r?
-1, -1/3, 1
Let o(z) be the third derivative of z**5/270 - 4*z**4/27 + 16*z**3/9 + 328*z**2. Determine y, given that o(y) = 0.
4, 12
Let p(c) = 8*c - 37. Let q be p(5). Let d(o) = -o**2 + 5*o + 8. Let t be d(6). Factor -b - t*b**4 + b - 4*b**q + 2 + 2*b + 2*b.
-2*(b - 1)*(b + 1)**3
Let h = 646 + -644. Let -30*c + 5/2*c**h + 90 = 0. What is c?
6
Let d(t) be the first derivative of 15 - 10*t**2 + t**5 - 35/3*t**3 + 0*t - 5/2*t**4. Determine m, given that d(m) = 0.
-1, 0, 4
Suppose -69*h + 68*h = -2. Let m be (h/5)/((-9)/(-15)). Factor 1/6*t**2 + 1/2*t - m.
(t - 1)*(t + 4)/6
Suppose -4*s - 12 = -3*u, 5*u = -2*s + 32 + 14. Suppose -i - u = -5*i. Let -8/5 - i*y**2 + 2/5*y**3 + 16/5*y = 0. What is y?
1, 2
Let q(g) be the first derivative of g**7/112 - 3*g**5/160 + g + 10. Let w(s) be the first derivative of q(s). Suppose w(t) = 0. What is t?
-1, 0, 1
Let f(m) = -4*m - 58. Let t be f(-15). Solve -4776 - t*r + 17*r + 4794 + 3*r**2 = 0 for r.
-3, -2
Let w(h) = h**3 - 6*h**2 - 15*h. Let f be w(8). Let r(t) = t**2 + 2*t - 4. Let m be r(-5). Factor -f + 36*g - 53*g**2 - 6*g**3 + m*g**2 + 2*g**2 + 18*g**3.
4*(g - 2)*(g - 1)*(3*g - 1)
Let k(m) = m**2 - 275*m - 2556. Let s be k(-9). Factor 3/4*g**4 + s*g - 3/4*g**2 + 0*g**3 + 0.
3*g**2*(g - 1)*(g + 1)/4
Find n such that 57*n**2 - 6 - 705*n - 16*n**2 - 78 + 24*n**2 - 26 = 0.
-2/13, 11
Let w(k) be the third derivative of k**7/84 - k**6/180 + 7*k**3/6 + 18*k**2. Let g(l) be the first derivative of w(l). Factor g(t).
2*t**2*(5*t - 1)
Let u(j) be the second derivative of -j**5/140 - 89*j**4/28 - 7921*j**3/14 - 704969*j**2/14 + 70*j. Factor u(w).
-(w + 89)**3/7
Let x(j) be the third derivative of -3/2*j**3 - 1/24*j**4 + 5*j**2 + 1/120*j**6 + 0 + 2*j + 3/20*j**5. Find y, given that x(y) = 0.
-9, -1, 1
Let d be 1*(0 + (4 - -1)). Suppose o = 2*m + 3, -d*o + 8 + 25 = -4*m. Factor 5*g**2 + 24*g + 7*g**2 + o + 2*g**3 + 7.
2*(g + 2)**3
Let n be (-2)/2 - -2 - -4. Suppose -n*y + 4*y + 8*y = 0. Determine s so that -3/5*s**3 + 0*s + y + s**4 - 2/5*s**2 = 0.
-2/5, 0, 1
Suppose -5*p = 7*p - 24. Let b(h) be the third derivative of 0*h**3 + h**p + 0*h + 1/108*h**4 + 0 + 1/540*h**6 - 1/135*h**5. Factor b(t).
2*t*(t - 1)**2/9
Let z(a) be the second derivative of 0 - 1/48*a**4 + 4*a - 1/2*a**2 - 5/24*a**3. Find v, given that z(v) = 0.
-4, -1
Let h(x) be the first derivative of -x**4/18 + 4*x**3/9 - 11*x**2/9 + 4*x/3 + 13. Determine y so that h(y) = 0.
1, 2, 3
Let r(y) = -y**2 + y. Let d(h) = -14*h**2 + 22*h. Let i = -81 + 93. Let w(q) = i*r(q) - d(q). Solve w(l) = 0 for l.
0, 5
Let b(s) = -s**3 - s**2 - 1. Let u(q) be the third derivative of -q**6/40 - q**5/20 + q**3/3 + 6*q**2. Let a(h) = 2*b(h) + u(h). Solve a(o) = 0.
-1, 0
Let a(l) be the first derivative of -3*l**3/2 - 321*l**2/4 + 54*l + 97. Find m such that a(m) = 0.
