) be the first derivative of j**6/90 + j**5/30 + j**4/36 - 4*j + 2. Let a(d) be the first derivative of x(d). Find w, given that a(w) = 0.
-1, 0
Let t(v) be the first derivative of -v**8/4200 + v**7/2100 + v**6/900 - v**5/300 + 2*v**3/3 + 2. Let q(f) be the third derivative of t(f). Factor q(z).
-2*z*(z - 1)**2*(z + 1)/5
Let d be (-1)/4 + (-12555)/84. Let o = d + 150. Factor o + 0*p - 2/7*p**2.
-2*(p - 1)*(p + 1)/7
Suppose -4*c + 4 = 4*n, -5*n + 0*n + 5 = 4*c. Let o be c - (-4)/(2/1). Solve 1/3*k**o - 2/3*k + 0 = 0.
0, 2
Factor -15 + 10*o + 8*o**2 + 7 - 2*o**2 + 2*o**4 - 10*o**3.
2*(o - 4)*(o - 1)**2*(o + 1)
Let z(o) be the first derivative of -o**4/8 + o**3/6 + o**2/4 - o/2 + 11. Solve z(s) = 0 for s.
-1, 1
Let 0 + 1/2*r**2 + 0*r = 0. Calculate r.
0
Let b(g) = 8*g**3 - 4*g**2 - 14*g + 10. Let t(v) = -v**3 + v + 1. Let m(k) = -2*b(k) - 12*t(k). Find n such that m(n) = 0.
-2, 2
Suppose -5*x + 0*x + 13 = 2*j, -5*x = -4*j + 11. Find d, given that 6 - 12*d - x + 13 + 2*d**2 = 0.
3
Suppose -15*z - z**3 - 4*z**2 - 92 + 6*z**2 + 90 + 16*z = 0. Calculate z.
-1, 1, 2
Let p(l) be the third derivative of l**8/1344 - l**7/210 + l**6/96 - l**5/120 - 12*l**2. Factor p(i).
i**2*(i - 2)*(i - 1)**2/4
Suppose 3*q + 17 = -5*p, 0*q + 13 = q - 3*p. Let f be q + 38/(-14) - -2. Find d, given that 2/7*d**2 - 2/7*d**4 - 2/7*d**5 + f*d**3 + 0*d + 0 = 0.
-1, 0, 1
Let w(g) be the third derivative of -g**8/20160 - g**7/2520 - g**5/30 - 3*g**2. Let k(d) be the third derivative of w(d). Factor k(v).
-v*(v + 2)
Let p(q) be the second derivative of q**6/15 + 3*q**5/50 - 2*q**4/5 + 4*q**3/15 + 4*q. Suppose p(s) = 0. What is s?
-2, 0, 2/5, 1
Let s(k) be the first derivative of k**8/1344 - k**7/420 + k**6/480 + 3*k**2 + 1. Let r(p) be the second derivative of s(p). Find w such that r(w) = 0.
0, 1
Solve 12 + 4*f - 16*f - f**2 + 4*f**2 = 0 for f.
2
Suppose 4 + 7 = 4*v + s, -5*v = -4*s - 19. Suppose 3 - 15 = -v*j. Determine t so that 2*t**j + 2*t**3 + 3*t**4 - t**2 - 6*t**4 = 0.
0, 1
Factor -8/5 - 6/5*g + 2/5*g**2.
2*(g - 4)*(g + 1)/5
Let n be 32/80 - 294/10. Let h = -85/3 - n. Factor -h*l**2 - 8/3 - 8/3*l.
-2*(l + 2)**2/3
Let l(c) be the third derivative of -1/50*c**5 + 1/175*c**7 + 0*c**3 + 0*c - 2*c**2 + 1/60*c**6 - 1/210*c**8 + 0 - 1/60*c**4. Find k, given that l(k) = 0.
-1, -1/4, 0, 1
Let n = -2 + -1. Let i(u) = u**3 + 4*u**2 + 2*u - 3. Let w be i(n). Factor -14*r + 2*r**4 + 18*r**2 + w + 4 - 12*r**3 + 2*r**3.
2*(r - 2)*(r - 1)**3
Let p(x) be the third derivative of x**6/60 + x**5/30 - x**4/12 - x**3/3 - 3*x**2. Solve p(r) = 0.
-1, 1
Suppose f - 13 = -3*q - 1, -q = -4. Suppose f*r = -4*r. Factor r*b + 0 - 2/3*b**2.
-2*b**2/3
Suppose -f = 3*f - 16. Suppose -f*i + 56 + 0 = 0. Let i + a**3 - 14 = 0. What is a?
0
Let p(y) be the second derivative of y**6/10 - 25*y. Factor p(u).
3*u**4
Let s(m) be the second derivative of -1/5*m**6 + 0 - 1/14*m**7 + 3*m**2 + 3/10*m**5 + 2*m**4 + 7/2*m**3 - 3*m. Factor s(v).
