 2
Let i(t) = 5*t - 30. Let w be i(6). Suppose w = 2*r - 1 - 3. Determine s, given that 1/2*s**3 + 3/2*s**r + 0*s + 0 = 0.
-3, 0
Let r be -4 - -1 - 10/(-2). Let h(o) be the first derivative of 3/7*o**r + 2 + 2/21*o**3 + 0*o. Factor h(c).
2*c*(c + 3)/7
Let n(s) = 5*s**2 - 29*s + 4. Let r(l) = 5*l**2 + 11*l - 16*l + 5 - 25*l. Let w(j) = 5*n(j) - 4*r(j). Solve w(t) = 0.
0, 5
Determine x so that 12*x**2 + 15*x**2 + 1152 - 25*x**2 + 93*x + 3*x = 0.
-24
Factor 664/5*y + 2/5*y**2 + 55112/5.
2*(y + 166)**2/5
Suppose 3*d - 4*n - 3 = 17, 2*n = 2*d - 10. Factor d*z - z**5 + 8*z**2 + 6*z**3 - z**5 - 4*z**4 - 8*z.
-2*z*(z - 1)**2*(z + 2)**2
Let w(v) be the third derivative of -v**7/70 + v**6/20 + v**5/20 - v**4/4 + 7*v**2. Factor w(u).
-3*u*(u - 2)*(u - 1)*(u + 1)
Let c(g) = -23*g**3 - 49*g**2 - 58*g - 24. Let k(t) = -8*t**3 - 16*t**2 - 19*t - 8. Let q(z) = -3*c(z) + 8*k(z). Factor q(j).
(j + 1)*(j + 2)*(5*j + 4)
Suppose -5*q = -0*q - 15. Determine i so that -159*i**2 - 8 - 16*i - 85*i**3 + 28*i**4 - 8 - 19*i**q + 267*i**2 = 0.
-2/7, 1, 2
Let t = -859 + 863. Let a(o) be the first derivative of 0*o + 20/3*o**3 - t*o**5 - 14/3*o**6 - 4*o**2 + 9*o**4 + 3. Determine y so that a(y) = 0.
-1, 0, 2/7, 1
Find b such that -12 - b**4 + 302*b - 42*b**2 - 24 - 10*b**3 + 11*b**2 - 362*b - 6*b**2 = 0.
-3, -2
What is n in -1299/2*n**2 + 26*n**3 - 1378*n - 1/4*n**4 - 2809/4 = 0?
-1, 53
Suppose -3/2*g**5 + 0 + 9/2*g**4 + 0*g**2 + 0*g - 3*g**3 = 0. Calculate g.
0, 1, 2
Let j(s) be the first derivative of -1/2*s**2 - 1/120*s**6 + 0*s**5 + 0*s**3 + 1/24*s**4 - 3 + 0*s. Let f(i) be the second derivative of j(i). Factor f(a).
-a*(a - 1)*(a + 1)
Let u(f) = -f**2 + 83. Let t be u(-9). Factor -3/2*j**2 + t*j**4 - 1/2 - 2*j + 2*j**3.
(j - 1)*(j + 1)*(2*j + 1)**2/2
Let b = -104/9 + 242/9. Let m = b - 175/12. Let m*k + 1/2 - 1/2*k**2 - 3/4*k**3 = 0. What is k?
-1, -2/3, 1
Suppose -5*l - 45 = 5*c, 4*c = 3*l - 40 - 24. Let w = -8 - c. Factor i + 22*i**3 + 5*i**w - 18*i**4 - 3*i**2 + 29 - 4*i - 27 - 5*i**2.
(i - 1)**4*(5*i + 2)
What is f in -14/3*f - 11/9*f**2 + 8/9 = 0?
-4, 2/11
Let -32/11*x - 2/11*x**2 - 10 = 0. What is x?
-11, -5
Let i = -1/1406 - -4225/9842. Factor 6/7 - 3/7*a**2 + i*a.
-3*(a - 2)*(a + 1)/7
Let w(m) be the third derivative of 8*m**2 + 1/90*m**5 + 0*m**4 + 0*m + 0*m**3 + 0. Suppose w(k) = 0. Calculate k.
0
Suppose -2*v + 2 = -4. Suppose -48 = -4*r - 2*w, 3*r = 4*r + v*w - 12. Solve k**4 - 8*k**3 - k**4 + 2 - 3*k**4 + r*k**2 - 8*k + 5*k**4 = 0.
1
Factor -735 + 84*u - 12/5*u**2.
-3*(2*u - 35)**2/5
Let a(t) be the third derivative of t**6/600 - 23*t**5/300 - t**4/5 - 557*t**2. Solve a(g) = 0 for g.
-1, 0, 24
Let g(x) be the third derivative of x**5/330 - 2*x**4 + 528*x**3 + 7*x**2 - 7*x. Let g(c) = 0. Calculate c.
