m) be the second derivative of m**6/30 + m**5/20 - m**4/3 - 2*m**3/3 - 5*m - 9. Determine t, given that f(t) = 0.
-2, -1, 0, 2
Suppose 7*z - 2*z = 50. Solve -10*t + 4 + 4*t**2 - z*t + 12*t = 0 for t.
1
Let t(k) be the second derivative of -k**6/60 + k**5/4 - 7*k**4/8 - 10*k**3/3 + 25*k**2 + 144*k. Solve t(q) = 0 for q.
-2, 2, 5
Let y(m) be the second derivative of -m**8/336 - m**7/210 + m**6/120 + m**5/60 - 20*m**2 - 9*m. Let i(s) be the first derivative of y(s). Factor i(z).
-z**2*(z - 1)*(z + 1)**2
Let j(p) be the third derivative of 35*p**2 + 0 - 1/420*p**6 - 1/210*p**5 + 0*p**3 + 1/735*p**7 + 1/84*p**4 + 0*p. Find d such that j(d) = 0.
-1, 0, 1
Let r(z) be the second derivative of -z**4/12 - 2*z**3/15 + 9*z + 2. Determine o, given that r(o) = 0.
-4/5, 0
Let j(s) be the first derivative of 7 + 0*s + 0*s**3 - 2/125*s**5 - 4/25*s**2 + 3/50*s**4. Factor j(o).
-2*o*(o - 2)**2*(o + 1)/25
Suppose -77*b + 105 = -49*b - 35. What is n in 0*n + 56/5*n**4 - 5*n**3 + 3/5*n**2 + 0 - 16/5*n**b = 0?
0, 1/4, 3
Let j be (-3)/12 + 7/(-4). Let b(k) = 2*k**2 + 2*k + 1. Let t be b(j). Factor 0*s**4 + 9*s**3 + 4*s**4 + 3*s**2 + 5*s**4 + t*s**5 - 2*s**5.
3*s**2*(s + 1)**3
Factor -16*k - 2/3*k**3 + 28/3*k**2 + 0.
-2*k*(k - 12)*(k - 2)/3
Let a(r) be the first derivative of 3*r**4/38 + 20*r**3/57 + 4*r**2/19 - 6*r + 17. Let z(v) be the first derivative of a(v). Factor z(j).
2*(j + 2)*(9*j + 2)/19
Let w(m) = m**3 - 9*m**2 + 8*m + 3. Let o be w(8). Factor -3/2*b**4 + 0 - 6*b + 9/2*b**o + 0*b**2.
-3*b*(b - 2)**2*(b + 1)/2
Let s(f) be the third derivative of f**5/390 - 2*f**4/13 + 92*f**2. Factor s(g).
2*g*(g - 24)/13
Let h(f) be the third derivative of 0 - 1/210*f**7 - 13/60*f**5 + 0*f - 1/2*f**4 - 2*f**2 - 2/3*f**3 - 1/20*f**6. Factor h(n).
-(n + 1)**2*(n + 2)**2
Let n(d) = -d**2 + 9*d + 2. Let x(q) = -q**2 - 8*q + 2. Let u be x(-7). Let y be n(u). Factor 4 - 5 - 3*f**2 + 6*f**y - 4*f**2 + 2*f.
-(f - 1)**2
Let x be (-1 - -7) + ((-144)/70)/(10/25). Solve -1/7*f**5 + x*f**4 - 2*f**3 - 9/7*f + 16/7*f**2 + 2/7 = 0 for f.
1, 2
Let g(j) be the first derivative of -j**6/120 + j**5/5 - 2*j**4 + 6*j**3 - 41. Let o(d) be the third derivative of g(d). Factor o(q).
-3*(q - 4)**2
Let q(t) = -t**2 - 4*t - 1. Let b be q(-3). Solve -60*j**3 - 9*j**2 + 7*j**2 - 19*j**2 + j**b - 45*j**4 = 0.
-2/3, 0
Solve 3440*m**2 - 3446*m**2 + 11*m**3 - 7*m**3 - 1 + 4*m - m**4 = 0 for m.
1
Suppose -3*j = -0*j - 48. Let h = j + -13. Factor -5/3*k**h + 0 - 1/3*k + 2*k**2.
-k*(k - 1)*(5*k - 1)/3
Let s(p) = -8*p**4 - 12*p**3 + 16*p**2 + 48*p + 24. Let j(v) = v**4 - v**2 - v. Let b(u) = 4*j(u) + s(u). Find k, given that b(k) = 0.
-3, -1, 2
Let t be (-192)/(-40) - (4 - (-2 + 4)). Suppose -i + 3 = 3*n, -i - 1 = n - 4. Factor 4/5*q**3 + 2*q**5 + 0*q + 0*q**2 + n - t*q**4.