-3*(v - 2)*(v + 1)**4
What is z in -45*z**2 + 10*z**3 + 32 + 5*z**2 - 4*z**5 + 4*z**3 + 6*z**3 - 16*z + 8*z**4 = 0?
-2, -1, 1, 2
Let k(d) = -6*d**5 + 4*d**4 - 3*d**2 - 3. Let f(r) = 12*r**5 - 8*r**4 + 7*r**2 + 7. Let b(y) = 3*f(y) + 7*k(y). Let b(m) = 0. What is m?
0, 2/3
Let i(r) be the first derivative of -r**3/3 - 2*r**2 - 4*r + 10. Let i(v) = 0. Calculate v.
-2
Let t = 32 + -30. Suppose -t*g = -g. Factor -1/4*d**4 + 1/4*d**5 + 0*d**3 + g*d + 0*d**2 + 0.
d**4*(d - 1)/4
Let f(q) be the second derivative of -1/6*q**3 + 0 - q**2 + 1/12*q**4 - 4*q. Solve f(c) = 0.
-1, 2
Factor 4 + 14*g**2 + 3*g**3 + 5*g - 7*g**5 - 16*g**4 - 2 + 6*g - 7*g**3.
-(g - 1)*(g + 1)**3*(7*g + 2)
Let t(n) = -3*n + 5. Let a(z) = -9*z + 16. Let p(v) = -4*a(v) + 11*t(v). Let i be p(6). Determine f, given that -i + 9 + 2*f**2 = 0.
0
Factor -4/5*y**2 + 0*y + 0 + 4/5*y**3.
4*y**2*(y - 1)/5
Suppose -l = 4*f + 2, 5*l - f - 3 = 50. Solve -6*y + 12*y**2 + y**4 - 4*y**2 + l*y + 5*y**3 = 0.
-2, -1, 0
Factor 2/5*i**5 + 6/5*i**3 + 0*i + 0 - 2/5*i**2 - 6/5*i**4.
2*i**2*(i - 1)**3/5
Let p(x) = x**2 - 6*x + 8. Let l be p(5). Suppose -5 = -3*f - w + 5, -6 = -f - l*w. Factor 2/5*k**f + 0 - 4/5*k**2 + 2/5*k.
2*k*(k - 1)**2/5
Factor 11 - 3 + 2*r**2 + 4*r**2 + 1 - 21*r.
3*(r - 3)*(2*r - 1)
Let v(q) = -q**4 - q**3 - q**2. Let s(g) = -2*g**4 + 29*g**3 + 81*g**2 + 40*g - 16. Let j(x) = 5*s(x) - 30*v(x). Let j(d) = 0. What is d?
-4, -1, 1/4
Let g = 499/210 - -1/42. What is l in -12/5*l + 16/5*l**2 - 18/5*l**4 + g*l**3 + 2/5 = 0?
-1, 1/3, 1
Let m(s) be the first derivative of -2*s**6/3 + 28*s**5/5 - 19*s**4 + 100*s**3/3 - 32*s**2 + 16*s + 14. Factor m(l).
-4*(l - 2)**2*(l - 1)**3
Factor 14*i**4 + 8/7*i + 0 + 6*i**3 - 48/7*i**2.
2*i*(i + 1)*(7*i - 2)**2/7
Let m(h) be the third derivative of -h**7/45 - 4*h**6/45 - 11*h**5/90 - h**4/18 - 10*h**2. Factor m(i).
-2*i*(i + 1)**2*(7*i + 2)/3
Let p be 282/(-255)*(-10)/(-24). Let g = 2/51 - p. Determine w so that 1/2 + w + g*w**2 = 0.
-1
Let u(v) = -v**5 + v**4 - 3*v**3 + 3*v**2 - 4*v. Let z(w) = w**4 + w**2 - w. Let h(c) = u(c) - 4*z(c). Solve h(n) = 0.
-1, 0
Let u(d) = -d + 13. Let l be u(0). Let r = l - 25/2. Factor -1/2*v**2 - r + v.
-(v - 1)**2/2
Let f(q) be the second derivative of q**7/56 - 3*q**6/40 + 9*q**5/80 - q**4/16 + 7*q. Solve f(z) = 0 for z.
0, 1
Let d(k) = 9*k**4 - 24*k**3 + k**2 + 4*k. Let h(i) = 13*i**4 - 36*i**3 + i**2 + 6*i. Let z(p) = 8*d(p) - 5*h(p). Factor z(r).
r*(r - 1)**2*(7*r + 2)
Let n be -1 - (-2 + (2 - 4)). Solve 0*t**3 - 2*t - 6*t**n - t**2 + 0*t + 7*t**3 = 0.