-36, 1/3
Suppose -4*c - 20*c = -3429 + 3429. Factor 1/2*g**3 - 2/3*g + c + 11/6*g**2.
g*(g + 4)*(3*g - 1)/6
Let a = 113 + -99. Let x be 6/(-15) + (2 - a/(-10)). Suppose 6/5*m + 6/5*m**2 + 2/5*m**x + 2/5 = 0. Calculate m.
-1
Suppose 15 = 17*b - 22*b + 3*c, -10 = 4*b - 2*c. Factor -1/3*o**4 + 1/3*o**3 + 0*o + 0*o**2 + b.
-o**3*(o - 1)/3
Let b = 2709 + -2709. Factor -5/2*m - 1/2*m**2 + b.
-m*(m + 5)/2
Let u(c) = 10*c**3 + 740*c**2 + 13668*c + 22. Let t(f) = -2*f**3 - 148*f**2 - 2734*f - 4. Let x(o) = 22*t(o) + 4*u(o). Solve x(p) = 0 for p.
-37, 0
Let x = 8749108/315 + -27775. Let a = 4/45 - x. Factor 2/7 + 1/7*i**3 - 2/7*i**2 - a*i.
(i - 2)*(i - 1)*(i + 1)/7
Determine n so that 2/19*n**2 + 3698/19 - 172/19*n = 0.
43
Let x(q) be the second derivative of -q**4/66 - 2*q**3/11 + 7*q**2/11 + 2*q - 6. Factor x(v).
-2*(v - 1)*(v + 7)/11
Let b be (-6)/(24/(-14)) - 3/(-6). Factor 27*f**2 + 6*f - 15*f**3 + 51*f**3 + 6*f**4 + 9*f**b.
3*f*(f + 1)**2*(5*f + 2)
Let z(l) be the third derivative of -l**5/80 - 5*l**4/16 - 9*l**3/8 - 115*l**2. Solve z(o) = 0 for o.
-9, -1
Let z(x) be the first derivative of -5/12*x**4 + 29/30*x**5 + 0*x - 1/2*x**2 - 24 + 5/18*x**6 - 23/18*x**3. Find w, given that z(w) = 0.
-3, -1/2, -2/5, 0, 1
Factor 3*x - 10*x**3 + 27*x**4 - 31*x**3 - 7*x**3 - 40*x**2 - 53*x**2 - 21*x.
3*x*(x - 3)*(x + 1)*(9*x + 2)
Suppose -16*d = -19*d. Let t(m) be the first derivative of 0*m**4 + 0*m**2 + d*m - 3 - 3/20*m**5 + 1/4*m**3. Factor t(k).
-3*k**2*(k - 1)*(k + 1)/4
Let g(m) be the first derivative of m**4/20 + 6*m**3/5 + 54*m**2/5 - 7*m + 30. Let b(k) be the first derivative of g(k). Suppose b(p) = 0. Calculate p.
-6
Let z(h) = h**2 + 7*h + 14. Let u be z(-2). Factor 6*v**3 - 11*v + v**5 - 3*v + 6*v**2 + 7*v + 3 - 4*v**2 - 5*v**u.
(v - 3)*(v - 1)**3*(v + 1)
Let a be (9 - (-1038)/(-126))*(-3)/(-8)*4. Suppose 2/7*l**3 + 0*l - 6/7*l**2 + a = 0. What is l?
-1, 2
Let l = -10/289 + -5877/22253. Let y = l - -8/11. Suppose 12/7*m - 12/7 - y*m**2 = 0. Calculate m.
2
Suppose -12*n + 6 - 6 = 0. Suppose n = -214*d + 210*d + 12. Determine x, given that -69/2*x**d + 3 - 39/2*x + 81/2*x**2 + 21/2*x**4 = 0.
2/7, 1
Suppose -13*n = 176 - 332. Determine k so that -45/2*k**2 + 24*k**4 - 3/2 - n*k + 12*k**3 = 0.
-1, -1/4, 1
Suppose 8*f - 4 = 20. What is k in -3 - 2*k**f + 3*k + 0*k**2 + 3*k**2 - k**3 + 0*k**2 = 0?
-1, 1
Suppose 110 = 2*i + 100. Let f(b) be the first derivative of -b - 4 + 1/15*b**i + 2/9*b**3 + 2/3*b**2 - 1/3*b**4. Determine g, given that f(g) = 0.
-1, 1, 3
Factor 3/5*l**4 + 6/5*l**3 + 0 + 3/5*l**2 + 0*l.
3*l**2*(l + 1)**2/5
Factor 3*z**2 + 6*z + 10 - 20 + 10.
3*z*(z + 2)
Suppose 3*a - 3*i - 21 = 0, 0*i - 4*i = -a + 22. Factor -4*c + c**a + 11*c**2 - 4*c.
4*c*(3*c - 2)
Let q(i) be the second derivative of i**5/200 + i**4/30 - 7*i**3/20 - 57*i. Determine c, given that q(c) = 0.
