- 2/11*h**3 + 2/11*h**2 = 0.
0, 1
Let k(v) be the second derivative of -7*v + 5/3*v**3 - 3*v**2 + 1/3*v**4 + 0. Determine d, given that k(d) = 0.
-3, 1/2
Suppose -v = 4*t - 3*v + 40, -5*t - 40 = -5*v. Let b = t + 14. Determine h so that 2/5 - 4/5*h**b + 2/5*h**4 + 0*h + 0*h**3 = 0.
-1, 1
Let q be 3/(6/4) - (-1188)/(-600). Let c(t) be the second derivative of 1/10*t**2 - 1/15*t**3 + 0 + 0*t**4 + q*t**5 - 2*t - 1/150*t**6. Factor c(f).
-(f - 1)**3*(f + 1)/5
Let p be 17/(-45) - (-39)/65. Determine l so that -6*l - 2*l**2 - 6 - p*l**3 = 0.
-3
Let a(t) be the first derivative of t**5/20 - 3*t + 3. Let k(z) be the first derivative of a(z). What is c in k(c) = 0?
0
Let c(x) be the third derivative of x**9/7560 - x**8/3360 - x**7/1260 + x**6/360 - x**4/8 + 3*x**2. Let s(o) be the second derivative of c(o). Factor s(d).
2*d*(d - 1)**2*(d + 1)
Let u(m) = -m**2 - m + 1. Let r(c) = 7*c**2 - 2*c - 4. Let v(x) = -r(x) - 4*u(x). Let v(h) = 0. Calculate h.
0, 2
Let j be (-8)/252*(-6)/40. Let b(r) be the third derivative of r**2 + 0 - 1/140*r**6 + 0*r**3 + 0*r + j*r**5 + 0*r**4. Solve b(y) = 0.
0, 1/3
Let z(n) be the third derivative of 1/360*n**6 + 0 + 0*n**4 + n**2 + 0*n + 0*n**5 + 1/6*n**3. Let c(y) be the first derivative of z(y). Factor c(i).
i**2
Let j be (-1 - -2)/(7/14). Let s(l) be the first derivative of 1/3*l**4 + 2/15*l**5 - 2/3*l**j - 2 + 0*l**3 - 2/3*l. Factor s(a).
2*(a - 1)*(a + 1)**3/3
Factor 3 - 3 - 2*k**3 + 3*k - 2*k**2 - k**5 - 3 + 3*k**4 + 2.
-(k - 1)**4*(k + 1)
Factor -9*s**3 - 9*s**3 + 15*s**3.
-3*s**3
Let y = -10 - -5. Let a be (-18)/(-15)*y/(-2). Let -2*f**2 + 7*f**a - 5*f**4 - f**4 - 13*f**3 - 2*f**5 = 0. What is f?
-1, 0
Suppose -5*j - 3 = 3*m, -2*m + 2 = -2*j + 4. Let x be 11/11*(4 + m). Factor -1/3*k**x + 1/3*k**2 + 0 + 0*k.
-k**2*(k - 1)/3
Let p be -3 - (-1 + -3 + 1). Factor 2/5*l**2 + p + 6/5*l.
2*l*(l + 3)/5
Let z(s) be the second derivative of s**6/165 - s**5/55 + s**4/66 - 5*s. Factor z(l).
2*l**2*(l - 1)**2/11
Let s = -723 + 725. Determine k so that 12/7*k**3 + 3/7*k - 15/7*k**s + 0 = 0.
0, 1/4, 1
Let a(d) be the first derivative of -1/4*d - 3 + 1/12*d**3 - 1/8*d**4 + 1/4*d**2. Factor a(x).
-(x - 1)*(x + 1)*(2*x - 1)/4
Let i(q) be the first derivative of -q**5/150 + q**4/60 - 3*q**2 + 9. Let r(x) be the second derivative of i(x). Find h, given that r(h) = 0.
0, 1
Let d(l) = 6*l**5 + 12*l**4 - 16*l**3 + 5*l. Let p(o) = -5*o**5 - 11*o**4 + 15*o**3 - o**2 - 4*o. Let v(c) = -6*d(c) - 7*p(c). Determine k so that v(k) = 0.
0, 1, 2
Factor -2*m + 3*m - 3*m - m**2 - 4*m - 9.
-(m + 3)**2
Suppose 5*d - 46*l = -42*l + 27, 27 = 4*d - 5*l. Suppose 0*c - 1/4*c**4 + 1/2*c**2 - 1/4*c**d + 0 = 0. What is c?
-2, 0, 1
Let q(b) = 1. Let u(s) = -2*s**2 - 2*s. Let m(d) = 4*q(d) + u(d). Factor m(g).