-1, 0, 2
Let c(w) be the second derivative of w**7/336 + w**6/120 + w**5/160 + 7*w. Let c(a) = 0. Calculate a.
-1, 0
Determine j, given that 12*j**2 + 3*j - 5*j**2 - 4*j**2 + 15*j + 24 = 0.
-4, -2
Let o(k) be the second derivative of k**6/165 - k**4/66 + 2*k. Let o(g) = 0. What is g?
-1, 0, 1
Let a = -3/1453 - -11723/47949. Let b = a + 1/11. Solve b*s**2 + 1/3*s**3 - 1/3*s + 0 - 1/3*s**4 = 0 for s.
-1, 0, 1
Let g(o) be the third derivative of -5*o**2 + 0*o**5 - 1/360*o**6 + 0*o**3 + 1/630*o**7 + 0 + 0*o**4 + 0*o. Find j such that g(j) = 0.
0, 1
Let u = -74 - -78. Factor 4/9*g + 14/9*g**5 + 0 + 6*g**3 - 26/9*g**2 - 46/9*g**u.
2*g*(g - 1)**3*(7*g - 2)/9
Determine g so that 1/2*g**4 + 0*g - 1/2*g**2 + 1/2*g**3 - 1/2*g**5 + 0 = 0.
-1, 0, 1
Let a be 2*(-155)/(-60) + 1/(-6). What is t in -10/3*t**3 - 4/9*t + 22/9*t**4 - 2/3*t**a + 0 + 2*t**2 = 0?
0, 2/3, 1
Let w(z) be the first derivative of z**3/12 + 9*z**2/8 + 2*z + 38. Suppose w(a) = 0. What is a?
-8, -1
Let o = 21 + -19. What is x in -x**3 + 1/2*x**4 + x + 0*x**o - 1/2 = 0?
-1, 1
Let p be (-2)/8 + 87/(-60)*-1. Let v(s) be the first derivative of 0*s + 0*s**2 - 3/4*s**4 + p*s**5 + 0*s**3 - 2 - 1/2*s**6. Factor v(z).
-3*z**3*(z - 1)**2
Let h(k) be the first derivative of -k**3/3 + k + 1. Find c such that h(c) = 0.
-1, 1
Let o = 2848/3 + -949. Factor r + o*r**3 + r**2 + 1/3.
(r + 1)**3/3
Let g(z) = -4*z**4 + 2*z**3 - z**2 + 3*z + 3. Let w(n) = 7*n**4 - 3*n**3 + n**2 - 5*n - 5. Let v(m) = 5*g(m) + 3*w(m). Suppose v(y) = 0. What is y?
-2, 0, 1
Suppose -8/7*k + 0 + 8/7*k**2 + 6/7*k**3 = 0. What is k?
-2, 0, 2/3
Let i be 218/1199 - 184/(-198). Factor -i*q**4 - 2*q**3 - 2/9*q**5 + 0 - 14/9*q**2 - 4/9*q.
-2*q*(q + 1)**3*(q + 2)/9
Let -1/4*n**2 - 1/2*n + 0 = 0. Calculate n.
-2, 0
Let d(o) be the second derivative of -7*o**7/30 - 7*o**6/30 - o**5/15 - 3*o**2/2 + 2*o. Let u(l) be the first derivative of d(l). Solve u(z) = 0 for z.
-2/7, 0
Suppose 3/5*w**5 + 1/5 - 11/5*w**4 + 14/5*w**3 - 1/5*w - 6/5*w**2 = 0. Calculate w.
-1/3, 1
Let l(y) = -3*y**2 + 14*y - 5. Let i be l(4). Factor 2/9*t**i + 8/3*t + 4/3*t**2 + 16/9.
2*(t + 2)**3/9
Let h = 25 + -17. Find k, given that 4 - h*k**4 + 20*k + k - 3*k - 5*k**3 + 4*k**2 - 13*k**3 = 0.
-2, -1, -1/4, 1
Let d(v) be the third derivative of 0 - 1/36*v**4 + 0*v**3 + 1/30*v**5 - 1/60*v**6 - 4*v**2 + 0*v + 1/315*v**7. Factor d(c).
2*c*(c - 1)**3/3
Let j be -4*((-5)/((-280)/108) - 2). Factor 4/7 + 6/7*u + j*u**2.
2*(u + 1)*(u + 2)/7
Find b such that 26*b**2 - 6*b**2 - 30*b**3 - 5*b**5 - 2*b - 3*b + 20*b**4 = 0.
0, 1
Suppose 3*j + 8 = 41. Let o = j + -8. Factor -2*g**4 + g**3 - 2*g**4 + o*g**4.
-g**3*(g - 1)
Factor 28*k**3 - 2 - 30*k**3 + 2 - k**4.
-k**3*(k + 2)
Let u(b) be the first derivative of -b**3 + 0*b**2 + 0*b - 3/5*b**5 -