*a**3 - 16*a**w = 0. What is a?
-1, 1/3, 2
Let o(d) be the second derivative of -d**5/70 + 17*d**4/14 - 289*d**3/7 + 4913*d**2/7 - 4*d - 3. Factor o(x).
-2*(x - 17)**3/7
Let f be 2/8*((-28)/19)/2. Let u = f - -277/266. Factor -8/7*c - u - 2/7*c**2.
-2*(c + 1)*(c + 3)/7
Let v be (2/(-78))/((-82)/533). Let k be (1 - -1) + (-10)/6. Factor -1/6*j**2 - v*j + k.
-(j - 1)*(j + 2)/6
Let o(g) be the third derivative of -g**5/300 + g**4/120 + 178*g**2. Factor o(x).
-x*(x - 1)/5
Let h(u) be the third derivative of -u**5/300 - 61*u**4/120 + 31*u**3/15 + 504*u**2. Factor h(p).
-(p - 1)*(p + 62)/5
Let k(q) be the second derivative of -q**4/8 - q**3 - 3*q**2 - 13*q - 2. Find h such that k(h) = 0.
-2
Let s = 57 - 45. Factor -18*l**4 - s*l**3 - 6*l**5 - 15*l**3 + 3*l**5.
-3*l**3*(l + 3)**2
Let b(c) be the third derivative of c**6/180 + c**5/18 - 2*c**4/9 - 4*c**3/3 + 2*c**2 - 3. Factor b(d).
2*(d - 2)*(d + 1)*(d + 6)/3
Suppose 5 - 16 = -5*g - 1. Suppose 4*m = -5*j + 2*m + 15, 3*j = 2*m + 9. Factor 2/11*z**j + 6/11*z + 2/11 + 6/11*z**g.
2*(z + 1)**3/11
Let b(z) be the first derivative of 2/27*z**3 + 2/9*z + 2/9*z**2 + 14. Determine y so that b(y) = 0.
-1
Let i(k) be the second derivative of -k**5/70 + 9*k**4/14 - 17*k**3/7 + 25*k**2/7 - 559*k. Factor i(q).
-2*(q - 25)*(q - 1)**2/7
Let f(y) = -616*y - 44998. Let p(o) = -o**2 + 8*o - 1. Let t(j) = f(j) + 2*p(j). Factor t(l).
-2*(l + 150)**2
Let c(h) = -1017*h**3 + 4*h**2 - 1 - 1 + 1018*h**3. Suppose 258 = -5*r + 93. Let q(w) = -6*w**3 - 21*w**2 + 11. Let j(u) = r*c(u) - 6*q(u). Factor j(b).
3*b**2*(b - 2)
Let m(b) = b**2 - 12*b - 16. Let j(t) = 12*t**2 - 132*t - 176. Suppose -4*f - 35 + 11 = 0. Let r(x) = f*j(x) + 68*m(x). Determine i, given that r(i) = 0.
-4, -2
Find j, given that 194/7*j - 20*j**2 - 18/7*j**3 - 36/7 = 0.
-9, 2/9, 1
Let r(n) = n**3 + 3*n**2 + 5*n - 5. Let h(x) be the third derivative of x**5/15 + x**4/6 - 2*x**3/3 - 23*x**2. Let k(s) = -5*h(s) + 4*r(s). Factor k(t).
4*t**2*(t - 2)
Factor -8/5*b**2 + 0 - 8/5*b + 2/5*b**3 + 2/5*b**4.
2*b*(b - 2)*(b + 1)*(b + 2)/5
Let -314 + 304 - 6*f + 5*f**3 + f + 0*f + 10*f**2 = 0. Calculate f.
-2, -1, 1
Let r(d) be the third derivative of d**9/12096 + d**8/3360 + d**7/3360 + 19*d**3/3 + 35*d**2. Let g(l) be the first derivative of r(l). Factor g(f).
f**3*(f + 1)**2/4
Suppose -30 = -3*s - 4*n, 449*s + 2*n = 453*s + 4. What is o in -2/5*o**3 + 0 + 2/5*o**4 - 2/5*o**s + 2/5*o = 0?
-1, 0, 1
Let s be ((-200)/(-22))/(530/1325). Suppose s*y + 32/11*y**4 + 2/11*y**5 + 180/11*y**3 + 400/11*y**2 + 0 = 0. What is y?
