 0*n**3. Determine q so that p(q) = 0.
-1/5, 0
Let r be 2/(8 - 4 - 2). Suppose 16 = w + 4*i, 5*w - i - r = 4*w. Determine g so that 6*g**2 + 0 + 15/8*g**3 + 3/2*g - 21/8*g**w = 0.
-1, -2/7, 0, 2
Let l = 25/8 + -67/24. Factor -l*v**2 + 1/3*v + 2/3.
-(v - 2)*(v + 1)/3
Let y(z) = -3*z - 73. Let x be y(-26). Suppose 3*k = x*i - 11, -k + 4*i + 1 - 14 = 0. Find q, given that 2/3*q - 2/3*q**2 + 2/3 - 2/3*q**k = 0.
-1, 1
Let s be -2 + -1 + 62 - 3. Factor -300*z - 72*z**3 - 23*z**3 - 37*z**3 - s - 404*z**2 + 28*z**4.
4*(z - 7)*(z + 1)**2*(7*z + 2)
Let x(a) = 266*a**3 - 150*a**2 + 6*a. Let g be (-4 + 2)*(-6)/(-4). Let f(n) = 53*n**3 - 30*n**2 + n. Let q(i) = g*x(i) + 14*f(i). Solve q(l) = 0 for l.
0, 1/4, 2/7
Let y(a) = 20*a - 37. Let m be y(2). Let g(q) be the second derivative of 0 + 8/3*q**m + 9*q - 4/3*q**4 - 2*q**2. Factor g(u).
-4*(2*u - 1)**2
Let f = 43 - 39. Let h be 18/f - (-3 - -6). Solve -3/2 + 3/4*t**5 + 3*t**3 - h*t**2 + 3*t**4 - 15/4*t = 0.
-2, -1, 1
Suppose 0 = -0*b + 3*b - 24. Suppose -4*c + b = 3*a - 11, 2*c = -a + 9. Determine q so that -q**3 + 4*q**2 - 5*q**2 + q**5 - q**4 + 4*q**4 - 2*q**c = 0.
-1, 0, 1
Let r(x) = -8*x**3 - 80*x - 3 - 10*x**3 - 27 - 66*x**2. Let a(j) = j**4 + j**3 + 1. Let h(f) = -2*a(f) + r(f). Let h(q) = 0. Calculate q.
-4, -1
Let i be (6/(-10))/((-2)/10). Let v be 17/(170/(-4))*(-3)/2. Factor 0*y**i + 0*y + 0 + v*y**2 - 3/5*y**4.
-3*y**2*(y - 1)*(y + 1)/5
Let c(l) be the first derivative of -l**6/24 - l**5/3 + 25*l**4/24 - l**2/2 + 2*l - 55. Let y(w) be the second derivative of c(w). Factor y(v).
-5*v*(v - 1)*(v + 5)
Let n(l) be the second derivative of -2*l**3 + 1/4*l**4 + 20*l + 0 + 6*l**2. Let n(y) = 0. Calculate y.
2
Let v(r) be the second derivative of -4/7*r**2 - 26*r - 5/28*r**5 - 19/42*r**4 - 2/3*r**3 - 4/105*r**6 - 1/294*r**7 + 0. Factor v(l).
-(l + 1)**2*(l + 2)**3/7
Let f(p) be the third derivative of 5/24*p**4 + 0 - 7/12*p**5 + 26*p**2 + 0*p + 0*p**3. Factor f(i).
-5*i*(7*i - 1)
Let y(v) be the first derivative of v**8/672 + v**7/140 - v**6/120 - v**5/10 - v**4/6 - 19*v**2 - 33. Let p(t) be the second derivative of y(t). Factor p(w).
w*(w - 2)*(w + 1)*(w + 2)**2/2
Let u(x) be the second derivative of 0*x**2 + 0 - 5/4*x**4 - 5/6*x**3 + x**5 - 6*x. Find i, given that u(i) = 0.
-1/4, 0, 1
Let s be (11 - -3) + (-2 - (-16)/6). Let a = s - 40/3. Factor -a + 10/3*z - 10/3*z**3 + 4/3*z**2.
-2*(z - 1)*(z + 1)*(5*z - 2)/3
Let d = -148 - -157. Factor d*g**4 - 410 + 3*g**5 + 205 + 205.
3*g**4*(g + 3)
Let p = -299774/165 - -19990/11. Let q = p - 2/33. Suppose 1/5*j**5 + 2/5*j**2 + 1/5 - 3/5*j**4 - 3/5*j + q*j**3 = 0. What is j?
-1, 1
What is m in 79/6*m + 0*m**3 - 5 + 4/3*m**4 + 1/6*m**5 - 29/3*m**2 = 0?
