65). Factor 0 + 0*q + 0*q**h - 3/2*q**3 - 9/4*q**4 - 3/4*q**5.
-3*q**3*(q + 1)*(q + 2)/4
Let m = 13901/100494 - 12/9305. Let q = m + 4/135. What is x in -2/3*x - 5/6*x**2 + q = 0?
-1, 1/5
Let b be (-4 - -2) + (-16)/(-2). Suppose -3*t = -0*t - b. Let t*p**4 - 5*p**5 - 4*p**4 + 3*p**5 + 4*p**4 = 0. What is p?
0, 1
Let k = 7 + -5. Suppose 3 = c + 1, 2*d - k*c = 2. Suppose -d*w + w + 3*w**2 - 5*w + w = 0. What is w?
0, 2
Factor -2*h + 7/4 + 1/4*h**2.
(h - 7)*(h - 1)/4
Let o(w) be the first derivative of -6/11*w - 10/33*w**3 - 7/11*w**2 + 31 - 1/22*w**4. Let o(k) = 0. Calculate k.
-3, -1
Let b(s) = 4*s**4 - 4*s**3 - 30*s**2 - 6*s + 6. Let k(d) = -12*d**4 + 12*d**3 + 89*d**2 + 17*d - 17. Let h(p) = -17*b(p) - 6*k(p). Factor h(u).
4*u**2*(u - 3)*(u + 2)
Suppose -5*l = -2*l - 54. Let m be 351/l*4/3. Find z such that -9*z**4 + 8 + 12*z**3 + 11*z**4 + 13*z + m*z**2 + 11*z = 0.
-2, -1
Let f = 47 + -42. Let c(j) = 5*j**3 + 5*j**2 - 5*j. Let d(x) = -3*x**3 - 2*x**2 + 2*x. Let b(r) = f*d(r) + 2*c(r). Factor b(v).
-5*v**3
Suppose 9/2*k**3 + 19/2*k**2 - 3 + 1/2*k - 5/2*k**4 - k**5 = 0. What is k?
-3, -1, 1/2, 2
Let 371*b + 3*b**4 - 317*b - 2*b**2 + 24*b**3 + 65*b**2 = 0. Calculate b.
-3, -2, 0
Factor -5*t - 19/6*t**2 + 2/3*t**3 + 0.
t*(t - 6)*(4*t + 5)/6
Let d(n) be the second derivative of n**7/42 - 2*n**6/15 + n**5/4 - n**4/6 - 44*n. Factor d(o).
o**2*(o - 2)*(o - 1)**2
Let d(g) be the second derivative of -g**4/78 - 16*g**3/13 - 576*g**2/13 - 5*g - 12. Suppose d(t) = 0. Calculate t.
-24
Let y(l) be the third derivative of 0 - 8/3*l**3 + 5/6*l**4 - 27*l**2 + 0*l - 1/15*l**5. Solve y(r) = 0 for r.
1, 4
Let f = 0 + 2. Suppose 8 = 3*m + m. Find t such that 2 - 8*t + 7*t**3 + 0*t**3 - f*t**m + t = 0.
-1, 2/7, 1
Let i(k) = 7*k**3 + 3*k**2 - 3*k + 1. Let w(s) = 105 + s - 105 - s**3. Let d(v) = i(v) + 6*w(v). Factor d(l).
(l + 1)**3
Let y(k) = k**3 + 10*k**2 - 15*k - 4. Let n(g) = -4*g**3 - 30*g**2 + 45*g + 11. Let s(b) = -4*n(b) - 11*y(b). Suppose s(x) = 0. What is x?
-3, 0, 1
Let 88/3*g**3 - 17/3*g**4 + 1/3*g**5 + 144 - 144*g - 24*g**2 = 0. What is g?
-2, 1, 6
Determine l so that -7*l**3 + 172*l**2 - 101 - 678 - 3*l**3 + 131 - 666*l = 0.
-4/5, 9
Suppose -622*v = -620*v - 4. Let l(z) be the second derivative of -2/5*z**5 + 2/15*z**6 + 0 + 2/3*z**3 + z + 2/21*z**7 + v*z**2 - 2/3*z**4. Factor l(i).
4*(i - 1)**2*(i + 1)**3
Suppose 7*o + 3197 - 3218 = 0. Let d(j) be the first derivative of 0*j**2 - 1/18*j**o + 1/12*j**4 + 11 + 0*j - 1/30*j**5. Let d(m) = 0. Calculate m.
0, 1
Find x, given that 12*x**3 - 3928*x**2 - 11 + 31 + 3860*x**2 + 36*x = 0.
-1/3, 1, 5
Suppose 12 - 2 = 5*l. Factor 3*g + 3*g**3 + 2*g**2 - 4*g**l - 4*g**2.
3*g*(g - 1)**2
Let p = 60 + -54. Let d(f) be the second derivative of f**2 - 2/3*f**3 - 4*f + 1/5*f**5 + 0*f**4 + 0 - 1/15*f**p. Solve d(j) = 0.