-5, -1, 0
Find f, given that 1/5*f**2 + 405 - 18*f = 0.
45
Solve -4*w**2 + 4*w**3 - 92*w - 36*w**2 + 783 - 831 = 0 for w.
-1, 12
Let w(i) be the first derivative of 7 - 10/7*i**2 + 5/7*i**4 - i**3 + 5/7*i**5 - 4/7*i. Factor w(s).
(s - 1)*(s + 1)*(5*s + 2)**2/7
Suppose -5*b + s - 1838 = 0, -4*b - 67 - 1395 = -5*s. Let j be b/(-936) - 4/(-18). Factor -j*n**2 + 10/13*n - 4/13 + 2/13*n**3.
2*(n - 2)*(n - 1)**2/13
Suppose -w**4 + 180*w**2 + 190*w**3 + 9*w**4 - 3*w - 115*w - 185 - 72*w - 3*w**4 = 0. Calculate w.
-37, -1, 1
Suppose -8*r + 10*r = -2*i + 6, -2*r + 14 = -2*i. Let j be (0*1*(i - -3))/(-1). Determine y, given that 4/7*y**2 + j - 16/7*y = 0.
0, 4
Let d(a) be the first derivative of -5*a**6/2 - 3*a**5/5 + 45*a**4/4 + 13*a**3 + 3*a**2 + 26. Determine s so that d(s) = 0.
-1, -1/5, 0, 2
Let o be ((-12)/36)/((-10)/15). Solve -o*g**2 - 1/4*g**3 + 0 - 1/4*g = 0.
-1, 0
Suppose 31149 - 19896*x**2 - 1104*x + 45027 + 19900*x**2 = 0. Calculate x.
138
Suppose 4*h = -14 + 26. Let g be ((-18)/5 + 12/h)/1. Factor 0*k**2 + 0 - g*k**3 + 2/5*k**5 + 0*k + 0*k**4.
2*k**3*(k - 1)*(k + 1)/5
Suppose 0*c - c - 12 = -3*h, 12 = 3*h. Suppose -f = s - 6, -2*s + 4*f + c = 6. Factor -11 - 7*b**3 + 15*b**s - 6*b**3 - 10*b**2 + 6*b + 29.
2*(b - 3)**2*(b + 1)
Let l(m) be the second derivative of 1/6*m**6 + 0*m**2 + 1/8*m**5 + 38*m + 0 - 5/84*m**7 - 5/12*m**4 + 0*m**3. What is s in l(s) = 0?
-1, 0, 1, 2
Factor 2*w**2 - 182 + 22*w + 338 - 180.
2*(w - 1)*(w + 12)
Let l(g) be the second derivative of 529*g**7/840 - 23*g**6/60 + g**5/10 - 7*g**4/12 - 5*g. Let y(r) be the third derivative of l(r). Factor y(i).
3*(23*i - 2)**2
Let p(i) be the second derivative of -11*i - 1/6*i**3 - 1/12*i**4 + i**2 + 0. Solve p(k) = 0 for k.
-2, 1
Suppose 411 = -14*c + 2595. Solve 0*x**4 - 3*x**4 - 180*x**2 + 54*x**3 + c - 150*x + 219 - 96*x**3 = 0 for x.
-5, 1
Let i be (-16)/25*((-2015)/26)/31. Let g = 1/96 + 187/480. Factor g + i*w + 6/5*w**2.
2*(w + 1)*(3*w + 1)/5
Let j(n) be the second derivative of 0 + 1/6*n**6 + 1/4*n**5 + 0*n**3 + 0*n**2 + 29*n - 5/6*n**4. Solve j(s) = 0 for s.
-2, 0, 1
Let v(u) be the second derivative of -u**6/150 + 17*u**4/60 - 6*u**3/5 + 2*u**2 - 133*u. Let v(n) = 0. What is n?
-5, 1, 2
Let f(c) be the first derivative of 0*c - 19 + 2/45*c**5 - 1/9*c**4 - 2/9*c**3 + 0*c**2. Factor f(l).
2*l**2*(l - 3)*(l + 1)/9
Let g = 2004/3745 + -4/2247. Find n such that g - 2/5*n - 2/15*n**2 = 0.
-4, 1
Let u(l) be the second derivative of 0 - 9/2*l**2 + 5/2*l**3 - 3/20*l**5 - 1/4*l**4 - 25*l. Let u(q) = 0. What is q?