-7, 0, 3
Let s(b) be the second derivative of -1/9*b**3 + 1/30*b**5 + 0*b**4 - b + 0 + 0*b**2. Factor s(g).
2*g*(g - 1)*(g + 1)/3
Suppose -4*m - 2*f = -10, -5*f + 2*f = 3*m - 3. Let z = -1 - -8. Let -38 - 5*n**2 + 9*n**3 + 2*n**5 + n - z*n**m + 38 = 0. Calculate n.
0, 1/2, 1
Let l(f) = f**2 - 5. Let i be l(3). Factor s**3 + i*s + 6*s**2 - 5*s**3 - 6*s**3.
-2*s*(s - 1)*(5*s + 2)
Suppose -4*w + 3*w = -3, -4*w = -3*u. Factor -510 - u*d**2 + 510 + d.
-d*(4*d - 1)
Let b = -3 + 5. Let f(s) = -18*s - 12*s**3 - 3 + 25*s**2 + s**b + 0 + 1. Let t(k) = 11*k**3 - 25*k**2 + 18*k + 1. Let n(q) = 5*f(q) + 6*t(q). Factor n(i).
2*(i - 2)*(i - 1)*(3*i - 1)
Let y = -89 + 74. Let p be 2*65/175 - 6/y. Factor p + 4/7*r - 8/7*r**2 - 4/7*r**3.
-4*(r - 1)*(r + 1)*(r + 2)/7
Let h be -12*(30 - 2709/90). Determine d so that -h - 21/5*d - 3*d**2 = 0.
-1, -2/5
Let b = 1666 - 1666. Factor -2/3*i + 2/9*i**3 + b*i**2 + 4/9.
2*(i - 1)**2*(i + 2)/9
Suppose -5*b = -20 + 10. Let v(c) be the second derivative of -1/36*c**4 + b*c + 1/6*c**3 + 0 + 0*c**2. Factor v(k).
-k*(k - 3)/3
Let y be ((-37)/(-10) - 33/(-110)) + 0. Let u(d) be the third derivative of 2/15*d**3 - 1/20*d**y + 1/150*d**5 + 0 + 0*d + 3*d**2. Factor u(g).
2*(g - 2)*(g - 1)/5
Let q(s) be the third derivative of s**6/180 + s**5/30 - 165*s**2. Factor q(x).
2*x**2*(x + 3)/3
Determine z so that -5/6*z + 1 + 1/6*z**2 = 0.
2, 3
Suppose 6*i - 2*i = 44. Let w(n) = -1 + 7 + 8 + 20*n**2 - 2 + 24*n. Let t(v) = 7*v**2 + 8*v + 4. Let x(q) = i*t(q) - 4*w(q). Factor x(d).
-(d + 2)*(3*d + 2)
Let n(l) be the third derivative of l**5/60 + l**4/4 - 9*l**3/2 + 28*l**2. Factor n(f).
(f - 3)*(f + 9)
Suppose 3*i - 7 = -83*x + 85*x, 4*i = -x + 24. Solve -4/3*l + 35/3*l**i + 0 - 4*l**2 + 59/3*l**3 + 34*l**4 = 0.
-2, -1, -1/5, 0, 2/7
Let j(o) = 405*o**4 - 1245*o**3 + 365*o**2 - 55*o + 55. Let b(k) = -29*k**4 + 89*k**3 - 26*k**2 + 4*k - 4. Let u(a) = 55*b(a) + 4*j(a). Factor u(i).
5*i**2*(i - 3)*(5*i - 2)
Suppose -5*l + 50 - 20 = 0. Let r be l/4*46/207. Determine j so that 0 + r*j**2 + 0*j - 1/3*j**3 = 0.
0, 1
Let m(d) be the second derivative of -d**4/102 - d**3/17 - 2*d**2/17 + 135*d - 2. Let m(k) = 0. What is k?
-2, -1
Let i(b) = -b - 2. Let u be i(-6). Let g be ((-6)/(-3) + u)*1. Solve 2*l + 30*l**2 + g*l - 26*l**2 + 4 = 0.
-1
Let x(r) = 20 + 8*r - 2*r**3 - 11*r**2 - 4*r**3 + 7*r**3. Let h be x(10). Factor 0 + 2/9*j**3 + h*j**2 - 2/9*j.
2*j*(j - 1)*(j + 1)/9
Factor 0 + 960/7*x**3 + 0*x + x**5 + 166/7*x**4 - 288/7*x**2.
x**2*(x + 12)**2*(7*x - 2)/7
Let b = 66 - 88. Let y = 47/2 + b. Solve -y*c**2 + 0*c + 0 + 3/2*c**4 + 0*c**3 = 0.
-1, 0, 1
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