 + 1)**2*(p + 2)
Let 69*r**2 + 4761*r + 1/4*r**3 + 0 = 0. What is r?
-138, 0
Let u(b) be the first derivative of -1/3*b**3 - 1/5*b**5 + 1/2*b**4 + 0*b + 0*b**2 - 12. What is h in u(h) = 0?
0, 1
Let c(n) be the third derivative of n**8/17920 - n**7/2240 + n**5/80 - n**4/24 - 2*n**2. Let k(i) be the second derivative of c(i). Suppose k(r) = 0. What is r?
-1, 2
Let h(w) be the third derivative of 0*w - 1/60*w**5 - 5*w**2 + 0*w**4 + 0 + 0*w**3. Factor h(z).
-z**2
Factor -62*x**2 - 19*x - 41*x - 98*x**2 - 3*x**3 - x**4 - 2*x**4 + 208*x**2.
-3*x*(x - 2)**2*(x + 5)
Factor 58/7*s + 62/7*s**3 + 118/7*s**2 + 2/7*s**4 + 0.
2*s*(s + 1)**2*(s + 29)/7
Let i(o) be the second derivative of o**6/50 - o**5/25 + o**4/60 + 33*o. Factor i(p).
p**2*(p - 1)*(3*p - 1)/5
Let g(u) be the first derivative of -u**6/9 + 31*u**4/6 - 212*u**3/9 + 44*u**2 - 112*u/3 + 276. What is i in g(i) = 0?
-7, 1, 2
Let l = -23/10 + 71/30. Let q(g) be the first derivative of l*g**5 - 1/6*g**4 + 0*g + 4 + 0*g**2 + 0*g**3. Determine k, given that q(k) = 0.
0, 2
Let h = -125 + 125. Let v(c) = -c**2 + 3*c + 5. Let r be v(h). Solve 32/7*k + 2/7*k**r - 50/7*k**2 - 8/7 - 2*k**4 + 38/7*k**3 = 0 for k.
1, 2
Let a = 11 - 203. Let r = a - -195. Suppose 2/3 - 14/9*p + 10/9*p**2 - 2/9*p**r = 0. What is p?
1, 3
Let u(p) be the third derivative of -p**5/30 + 31*p**4/6 - 961*p**3/3 - 2*p**2 - 17. Factor u(j).
-2*(j - 31)**2
Let w be 4/(8/5) + (-140)/560. Let b = 0 + 2. Factor 3/2*s - w - 1/4*s**b.
-(s - 3)**2/4
Let x be (3 + (2 - 7))*-2. Suppose 4*c - 5*q = 33, 2*c + 5*q + 17 = -x. Factor -m**5 + 12*m**2 + c*m**3 - m**5 - 12*m**2.
-2*m**3*(m - 1)*(m + 1)
Let h(y) be the second derivative of 7*y + 3/10*y**5 + 1/15*y**6 - y**3 + 1/6*y**4 - 2*y**2 + 0. Let h(u) = 0. Calculate u.
-2, -1, 1
Let v be ((-1)/(-135)*-5)/((-1)/24*2). Factor v*k**3 + 0*k**2 + 0*k + 0 + 2/9*k**4.
2*k**3*(k + 2)/9
Let a = 8 - 5. Suppose -a*t + 20 = 2. Solve t*w**5 + 3*w**4 - 4*w**5 - w**2 + w**2 - w**2 = 0.
-1, 0, 1/2
Let b(q) be the first derivative of -q**4/2 - 4*q**3 + q**2 + 12*q + 625. Factor b(c).
-2*(c - 1)*(c + 1)*(c + 6)
Suppose 31 = 3*t + 10. Suppose 13 = t*r - 8. Determine z so that 0 - 2/7*z**2 + 0*z + 2/7*z**r = 0.
0, 1
Let d(z) be the first derivative of 3*z**5/20 - 45*z**4/8 + 253*z**3/4 - 315*z**2/2 + 147*z - 8. Solve d(k) = 0 for k.
1, 14
Let p(t) be the third derivative of -t**8/1120 + 3*t**7/280 - 3*t**6/80 + 5*t**3/2 - 17*t**2. Let u(v) be the first derivative of p(v). Factor u(q).
-3*q**2*(q - 3)**2/2
Let b be 5*(-6)/(-6) + 116/(-24). Factor -1/6*w**4 + b*w**2 - 1/2*w**3 + 0 + 1/2*w.
-w*(w - 1)*(w + 1)*(w + 3)/6
Let z(j) = 3*j**2 - 79*j - 4 + 18 + 74*j. Let h(m) = 8*m**2 - 16*m + 41. Let u(a) = 4*h(a) - 11*z(a). Factor u(y).