132
Factor 14/11*c**3 - 64/11*c - 74/11*c**2 + 24/11.
2*(c - 6)*(c + 1)*(7*c - 2)/11
Let w(x) be the third derivative of -1/15*x**5 + 5/12*x**4 - 8/9*x**3 + 0*x + 54*x**2 - 1/180*x**6 + 0. Determine m so that w(m) = 0.
-8, 1
Let a(q) be the second derivative of -3*q**7/7 - 3*q**6/5 + 2*q**5/5 + 2*q**4/3 + 24*q - 7. Suppose a(r) = 0. Calculate r.
-1, -2/3, 0, 2/3
Let s be 10/8 + (-1)/4. Let y be 0/(-4 + s + 4). Let y - 1/2*v**2 + 0*v = 0. Calculate v.
0
Suppose 0*j - 5*l = -4*j + 8, 8 = 4*j - l. Suppose -o - 3 = -j*o. Determine b so that -14*b**3 - 6*b**4 + b**5 + 16*b**o + 3*b**5 = 0.
0, 1/2, 1
Let o(m) = -27*m**2 + 9*m + 21. Let z(l) = 55*l**2 - 22*l - 42. Let q(n) = -7*o(n) - 3*z(n). Factor q(y).
3*(y + 1)*(8*y - 7)
Let f(g) = -g**2 + 7*g - 6. Let n be f(5). Suppose 2*o - 2*j + 1 = j, 3*o - 5*j = -n. What is p in -o*p**2 + p**2 + 7*p**2 = 0?
0
Let r be (7 - 5)/((-6)/(-4)*2). Let c(o) be the first derivative of 3*o**2 + 4*o + r*o**3 + 2. Factor c(x).
2*(x + 1)*(x + 2)
Let b(p) = p**2 + 14*p. Let u be b(0). Let v(d) be the first derivative of -8 + 2/9*d**3 - d**2 + u*d. Factor v(s).
2*s*(s - 3)/3
Solve -3/7*c**2 + 27 - 186/7*c = 0.
-63, 1
Let s(j) be the third derivative of j**8/2688 + j**7/560 - j**6/320 - 7*j**5/480 + j**4/32 + 189*j**2. Factor s(c).
c*(c - 1)**2*(c + 2)*(c + 3)/8
Factor -39/2*m + 45 + 3/2*m**2.
3*(m - 10)*(m - 3)/2
Let r(w) be the first derivative of 4*w**3/3 + 4*w**2 + 4*w - 23. Factor r(x).
4*(x + 1)**2
Factor 5 - 40*v**3 - 12 + 7 - 4*v**4.
-4*v**3*(v + 10)
Suppose -22*g + 90 = -7*g. Let f(d) be the third derivative of 1/30*d**g - 1/168*d**8 + 0*d - 3*d**2 + 0*d**4 + 0*d**5 + 0*d**3 + 0 - 1/105*d**7. Factor f(k).
-2*k**3*(k - 1)*(k + 2)
Let v(k) be the second derivative of k**6/75 + 11*k**5/150 + 11*k**4/90 + k**3/45 - 2*k**2/15 - 113*k. Solve v(j) = 0 for j.
-2, -1, 1/3
Let y(k) = 36*k**2 + 27*k - 25. Let p(a) = 9*a**2 + 7*a - 6. Let n(r) = 18*p(r) - 4*y(r). Factor n(c).
2*(3*c - 1)*(3*c + 4)
Let k(g) be the third derivative of g**6/30 + g**5/5 + g**4/2 + 2*g**3/3 - 185*g**2. Suppose k(c) = 0. What is c?
-1
Factor -10*u**3 + 8*u**2 + 2*u**4 - 5 + 5 + 0*u**2.
2*u**2*(u - 4)*(u - 1)
Let p be 1 - (-5 - (-8 - -5)). Let j(m) be the second derivative of -1/75*m**6 - 1/50*m**5 + m + 1/15*m**p + 0*m**2 + 0 + 1/30*m**4. Factor j(l).
-2*l*(l - 1)*(l + 1)**2/5
Suppose -d = d + c + 23, -3*c = 2*d + 13. Let t = d + 16. What is m in -8/3*m**3 - 5/3*m**4 + 0*m - 4/3*m**t + 0 - 1/3*m**5 = 0?
-2, -1, 0
Let q(g) be the third derivative of 5/12*g**3 + 11/120*g**5 + g + 4*g**2 + 1/80*g**6 - 19/48*g**4 + 0. Factor q(n).