-2*(g - 1)*(g + 2)
Let v(a) = a**2 - a + 8. Let t be v(-8). Suppose 63*o - 2 - 11*o - t*o**2 + 36*o**3 - 2 - 4 = 0. What is o?
2/9, 1
Let l(b) be the second derivative of b**4/60 - b**3/30 - 22*b. Factor l(k).
k*(k - 1)/5
Suppose 8 = i + 2*q, -2*q - 2*q = 3*i - 16. Factor -2/11*v**2 + i - 2/11*v.
-2*v*(v + 1)/11
Let w be (3 - -2)/((-130)/(-4)). Find s, given that -6/13 - 8/13*s - w*s**2 = 0.
-3, -1
Factor -3*p**2 + 24*p**3 + 41*p - p**2 + p**2 - 15*p**4 - 47*p.
-3*p*(p - 1)**2*(5*p + 2)
Factor 12*u + 7*u + 2 + u**3 - 13*u + 6*u**2 + u**3.
2*(u + 1)**3
Let r = -86/5 + 632/35. Solve r*t + 0 + 9/7*t**2 + 3/7*t**3 = 0 for t.
-2, -1, 0
What is q in 8/3*q**2 + 32*q**3 + 238/3*q**4 + 0 + 0*q = 0?
-2/7, -2/17, 0
Suppose 0*b = 3*b - 30. Let k be 1/((b/(-4))/(-5)). Factor -m + m**2 - 1 - 6*m**2 - 3*m - k*m**3.
-(m + 1)**2*(2*m + 1)
Let i = -11/8 + 23/8. Factor i*w**3 - 6*w**2 + 15/2*w - 3.
3*(w - 2)*(w - 1)**2/2
Let j = -55 - -79. Find r such that 24 - 3*r**3 - j = 0.
0
Let y(j) be the second derivative of j**5/20 + j**4/3 - j**3/6 - 2*j**2 + 12*j. Factor y(i).
(i - 1)*(i + 1)*(i + 4)
Let y(a) be the first derivative of -a**8/5880 - a**7/980 - a**6/420 - a**5/420 - 4*a**3/3 - 3. Let p(x) be the third derivative of y(x). What is m in p(m) = 0?
-1, 0
Suppose -5*c = -c - 28. Suppose 2*m + 5*a + 2 = c, 4*m + 4*a - 16 = 0. Find d, given that -25/4*d**3 + 0 - d - m*d**2 = 0.
-2/5, 0
Let i(r) be the first derivative of 25*r**6/3 - 58*r**5 - 23*r**4 + 200*r**3/3 - 24*r**2 + 36. Suppose i(a) = 0. What is a?
-1, 0, 2/5, 6
Let s(y) = y**2 + y - 1. Let a(f) = -12*f**2 - 7*f + 7. Let g(v) = -v**2 - 4*v + 7. Let r be g(-5). Let n(o) = r*a(o) + 22*s(o). Factor n(c).
-2*(c - 2)**2
Suppose 52 = -3*x + 16*x. Let -1/3*p**3 - 5/3*p**x + 0*p + 1/3*p**2 - p**5 + 0 = 0. Calculate p.
-1, 0, 1/3
Let -1/3*p**2 + 2/3 - 1/3*p = 0. What is p?
-2, 1
Let q(f) be the second derivative of f**6/360 + f**5/120 - f**4/12 - 3*f**3/2 - 4*f. Let c(t) be the second derivative of q(t). Factor c(x).
(x - 1)*(x + 2)
Let c(a) = -3*a**3. Let w(u) = -2*u**3. Let k(g) = 6*c(g) - 10*w(g). Determine t so that k(t) = 0.
0
Let k(f) be the second derivative of 0 + 0*f**3 - 1/20*f**5 + 0*f**4 + 1/30*f**6 + 3*f + 0*f**2. Factor k(d).
d**3*(d - 1)
Let y(s) = 1 - 5*s + 6*s + 4*s**2 - 3*s**2. Let z(n) = -2*n**3 + 4*n**2 + 6*n + 6. Let p(q) = -6*y(q) + z(q). Factor p(v).
-2*v**2*(v + 1)
Solve 0*k**3 + 0*k**2 + 0*k + 1/2*k**4 + 0 = 0.
0
Find o, given that 1/4*o**2 + 1 - o = 0.
2
Suppose -3*g + 16 = 5*o, 0 = 3*g - 4*o + 2 - 0. Factor 2 + 0*q**2 + 7*q**2 - q**g + 18*q**3 - 6*q - 4*q.
2*(q + 1)*(3*q - 1)**2
Let y(v) be the second derivative of v**6/1440 - v**4/96 + v**3/3 - v. Let m(u) be the second derivative of y(u). Determine l so that m(l) = 0.