-6, -5, 1
Let v(a) = -2*a**3 + 66*a**2 + 2*a - 66. Let m be v(33). Determine l, given that 2/3*l**3 + 0*l + m - 2/3*l**2 = 0.
0, 1
Let y(n) = -2*n + 7. Let o be y(1). Let b(h) be the second derivative of 1/14*h**7 - 3*h + 0*h**4 + 0*h**6 + 0 + 0*h**2 + 0*h**3 - 3/20*h**o. Factor b(m).
3*m**3*(m - 1)*(m + 1)
Let b(i) be the third derivative of i**6/210 + i**5/15 + 5*i**4/14 + 6*i**3/7 - 79*i**2. Factor b(v).
4*(v + 1)*(v + 3)**2/7
Find u, given that 4*u**3 + 20*u**2 + 267*u + 816*u - 88*u**2 - 46*u**2 - u**3 = 0.
0, 19
Let m(d) be the third derivative of 5*d**8/336 - 37*d**7/42 + 215*d**6/12 - 611*d**5/6 - 19435*d**4/24 - 10985*d**3/6 + 32*d**2. Suppose m(c) = 0. What is c?
-1, 13
Let k(l) = -2*l**2 - l + 380. Let v be k(-14). Factor 2/9 - 4/9*m**v + 2/9*m**4 + 0*m**3 + 0*m.
2*(m - 1)**2*(m + 1)**2/9
Suppose 5*k - 55 = 5*i, 136*i - 135*i = -3*k + 25. Let t(z) be the first derivative of 0*z**2 + z**3 + 0*z - 3/4*z**4 - k. Factor t(v).
-3*v**2*(v - 1)
Let s(q) = 173*q**4 - 109*q**3 + 31*q**2 + 5*q. Let g(u) = 86*u**4 - 54*u**3 + 14*u**2 + 2*u. Let b(i) = 5*g(i) - 2*s(i). Find y such that b(y) = 0.
0, 2/7, 1/3
Let s be ((-27)/(-18))/((-4)/(-8)). Let q(b) be the first derivative of -3 + 0*b**s + 0*b + 0*b**2 + 1/2*b**4. Factor q(u).
2*u**3
Let c be -1 - -30*(-8)/12. Let b be (-37)/(-7) + 6/c. Factor -6*v - 3*v**2 + b*v + 2*v**2.
-v*(v + 1)
Suppose 0 = -3*f - f + 12. Let h(d) = -4*d**2 + 7*d + 11. Let l(a) = -2*a**2 + 3*a + 5. Let s(o) = f*h(o) - 5*l(o). Find n, given that s(n) = 0.
-1, 4
Let o(h) = -h**2 + 16*h + 17. Let p be (56/(-35))/(4/10). Let u(k) = -8*k - 8. Let z(n) = p*o(n) - 10*u(n). Factor z(a).
4*(a + 1)*(a + 3)
Determine k so that 63/4 - 1/4*k**2 + 31/2*k = 0.
-1, 63
Let c be (-12)/112*(-1 + (-4)/(-12)). Let p(u) be the first derivative of 4 + 2/7*u**2 + 0*u - 2/7*u**3 + c*u**4. Factor p(a).
2*a*(a - 2)*(a - 1)/7
Let f(g) = 3*g**2 + 4*g + 2. Let s(p) = p**2 - 1. Let l = 38 - 36. Let u(q) = l*s(q) - f(q). Factor u(z).
-(z + 2)**2
Let s(l) be the second derivative of -1/3*l**6 - 5/42*l**7 + 2*l + 0*l**3 + 0 + 3/4*l**5 + 0*l**2 + 0*l**4. Solve s(k) = 0 for k.
-3, 0, 1
Suppose 10*y - 5*y + 65 = 0. Let h(r) = -6*r**3 + 83*r**2 - 371*r. Let i(u) = 3*u**3 - 42*u**2 + 186*u. Let x(s) = y*i(s) - 6*h(s). Find b such that x(b) = 0.
0, 8
Let o(s) be the second derivative of 0*s**2 + 1/40*s**5 - 2*s - 1/12*s**3 - 1/24*s**4 - 7 + 1/60*s**6. Find c, given that o(c) = 0.
-1, 0, 1
Let b(x) be the third derivative of x**5/105 + x**4/42 - 4*x**3/21 - x**2 + 156*x. Suppose b(o) = 0. What is o?
-2, 1
Let v(x) = 36*x**2 - 36*x + 16. Let l(s) = -7*s**2 + 7*s - 3. Let q be (-357)/27 - 3 - 6/(-27). Let g(j) = q*l(j) - 3*v(j). Find n such that g(n) = 0.
0, 1
Let o(m) = 4*m**2 - 56*m + 52. Let p(d) = 4*d**2 - 56*d + 52. Let h(k) = -3*o(k) + 4*p(k). Factor h(r).