-3, 1
Determine j so that -j**3 - 4*j**2 + 5*j**3 - 44*j + 33 - 4*j**2 + 15 = 0.
-3, 1, 4
Let g(l) be the third derivative of -l**7/105 - l**6/20 + 3*l**5/10 - 5*l**4/12 - 6*l**2 - 4. Find r, given that g(r) = 0.
-5, 0, 1
Let w be ((-12)/(-8) - 1)*10. Factor -4*q**4 + 14*q - 2*q**w - 12*q + 4*q**2 - q**5 + q**5.
-2*q*(q - 1)*(q + 1)**3
Let n(g) = g**2 - 3*g - 31. Let w(f) = -f**2 + 5*f + 32. Let x(d) = -4*n(d) - 3*w(d). Solve x(h) = 0.
-7, 4
Suppose -124/7*w**2 + 2/7*w**3 + 1922/7*w + 0 = 0. What is w?
0, 31
Let w(f) be the third derivative of f**6/150 + f**5/3 - 14*f**4/15 - 104*f**3/15 - 214*f**2. Factor w(h).
4*(h - 2)*(h + 1)*(h + 26)/5
Let r = -5391 - -5394. Find c, given that 0*c + 0 + 2/7*c**r - 2/7*c**2 = 0.
0, 1
Solve -25/4 + 1/8*j**3 + j**2 + 5/8*j = 0 for j.
-5, 2
Let h(c) be the third derivative of 0*c**3 + 0*c - 1/8*c**4 + 0 - 1/60*c**5 + 28*c**2. Solve h(z) = 0 for z.
-3, 0
Let b(r) be the second derivative of -r**9/1008 - r**8/168 - r**7/72 - r**6/72 - 2*r**4 + 8*r. Let u(m) be the third derivative of b(m). Factor u(j).
-5*j*(j + 1)**2*(3*j + 2)
Factor -8*t**2 + 4*t**3 + 8*t**4 - 3*t**4 - 5*t + 3*t**2 + 6*t**3 - 5*t.
5*t*(t - 1)*(t + 1)*(t + 2)
Let x(g) be the third derivative of -2*g**7/105 - 2*g**6/15 + g**5/3 + 2*g**2. Solve x(h) = 0 for h.
-5, 0, 1
Let w(t) = -5. Let i(j) = -196*j**2 + 84*j + 11. Suppose -6*c + 3*z = -c + 25, -5*c + z = 25. Let a(q) = c*i(q) - 20*w(q). Determine d so that a(d) = 0.
3/14
Suppose 2*y - 1/2 - 1/2*y**4 + 2*y**5 - 4*y**3 + y**2 = 0. Calculate y.
-1, 1/4, 1
Suppose -36 + 40 = 2*x. Suppose -3*i + 1 = -17. Find q such that 8 + 108*q**4 - i*q**x - 4 - 4 - 3*q + 45*q**3 = 0.
-1/3, 0, 1/4
Let l = -28 - -85. Let v be 15/(-6)*(-1 - l/(-65)). Factor -2/13*q**2 - 2/13 + v*q.
-2*(q - 1)**2/13
Factor -11 - 1 + 39*o + 31*o**3 - 41*o**2 + 12*o**2 - 16*o**2 - 10*o**3 - 3*o**4.
-3*(o - 4)*(o - 1)**3
Let u = 1935 + -9669/5. Suppose 8/5*l**4 + 0*l**2 + 2/5*l**5 + u*l**3 + 0*l + 0 = 0. What is l?
-3, -1, 0
Let b = 3483/7 - 493. Let s = -5 + 10. Factor 4*n**3 + 12/7*n**4 + 2/7*n**s + 4/7 + 18/7*n + b*n**2.
2*(n + 1)**4*(n + 2)/7
Let -2*u - 4/3 + 4/3*u**2 = 0. What is u?
-1/2, 2
Let b(f) be the third derivative of f**7/84 + 17*f**6/48 + 11*f**5/6 + 35*f**4/12 + 171*f**2. Solve b(k) = 0 for k.
-14, -2, -1, 0
Factor 2/3*z + 0 - 2/9*z**2.
-2*z*(z - 3)/9
Let h(i) be the third derivative of i**6/420 + i**5/210 