(n - 1)*(n + 5)*(3*n - 1)/2
Suppose 67 = 66*x - 151 - 46. Factor 38*g**3 + 0 + 12*g**2 + 7/6*g**5 + 0*g - 41/3*g**x.
g**2*(g - 6)**2*(7*g + 2)/6
Let l = -264 - -1321/5. Let b(f) be the second derivative of 3/5*f**4 - 4*f + 0 + 4/5*f**2 + 2/75*f**6 + 14/15*f**3 + l*f**5. Let b(o) = 0. Calculate o.
-2, -1
Let m(v) be the third derivative of v**6/36 + 4*v**5/45 - 19*v**4/36 + 2*v**3/3 - 31*v**2. What is a in m(a) = 0?
-3, 2/5, 1
Let n(l) be the third derivative of 5*l**8/84 - 5*l**7/14 - 55*l**6/24 + 15*l**4/2 - 67*l**2. Suppose n(j) = 0. Calculate j.
-2, -1, 0, 3/4, 6
Find a such that -92/3 - 2/3*a**2 + 94/3*a = 0.
1, 46
Determine i, given that -126/5*i**3 + 192/5*i**2 - 2*i**4 - 56/5*i + 0 = 0.
-14, 0, 2/5, 1
Determine n so that 2*n**3 + 11*n**2 - 9*n**2 - 3*n**3 - 12*n**2 = 0.
-10, 0
Let i(m) be the third derivative of m**9/756 - m**8/210 + m**7/210 + 2*m**3 - 8*m**2. Let x(b) be the first derivative of i(b). Factor x(d).
4*d**3*(d - 1)**2
Suppose -7 = 2*g - 11. Determine u so that 5*u - 19 + 9 + 14 + u**g = 0.
-4, -1
Let m(x) be the first derivative of 14*x**5/15 + 9*x**4/8 - x**3/6 - x**2/6 + 128. Determine b, given that m(b) = 0.
-1, -1/4, 0, 2/7
Let y(g) = -12*g**4 - 139*g**3 + 133*g**2 + 134*g - 131. Let x(k) = 5*k**4 + 69*k**3 - 67*k**2 - 67*k + 66. Let p(a) = -5*x(a) - 2*y(a). Factor p(c).
-(c - 1)**2*(c + 1)*(c + 68)
Suppose -5*c = -2*g + 14, 12*c = 17*c + 10. Let z(n) be the first derivative of 1/24*n**4 - 1/30*n**5 + 0*n**3 - 1 + 0*n**g + 0*n. Let z(j) = 0. What is j?
0, 1
Factor 53792 + 97*b + 200*b + 12*b**2 - 10*b**2 + 295*b + 64*b.
2*(b + 164)**2
Let k(l) = l - 16. Let u be k(10). Let i be 1 + -2 + u/(-2). Factor 0*b + 0 - 2/7*b**i.
-2*b**2/7
Let g(j) be the first derivative of -2/15*j**2 + 1 + 2/45*j**3 - 2/5*j. Solve g(y) = 0.
-1, 3
Let z(r) = -r**2 - 7*r - 3. Let y be z(-9). Let l be ((-14)/y)/((-2)/(-6)). Factor l*w**3 - 1/2 - 1/2*w**4 - 3*w**2 + 2*w.
-(w - 1)**4/2
Let a(j) = 5*j**4 - 2*j**3 + 20*j**2 - 4*j - 3. Let n(q) = -3*q**4 + q**3 - 11*q**2 + 3*q + 2. Let r(s) = 4*a(s) + 7*n(s). Let r(f) = 0. Calculate f.
-1, 2
Let t(y) be the third derivative of -5*y**8/336 - y**7/6 + y**6 + 15*y**5 - 792*y**2. What is j in t(j) = 0?
-6, 0, 5
Find f such that 0 - 2/11*f**2 - 2*f = 0.
-11, 0
Factor 0 + 14/9*j**3 - 20/3*j**2 + 16/9*j.
2*j*(j - 4)*(7*j - 2)/9
Suppose 0 = c - 2*x - 3 - 2, 4*c = 5*x + 20. Let f = 7 - c. Find w such that -2*w - f*w**2 - w**2 - 4*w - 3 + 0 = 0.
-1
Let z(r) be the first derivative of -r**6/15 - 7*r**5/15 - 2*r**4/3 + 8*r**3/3 - r**2 + 2. Let u(y) be the second derivative of z(y). Factor u(k).
-4*(k + 2)**2*(2*k - 1)
Suppose 0 = 5*h - 10. Suppose 4*a**5 - 2*a**h + 10*a - 2*a**4 + 12 - 8 - 9*a**3 - 5*a**3 = 0. Calculate a.
-1, -1/2, 1, 2
Factor -1/8*q**5 + 9/8*q - q**3 - 1/2 + 3/4*q**4 - 1/4*q**2.
-(q - 4)*(q - 1)**3*(q + 1)/8
Let i(q) be the second derivative of -q**5/40 + 51*q**4/2 - 10404*q**3 + 2122416