-(y - 1)*(y + 10)
Let f(x) = -x**3 - 6*x**2 + 35*x + 198. Let s be f(-7). Solve -4/9*m + 0*m**s + 4/9*m**3 + 0 = 0 for m.
-1, 0, 1
Let j = -28 - -29. Suppose -p - 12 = -m, -4*p - j = 3*m - 2. Determine s so that -7*s**2 + m*s**2 - 2*s**2 - 8*s = 0.
-4, 0
Let k(s) be the first derivative of s**6/24 - 111*s**5/20 + 109*s**4/8 + s**3/6 - 219*s**2/8 + 109*s/4 + 134. Factor k(l).
(l - 109)*(l - 1)**3*(l + 1)/4
Factor 154/3*c + 316/3 - 2/3*c**2.
-2*(c - 79)*(c + 2)/3
Let p(y) be the first derivative of -3*y**4/4 + 2*y**3 + 21*y**2/2 + 12*y + 61. Determine v so that p(v) = 0.
-1, 4
Find w, given that -1/3*w**4 - 125/3 + 200/3*w + 16/3*w**3 - 30*w**2 = 0.
1, 5
Let v be -1 - 249/(-198) - (-48)/(-528). Let -1/3*d**2 + 0 + v*d = 0. What is d?
0, 1/2
Suppose -w = 13*w. Let q(h) be the second derivative of 1/4*h**3 - 3/40*h**5 + h + w*h**2 + 0*h**4 + 0. Factor q(k).
-3*k*(k - 1)*(k + 1)/2
Let x(v) be the first derivative of v**4/8 + v**3 + 11*v**2/4 + 3*v - 227. Factor x(t).
(t + 1)*(t + 2)*(t + 3)/2
Let v(y) = y**3 + 9*y**2 + 8*y. Let t be v(-8). Let i be 2 + t/(2 + -5). Factor 2*z**i + 5*z**4 - 2*z**2 + 3*z**2 - 4*z**4 + 3*z**3 + z.
z*(z + 1)**3
Let o be 7/3 - 19/57. Suppose 4*r + 3 = d + 6, -24 = -2*d - o*r. Factor -b**5 + b**5 + d*b**4 + 0*b**5 - 3*b**5.
-3*b**4*(b - 3)
Solve 11*a**2 - 14*a + 0*a**2 - 240 - 8*a**2 - 100*a = 0 for a.
-2, 40
Let b(v) be the first derivative of 14 - 7*v**3 - 27/4*v**4 + 30*v**2 - 12*v. Factor b(i).
-3*(i - 1)*(i + 2)*(9*i - 2)
Let i(r) = r**3 - 9*r**2 + 10*r - 9. Let q be i(8). Let m be 4/(0 + -2 + 4). Let -72*t - 16 + 9*t**2 + 12*t + q*t**m = 0. What is t?
-1/4, 4
Suppose 24 = -6*s + 3*s. Let o be 4 + -1 - s/8. Factor -3 + 12*l**3 - 13*l**2 + 12*l - 3*l**4 - 5*l**2 + 0*l**o.
-3*(l - 1)**4
Let o(l) be the second derivative of l**7/280 - l**6/5 + 24*l**5/5 - 64*l**4 + 2*l**3 - 4*l. Let g(j) be the second derivative of o(j). Factor g(d).
3*(d - 8)**3
Let s(f) be the first derivative of -4/3*f**3 - 8*f**2 - 9 - 12*f. Find w such that s(w) = 0.
-3, -1
Let o = -16 + 18. Suppose 3*f + o = 8. Factor -3 + 1 + 2 + 60*j**4 + 9*j**3 - 6*j**f.
3*j**2*(4*j - 1)*(5*j + 2)
Let g = -8/701 - -82774/4907. Let p = 521/28 - g. Factor -5/4*j**3 + p*j**4 + 5/4*j + 1/2 - 9/4*j**2.
(j - 1)**2*(j + 1)*(7*j + 2)/4
Let h(s) be the third derivative of s**8/11088 - s**7/3080 - s**6/3960 - 11*s**5/30 + 29*s**2. Let d(f) be the third derivative of h(f). Factor d(y).
2*(y - 1)*(10*y + 1)/11
Let j(x) be the third derivative of -24*x**2 + 1/525*x**7 + 0*x**4 - 1/600*x**6 - 1/1680*x**8 + 0 + 0*x**3 + 0*x + 0*x**5. Let j(o) = 0. What is o?
0, 1
Let q(y) be the first derivative of y**6/6 - 3*y**4/4 - 2*y**3/3 - 168. Factor q(o).
o**2*(o - 2)*(o + 1)**2
Factor 16 + z**3 - 4152*z + 4172*z + 2*z**2 - 2*z**2 + 8*z**2.