-1, 1
Let b(p) be the second derivative of -2*p**2 - 21*p - 31/2*p**5 + 11/2*p**4 + 0 - 35/3*p**6 + 11/3*p**3. Solve b(t) = 0.
-1, -2/7, 1/5
Let c(p) be the third derivative of p**6/24 - 3*p**5/4 - 95*p**4/8 + 325*p**3/6 + 691*p**2. Factor c(k).
5*(k - 13)*(k - 1)*(k + 5)
Let q = 129 - 129. Let b(y) be the third derivative of -2*y**2 + 1/210*y**5 - 1/735*y**7 + 0*y**3 - 1/42*y**4 + q*y + 1/210*y**6 + 0. Factor b(r).
-2*r*(r - 2)*(r - 1)*(r + 1)/7
Let h(o) be the second derivative of -o**6/20 + 21*o**5/40 - 15*o**4/8 + 9*o**3/4 - 31*o - 2. Factor h(t).
-3*t*(t - 3)**2*(t - 1)/2
Let j(i) = i**3 - 2*i**2 + 1. Let x(f) = -12*f**3 + 26*f**2 - 18. Let m(d) = 10*j(d) + x(d). Find o, given that m(o) = 0.
-1, 2
Let j = 14983/2611 - 9/373. Factor j*n - 8/7 - 18/7*n**2.
-2*(n - 2)*(9*n - 2)/7
Let z(k) = -29*k**3 + 60*k**2 - 18*k + 2. Let x(v) = -60*v**3 + 120*v**2 - 35*v + 5. Let u(c) = 2*x(c) - 5*z(c). Determine h so that u(h) = 0.
0, 2/5, 2
Find i such that 40/7*i + 24/7 + 18/7*i**2 + 2/7*i**3 = 0.
-6, -2, -1
Let j be 9*2/3 - 3. Factor 6*t**5 - 13*t**5 + 21 - 47*t**4 - 104*t**2 - 16*t - 112*t**j - 5.
-(t + 1)*(t + 2)**3*(7*t - 2)
Suppose 18/11*z**2 - 2064/11*z + 59168/11 = 0. What is z?
172/3
Let h be 0/((-9)/45*5). Let q(d) be the first derivative of -11 + 5/8*d**4 + 4/3*d**3 + h*d + d**2 + 1/10*d**5. Factor q(c).
c*(c + 1)*(c + 2)**2/2
Let f(w) be the third derivative of -w**6/30 + 11*w**5/15 - 8*w**2 + 5. Suppose f(t) = 0. Calculate t.
0, 11
Let w(i) = -i**2 - i + 5. Let r(g) = -g + 3. Let k(q) = 3*q - 10. Let o(y) = 2*k(y) + 7*r(y). Let v(j) = 10*o(j) - 2*w(j). Factor v(s).
2*s*(s - 4)
Suppose 66*i = 44*i + 31*i - 27. Solve 4/5 + 8/5*w + w**2 + 1/5*w**i = 0.
-2, -1
Let i be (2/8)/((-9)/(-24)). Suppose 23*g + 275 = 321. Find d, given that -i*d**g + 2/3*d + 4/3 = 0.
-1, 2
Let u(w) = 3*w**4. Let i(q) = 15*q**4 - 31*q**3 + 50*q**2 + 156*q + 72. Let k(g) = -i(g) + 4*u(g). Factor k(v).
-(v - 6)**2*(v + 1)*(3*v + 2)
What is w in -22 + 33 - 1 + 5*w - 5*w**2 = 0?
-1, 2
Let u(h) = 2*h**4 + 3*h**3 - 2*h**2 - h + 1. Let n(q) = -q**3 - q - 1. Let x(c) = -n(c) - u(c). Factor x(l).
-2*l*(l - 1)*(l + 1)**2
Let t = 77 - 76. Let f(c) = 5*c**4 - 4*c**3 + 25*c**2 - 22*c + 4. Let z(a) = a**4 + a**3 + a**2 - a + 1. Let j(v) = t*f(v) - 4*z(v). Factor j(i).
i*(i - 3)**2*(i - 2)
Suppose 5*f + 15 = 5*y, 3*y - 9 = -4*f + 9*f. Let g(n) be the first derivative of 8 + 2/27*n**3 - 1/3*n**2 + f*n. Factor g(s).
2*s*(s - 3)/9
Factor -86/7*p + 2/7*p**2 - 88/7.
2*(p - 44)*(p + 1)/7
Find b such that -174/11*b**2 - 2/11*b**3 + 174/11 + 2/11*b = 0.
-87, -1, 1
Let k be 4 + 1 + (1*-1)/(-17 - -18). Factor 3*z**2 + 3/2*z**k + 0 + 3/4*z**5 + 0*z - 21/4*z**3.