2*q**3*(q - 1)*(5*q - 2)/5
Let y(n) be the first derivative of 2/3*n**3 + 5/2*n**2 - 1/6*n**6 - n**4 + 2*n - 4/5*n**5 - 19. Find c such that y(c) = 0.
-2, -1, 1
Let d = -16 - -18. Let m be d/(1*3/6). Factor -9*g**2 - 10*g - 22*g**m + g**4 + 36*g**3 + 4*g.
-3*g*(g - 1)**2*(7*g + 2)
Let s(x) be the second derivative of x**5/150 - 15*x**2/2 - 16*x. Let u(a) be the first derivative of s(a). What is o in u(o) = 0?
0
Factor -8 - 4 - 4*m**3 - 9*m**2 - 25*m - 4*m**2 - 3*m - 7*m**2.
-4*(m + 1)**2*(m + 3)
Let d(o) be the second derivative of -2/3*o**2 - 7/18*o**4 + 40*o + 0 + o**3. Determine m, given that d(m) = 0.
2/7, 1
Let q be 36/(-81)*(11/14 + -1). Let d(v) be the second derivative of -13/20*v**5 + 6*v + 3/2*v**3 + 1/12*v**4 + q*v**7 - 1/10*v**6 + v**2 + 0. Solve d(k) = 0.
-1, -1/4, 1, 2
Determine a, given that 0 + 4/5*a**2 - 4/5*a**4 - 16/5*a + 16/5*a**3 = 0.
-1, 0, 1, 4
Let r = -1/12915 - -10333/12915. Solve 24/5 + 28/5*g**2 + 4/5*g**3 - r*g**4 - 52/5*g = 0.
-3, 1, 2
Let p be (9/3)/((-6)/(-44)). Suppose 17*m - p*m = -10. Factor -m*z + 4*z**3 - z - 3*z**2 + 3 - z**3.
3*(z - 1)**2*(z + 1)
Solve 41*w - 8 - 5 + 4*w**2 - w**2 - 8 - 59*w = 0.
-1, 7
Let f(k) = -k - 1. Suppose u + 5*d = 3 + 3, 4*u + 5*d + 6 = 0. Let v = u - -3. Let h(z) = 3*z**2 + z - 2. Let c(i) = v*h(i) + 2*f(i). Factor c(j).
-3*j*(j + 1)
Let p(v) be the first derivative of 4 + 0*v + 1/16*v**4 - 3/2*v**2 - 1/6*v**3 - 1/120*v**5. Let i(g) be the second derivative of p(g). Factor i(b).
-(b - 2)*(b - 1)/2
Let b = -36932 + 184667/5. Let 3*h**2 + 1/5*h + b*h**4 - 2/5 + 19/5*h**3 = 0. Calculate h.
-1, 2/7
Suppose 5*c = 3 - 28, -2*a - 3*c = 9. Determine u, given that 70*u**2 + 45*u**2 - 105*u**4 + 5*u**a - 10 - 5*u + 0*u**2 = 0.
-1, -2/7, 1/3, 1
Let b(n) be the third derivative of n**7/70 - 3*n**6/40 - 2*n**5/9 + 2*n**4/9 - 27*n**2 + 7*n. Suppose b(v) = 0. What is v?
-4/3, 0, 1/3, 4
Let b(t) be the second derivative of -1/9*t**4 + 4/9*t**3 + 0 - 5*t - 5/2*t**2 + 1/90*t**5. Let w(y) be the first derivative of b(y). Let w(r) = 0. What is r?
2
Suppose -g - 10*o = -5*o + 30, 5*g - 2*o = -69. Let a be 100/(-750) - 2/g. Find w such that 8/7*w + 1/7*w**4 + 6/7*w**3 + a + 12/7*w**2 = 0.
-2, 0
Let v(f) be the first derivative of -2*f**3/21 - 2*f**2/7 - 2*f/7 - 15. Determine c, given that v(c) = 0.
-1
Let h = -28 + 34. Factor 15*k + h*k**3 - 2*k**5 + 3*k**3 - 5*k**3 - 17*k.
-2*k*(k - 1)**2*(k + 1)**2
Suppose 11/3*c - 1/3*c**2 - 6 = 0. Calculate c.
2, 9
Let q(m) be the second derivative of -m**7/280 + m**6/120 + m**5/40 - m**4/8 + 7*m**3/3 + m. Let n(d) be the second derivative of q(d). Factor n(p).
-3*(p - 1)**2*(p + 1)
Let t(s) be the third derivative of -s**8/448 + s**7/280 + s**6/160 - s**5/80 + 121*s**2. Factor t(o).
-3*o**2*(o - 1)**2*(o + 1)/4
Let z be 118/1652 + 4/(-56)*-1. Factor z*p**3 - 6/7*p**2 + 2/7*p**4 + 2/7 + 1/7*p.