(z + 2)**2*(z + 4)
Let x(j) = -j**2. Let q(c) = 2*c**3 + 2*c**2 - 26*c - 30. Let o(g) = q(g) - 4*x(g). Factor o(l).
2*(l - 3)*(l + 1)*(l + 5)
Let i(u) be the third derivative of -2*u**7/525 + u**6/50 + u**5/5 + 17*u**4/30 + 4*u**3/5 + 309*u**2. Find m such that i(m) = 0.
-1, 6
Let i = -2944 + 2947. Factor 1/2*s + 0 + 5/6*s**i - 7/6*s**2 - 1/6*s**4.
-s*(s - 3)*(s - 1)**2/6
Let k(z) be the first derivative of 23 + 2/9*z - 1/27*z**3 + 1/18*z**2. Suppose k(n) = 0. Calculate n.
-1, 2
Factor -4/5*n**2 - 68/5 - 72/5*n.
-4*(n + 1)*(n + 17)/5
Suppose -9*y + 0*y + 0*y = -27. Factor 0*u**2 - u - 2/3 + 1/3*u**y.
(u - 2)*(u + 1)**2/3
Let i be (-44)/(-2)*-2 + 3. Let o = i - -41. Solve o + 1/2*s**2 - s = 0.
0, 2
Let r(k) = k**3 + 8*k**2 - 16*k + 40. Let l be r(-10). Let i(u) be the first derivative of 3/2*u**4 + 3 + u**3 + 0*u**2 + l*u. Suppose i(p) = 0. What is p?
-1/2, 0
Let f(a) = -a**3 + 16*a**2 + 266*a + 60. Let h be f(-10). Let 46/11*z**2 + 34/11*z**4 - 8/11 - 6*z**3 - 6/11*z**5 + h*z = 0. Calculate z.
-1/3, 1, 2
Let n(w) be the third derivative of -w**5/42 - w**4/168 - 19*w**2. Factor n(k).
-k*(10*k + 1)/7
Let u = -1 + 5. Suppose -l = l - u. Solve 7*n**l + 2 + 0 + 0*n - 13*n**2 - 4*n = 0.
-1, 1/3
Let r(o) = 4*o + 8. Let d be r(3). Suppose d = 5*p + 5*q, 4*p + 2*q + 9 = 25. Factor -2/17*w**p - 54/17*w - 54/17*w**2 - 18/17*w**3 + 0.
-2*w*(w + 3)**3/17
Let z(l) be the third derivative of 4/3*l**3 - 10*l**2 - 1/60*l**6 + 0*l + 1/5*l**5 + 0 - 3/4*l**4. Solve z(p) = 0 for p.
1, 4
Suppose 5*x - 23 - 2 = 5*i, -12 = 4*i. Determine f so that 34*f + 33*f**2 + x*f**3 + 7*f**3 - 16*f = 0.
-3, -2/3, 0
Suppose 2*z - 18 = -4*z. Solve 3*x + 0*x - 4*x**4 + 5*x - 2*x**5 + 16*x**2 - 7*x**z + 13*x**3 = 0 for x.
-2, -1, 0, 2
Let p(d) = d**2 - 2*d + 1. Let k be p(3). Suppose -4 = -4*i + 16. Factor -q**2 + 2*q**3 - 3*q**k - i*q**4 + 3*q**3 + 5*q**4 - q.
-q*(q - 1)**2*(3*q + 1)
Suppose -26*w + 14 = -38. Factor 0*z**w - 2/5*z**4 + 0 + 0*z + 2/5*z**5 + 0*z**3.
2*z**4*(z - 1)/5
Solve 42 - 23*h + 354*h**2 + 360*h**2 - 713*h**2 = 0.
2, 21
Let a(k) be the first derivative of k**6/7 + 2*k**5/35 - 3*k**4/14 - 2*k**3/21 + 212. Let a(z) = 0. What is z?
-1, -1/3, 0, 1
Suppose -25*y = -16*y - 36. Let w(f) be the second derivative of 0 + 7*f - f**2 + 17/20*f**5 + 11/6*f**3 - 7/4*f**y - 1/6*f**6. Suppose w(t) = 0. Calculate t.
2/5, 1
Suppose 3*d + 7 = -3*g + 10, -2*g - 8 = -3*d. Suppose -24/7*x - 3/7*x**d - 48/7 = 0. Calculate x.
-4
Let y(t) be the second derivative of -3*t**5/20 + 25*t**4/24 + t**3 + 21*t**2/2 + 6*t. Let l(b) be the first derivative of y(b). Factor l(u).
-(u - 3)*(9*u + 2)
Suppose 326/3 - 2/3*g**2 + 108*g = 0. What is g?
-1, 163
Let a(b) = b - 16. Let q be a(16). Suppose q = 3*i - 10*i + 91. Factor -t - i*t**2 + 24*t**2