3*z**2*(z - 1)**2*(z + 4)/4
Let h(f) be the second derivative of 4/9*f**3 + 0*f**2 - 1/9*f**4 - 22*f - 1/30*f**5 + 1/90*f**6 + 0. Determine r, given that h(r) = 0.
-2, 0, 2
What is q in -12*q**3 + 7*q**3 + 4*q**3 - 400 - 260*q - 3*q**3 - 56*q**2 + 0*q**3 = 0?
-5, -4
Suppose v = 5*d + 28, 4*v - 4*d + 6*d = 2. Solve 2*t**2 + 4/3 - v*t - 1/3*t**3 = 0 for t.
1, 4
Suppose -85*h + 40*h + 38*h = 0. Let d(z) be the third derivative of 3/25*z**5 + 0 + 1/150*z**6 + 18/5*z**3 + 9/10*z**4 + 6*z**2 + h*z. Factor d(w).
4*(w + 3)**3/5
Let h(n) = -2*n - 1. Suppose -2 = 2*p + 4. Let c be h(p). Factor -2*b**2 + 2*b**3 + 2*b**2 - 7*b**c + 5*b**5.
-2*b**3*(b - 1)*(b + 1)
Let c(a) = -27*a**2 + 48*a - 18. Suppose 4*j + k - 9 = 0, -5*k - 2 = 2*j + 7. Let y(s) = 2 + 13*s**2 - 7*s - 17*s + 7. Let u(l) = j*c(l) + 5*y(l). Factor u(w).
-(4*w - 3)**2
Let m(i) be the third derivative of -i**5/330 - 19*i**4/132 - 6*i**3/11 + 96*i**2. Find y such that m(y) = 0.
-18, -1
Let y(m) be the third derivative of -m**8/168 + m**7/105 + m**6/30 - m**5/15 - m**4/12 + m**3/3 - 3*m**2 + 9. Factor y(g).
-2*(g - 1)**3*(g + 1)**2
Suppose -b + 7 + 0 = n, 5*b - 14 = 2*n. Suppose 0 = m - n, 5*m - 107 = z - 3*z. What is s in s**4 + 51*s**3 - 2*s - 1 - 95*s**3 + z*s**3 = 0?
-1, 1
Factor -18*r - 26*r**4 + 38*r**4 + 4*r**3 + 12*r**3 + 2*r**5 - 8 - 4*r**2.
2*(r - 1)*(r + 1)**3*(r + 4)
Let g be 6/12*(21/3 + 1). Let i(q) be the third derivative of 0 - 1/2*q**g + q**2 - 2*q**3 + 0*q - 1/20*q**5. Factor i(a).
-3*(a + 2)**2
Let l(g) be the first derivative of 2*g**4 - 7*g**3/3 - g**2/2 + 14. Determine n, given that l(n) = 0.
-1/8, 0, 1
What is z in 45*z**3 + 13*z**2 - 160*z - 35*z**4 + 8393 - 5*z**3 - 8373 + 122*z**2 = 0?
-2, 1/7, 1, 2
Suppose 1 - 11 = -2*f. Let d = 4 + -3. Factor 1 - 3*n**f - d + 5*n**4 - 8*n**4.
-3*n**4*(n + 1)
Let m = 53/18 - 193/90. Suppose -2/5*v**2 + 6/5*v - m = 0. What is v?
1, 2
Let r(s) = 3*s**2 - 39*s - 30. Let u be r(14). Let x(v) be the third derivative of 0*v + 0*v**3 - 1/42*v**4 - 1/210*v**5 + 0 + 1/420*v**6 + u*v**2. Factor x(o).
2*o*(o - 2)*(o + 1)/7
Let i(h) = 5*h**3 + 7*h**2 - 5*h - 1. Let u = 17 + -23. Let m(l) = -29*l**3 - 41*l**2 + 29*l + 7. Let w(s) = u*m(s) - 34*i(s). Factor w(k).
4*(k - 1)*(k + 1)*(k + 2)
Suppose 5*z = 9*z. Suppose k + z*k - 2 = 0. Solve 5*a - a**3 + 6*a**2 - 7*a**4 - 4*a**3 + 3*a**k - 2 = 0 for a.
-1, 2/7, 1
Factor 126405 - 19*o**2 + 31*o**2 - 7*o**2 + 1590*o.
5*(o + 159)**2
Suppose 2 = -s - s - 4*u, 25 = 5*s - 5*u. Suppose 3*m**2 - 1 + 4 + 6*m - s = 0. What is m?
-2, 0
Let l be 3/(-1*6/(-8)). Let -5*b**2 + 7*b**2 + 2*b**5 - 14*b**4 + 14*b**3 - 16*b + l*b**4 + 8 = 0. What is b?
-1, 1, 2
Let r(w) = w**2 + 120*w - 241. Let q(a) = 40*a - 81. Let m(g) = 8*q(g) - 3*r(g). Determine n so that m(n) = 0