(p - 1)**2*(p + 2)*(2*p + 1)/7
Let n be (-266)/98 + (-8)/28 + 32/10. Determine f so that 0*f**2 + 0*f - n*f**3 + 0 = 0.
0
Solve -8/5*o**2 + 0*o + 2/5*o**4 - 2/5*o**5 + 8/5*o**3 + 0 = 0 for o.
-2, 0, 1, 2
Let j = -4 + 15. Let 14 - 5*z**2 + 2*z**2 + j*z - 2 + 2*z**2 = 0. What is z?
-1, 12
Let l = -6543/2 - -1766611/540. Let z(m) be the third derivative of 0 - 1/9*m**4 + 8/27*m**3 - l*m**6 + 0*m + 1/45*m**5 + 6*m**2. Factor z(t).
-2*(t - 2)**3/9
Let c be 145/(-87)*(-5 - -2). Let s(n) be the first derivative of 5/16*n**2 - 1/24*n**3 - 1/2*n + c. Factor s(a).
-(a - 4)*(a - 1)/8
Let j be (-8 + 7 + (-24)/(-18))/1. Let -j*r + 2/3 - 4/3*r**2 + r**3 = 0. Calculate r.
-2/3, 1
Let r(b) = b**3 - 2*b**2 + b + 11. Let s be r(0). What is u in 2*u**2 - 3*u**2 + 14*u - 20 + s*u - 4*u**2 = 0?
1, 4
Let g = 24898/15 + -4979/3. Determine c, given that 0 - g*c**3 + 2/5*c - 1/5*c**2 = 0.
-2, 0, 1
Suppose -3*g = 3*c - 33, 0*g - 4*c = -g + 1. Factor 9*r**3 - 5*r - 4*r**3 + g - 15 - 5*r**2 + 11.
5*(r - 1)**2*(r + 1)
Let z(j) be the second derivative of j**4/126 - 22*j**3/63 + 121*j**2/21 - 321*j. Suppose z(u) = 0. Calculate u.
11
Factor 36/7*n - 9/7*n**3 - 3/7*n**4 + 0 + 12/7*n**2.
-3*n*(n - 2)*(n + 2)*(n + 3)/7
Suppose 0 = 4*k - a - 24, 5*k - 9 = -a - 3*a. Suppose 0 = d, 3*b + 3*d - k - 4 = 0. Factor -w + 10*w - 2*w**b - w**3 + 6.
-3*(w - 2)*(w + 1)**2
Let r = -174 + 176. Let p(w) be the third derivative of 0*w + 2*w**r + 0 - 1/3*w**5 + 13/24*w**4 - 1/3*w**3. Determine h so that p(h) = 0.
1/4, 2/5
Let h(b) be the third derivative of -7*b**2 + 1/40*b**6 + 1/20*b**5 + 1/210*b**7 + 0 + 1/24*b**4 + 0*b + 0*b**3. Factor h(u).
u*(u + 1)**3
Suppose 0 = 5*u + 5 - 10, 13 = 4*w + u. Suppose 5*f**w + 0 - 5/3*f**5 + 0*f**4 + 10/3*f**2 + 0*f = 0. What is f?
-1, 0, 2
Suppose -4*f - 6 = -2*f. Let r be (f + 5)*(-4)/(-2). Solve 6*y**2 + 3*y**r + 9*y**3 - 10 + 10 = 0 for y.
-2, -1, 0
Let n = 72922/127589 + -2/18227. Factor -1/7*j**4 - 5/7*j**3 + 0*j - n*j**2 + 0.
-j**2*(j + 1)*(j + 4)/7
Suppose 1517*a - 5*a**3 - 297*a - 1240 + 142*a**2 - 432*a**2 = 0. What is a?
-62, 2
Let b(f) be the second derivative of f**7/105 + f**6/40 + 9*f**5/320 - 7*f**4/6 + 20*f. Let k(x) be the third derivative of b(x). Let k(h) = 0. What is h?
-3/8
Let h(y) = -y + 4. Let c be h(7). Let k be 1 + (c - 65/(-25)). Solve -k + 0*n + 3/5*n**2 = 0.
-1, 1
Let d(f) be the third derivative of 2*f**8/35 + 8*f**7/75 - 173*f**6/300 - 37*f**5/25 - 19*f**4/15 - 8*f**3/15 + 16*f**2 - 3. Determine h, given that d(h) = 0.
-2, -2/3, -1/4, 2
Let v(q) = -3*q**2 - 3*q. Suppose -n = 68 - 67. Let p be v(n). Factor 3*k + 3/2*k**4 - 3*k**3 - 3/2*k**2 + p.
3*k*