-1, 1
Let o(n) be the first derivative of -n**4/30 + 2*n**3/3 - 5*n**2 + 50*n/3 - 11. Factor o(b).
-2*(b - 5)**3/15
Let q be 0/(-3 - (0 + -1)). Let s be q - (1 - 12/8). Factor s*b + 0 - 1/2*b**3 + 1/2*b**2 - 1/2*b**4.
-b*(b - 1)*(b + 1)**2/2
Find t, given that -1/4*t + 1/4*t**2 + 0 = 0.
0, 1
What is x in 12*x**3 + 25*x**2 + 20*x + 27 - 21 + 2*x**4 - x**2 = 0?
-3, -1
Let h(m) = m**3 - 6*m**2 - m + 6. Let u be h(6). Let z(x) be the second derivative of -x**2 - 1/24*x**4 - x + u + 1/3*x**3. Factor z(n).
-(n - 2)**2/2
Let s(b) be the third derivative of b**7/105 - b**5/30 - 3*b**2. What is j in s(j) = 0?
-1, 0, 1
Let d(c) be the third derivative of -c**8/1512 - 2*c**7/945 + c**6/180 + 2*c**5/135 - c**4/27 - 8*c**2. Suppose d(o) = 0. Calculate o.
-2, 0, 1
Let q be (0 - 0)*(1 - 2). Let 4*j**2 + 5*j - 5*j**3 + 2 + 2*j**3 + q + 4*j**3 = 0. Calculate j.
-2, -1
Let n be 1 - (586/35 + -1). Let i = n - -106/7. Solve -2/5 + 4/5*g - 4/5*g**3 + i*g**4 + 0*g**2 = 0 for g.
-1, 1
Let k(o) be the second derivative of 0 - 1/6*o**4 - 2*o + 0*o**2 + 1/3*o**3. Suppose k(h) = 0. Calculate h.
0, 1
Let p(l) be the second derivative of l**6/60 - l**4/12 + l**2/4 - 8*l. Factor p(s).
(s - 1)**2*(s + 1)**2/2
Determine i so that 1/2*i + 0 - 1/2*i**2 = 0.
0, 1
Let h(u) = -35*u**3 + 10*u**2 + 50*u - 10. Let p(w) = -w**3 + w + 1. Let n(f) = -h(f) + 30*p(f). Factor n(v).
5*(v - 2)**2*(v + 2)
Suppose 18 = 2*w - w - 4*d, -14 = 3*w + 5*d. Let f(j) be the second derivative of 0*j**5 + 0 + 1/120*j**6 + 0*j**3 + j + 1/8*j**w - 1/24*j**4. Factor f(y).
(y - 1)**2*(y + 1)**2/4
Find j, given that -9*j**2 - j**5 - 11*j**3 - 6*j**4 + 12*j + 8 - j**2 + 8*j**2 = 0.
-2, -1, 1
Let d(p) be the first derivative of -p**5/150 + p**4/60 + 4*p**2 + 8. Let f(h) be the second derivative of d(h). What is q in f(q) = 0?
0, 1
Let w = 75 - 70. Let r(m) be the second derivative of 0*m**2 + 1/30*m**6 + 1/84*m**7 + 0 + 0*m**w + 4*m - 1/12*m**3 - 1/12*m**4. Determine v so that r(v) = 0.
-1, 0, 1
Let l(d) = -6*d**2 + 51*d - 63. Let y(v) = -3*v**2 + 26*v - 31. Let i(m) = -4*l(m) + 9*y(m). Let i(g) = 0. What is g?
1, 9
Suppose -4*f + 16 = 2*a + 2, 0 = -2*f - 2*a + 6. Find u, given that 0*u - 1/2*u**5 + 1/2*u**3 + 1/2*u**2 + 0 - 1/2*u**f = 0.
-1, 0, 1
Let c = -2 + 6. Suppose 4*t - c*d + 2*d - 36 = 0, 5*t - d = 45. Factor 1 - 39*o**2 - 7 + 42*o + 2*o**3 - t*o + 10*o**3.
3*(o - 2)*(o - 1)*(4*o - 1)
Let r(l) = -2*l - 8. Let x be r(-6). Factor -6 + 4 - x*g**2 + g**2 + 5*g**2.
2*(g - 1)*(g + 1)
Factor 54 + 27*x - 7*x**3 - 9*x**2 - 23*x**4 + 37*x**4 - 15*x**4.
-(x - 2)*(x + 3)**3
Let l = -292/3 + 100. Let c(a) be the first derivative of -3 - 2/9*a**3 + 4/3*a**2 - l*a. Suppose c(f) = 0. What is f?
2
Let y(g) be the first derivative of 5*g**6/6 - 8*g**5