4*(r - 13)*(r - 1)
Let x be -11 - 9/(243/(-99))*3. Factor -3/5*b**3 - 2/5*b - b**2 + x.
-b*(b + 1)*(3*b + 2)/5
Suppose -2*b = 4*z, 4*b + z = 2*b. Factor 6/5*x**3 - 2/5*x**2 + b + 0*x.
2*x**2*(3*x - 1)/5
Suppose 0 = 3*x - 39 + 30. Let n(p) = -p - 6. Let b be n(-8). What is u in -u**5 + 6*u**4 + 2*u**2 - 5*u**3 + u**5 - b*u**5 - u**x = 0?
0, 1
Let b(r) be the first derivative of -3*r**4/4 + 15*r**3 - 18*r**2 - 84*r + 414. What is g in b(g) = 0?
-1, 2, 14
Let l(i) = -i**2 - 5*i - 1. Let s(a) = 2*a**2 + 19*a + 1. Let u(n) = 5*l(n) + 5*s(n). Find k, given that u(k) = 0.
-14, 0
Suppose 4*k + a = 3, -a + 6*a + 17 = -4*k. Suppose 2*b**5 - b**2 + b**4 + b**3 - k*b**3 - b**5 = 0. What is b?
-1, 0, 1
Factor -544 + 4*q - 1132*q + 676 + 51*q**2.
3*(q - 22)*(17*q - 2)
Suppose 3*m - 22*n = -24*n + 23, -4*m = n - 19. Determine q, given that 32/13*q + 2/13*q**m - 14/13*q**2 - 24/13 = 0.
2, 3
Let x be (-6)/(-4)*24/9. Suppose -x*k + 36 = -5*t, -24 = -2*k - 0*t + 4*t. Let 4*u - 185 - 4*u**3 - 4*u**2 + k*u**4 + 185 = 0. Calculate u.
-1, 0, 1
Suppose 0 = 4*a + 4*a. Suppose a = -5*j + 8 + 2. Suppose y**2 - y**3 + 5*y**3 + 7*y**j + 4*y = 0. Calculate y.
-1, 0
Suppose l + 10 + 10 = 0. Let x be -7*(l/(-14))/(-2). Factor 3*t**4 + 44*t**5 - 9*t**3 - 15*t**2 + 3*t - 9*t - 41*t**x.
3*t*(t - 2)*(t + 1)**3
Let v = 94 + -92. Suppose -v*l = 3*l. Solve -2/5*k**2 + l*k + 0 = 0.
0
Let q(d) be the third derivative of -d**8/11760 + 2*d**7/2205 - 11*d**4/24 - 23*d**2. Let c(a) be the second derivative of q(a). Let c(y) = 0. What is y?
0, 4
Suppose -9*c + 7*c + 18 = 5*v, 5*c - 3*v = 14. Let a(r) be the second derivative of -r - 32*r**2 + 16/3*r**3 - 1/3*r**c + 0. Solve a(k) = 0 for k.
4
Let z be (2220/(-18))/(2*3/(-9)). Let 2*o**2 - 5*o - z - o + 189 = 0. What is o?
1, 2
Let q be (-60)/(-27) + 3 + 2/(-9). Suppose -6*m + 29 = q. What is g in -10/9*g**3 + 2/3*g**2 + 8/9*g**5 + 2/9*g + 0 - 2/3*g**m = 0?
-1, -1/4, 0, 1
Let h(n) be the first derivative of 7/20*n**2 + 3/10*n - 15 + 1/15*n**3. Factor h(j).
(j + 3)*(2*j + 1)/10
Factor -56*a**3 + 22*a**2 + 17*a**4 + 48*a**4 - 35*a**4 - 2*a + 6*a.
2*a*(a - 1)**2*(15*a + 2)
Let k(t) be the first derivative of 0*t - 1/2*t**2 - 1/4*t**4 - 2/3*t**3 - 2. Let k(c) = 0. What is c?
-1, 0
Let o(k) be the first derivative of -k**4 + 4*k**3/3 + 4*k**2 + 58. Determine c so that o(c) = 0.
-1, 0, 2
Let u(o) be the second derivative of -o**4/6 + 58*o**3/3 - 841*o**2 - 149*o. Factor u(v).
-2*(v - 29)**2
Let j(q) = q**3 - 15*q**2 + 24*q + 16. Let l be j(13). Let a(t) = -t**3 + t - 1. Let p(i) = -6*i**3 + 8*i**2 + 6*i - 18. Let n(m) = l*a(m) + p(m). Factor n(k).
4*(k - 1)*(k + 1)*(k + 2)
Let s be 374/69 + 112/(-1288). Solve 4/3*c**2 - 4/3*c**3 + 16/3*c - s = 0 for c.
-2, 1, 2
Factor 756*z*