 - 3 = -3*t. Let b(g) be the first derivative of 2/27*g**3 - 4 + 0*g + y*g**2. Determine m so that b(m) = 0.
0
Factor -3*v**2 - 10*v**5 - 3254*v**4 + 2769*v**4 + 3*v**2 - 10*v**5.
-5*v**4*(4*v + 97)
Let c(q) = -q**2 - 20*q - 28. Let p be c(-16). Let h be 1*((-8)/p + 164/252). Find j, given that h + 4/7*j + 1/7*j**2 = 0.
-3, -1
Let j(w) be the first derivative of -w**7/105 + w**6/20 - w**5/15 - 27*w**2/2 - 3. Let v(q) be the second derivative of j(q). Factor v(c).
-2*c**2*(c - 2)*(c - 1)
Let j = -69 + 74. Let k be 69*j/90 + 2/12. Factor -5*h**5 + 0*h**3 - 2*h**3 + 4*h**5 - 3*h**k.
-h**3*(h + 1)*(h + 2)
Suppose 5*c = q - 30, 0 = -8*q + 10*q - c - 15. Factor -52*v**2 - 20 - 65*v - 21*v**2 - 13*v**2 - 35*v**3 + 11*v**2 - q*v**4.
-5*(v + 1)**3*(v + 4)
Solve 0 + 1/6*n**3 - 121/6*n - 20*n**2 = 0.
-1, 0, 121
Find s, given that 1/8*s**4 + 0 + 9/2*s**3 + 17/4*s + 69/8*s**2 = 0.
-34, -1, 0
Let m(b) be the first derivative of -134*b**3/39 + 70*b**2/13 - 6*b/13 - 2545. Factor m(o).
-2*(o - 1)*(67*o - 3)/13
Let d(f) = 1441*f**2 - 2. Let h be d(1). Factor 2*b + 1440*b**2 - h*b**2 - 24 + 0*b.
(b - 4)*(b + 6)
Factor 848/3*x**3 + 87344*x - 4/3*x**4 - 127308 - 47416/3*x**2.
-4*(x - 103)**2*(x - 3)**2/3
Let l(w) be the second derivative of 15*w**2 - 1 + 3/2*w**3 - 1/4*w**4 - w. What is b in l(b) = 0?
-2, 5
Find i such that 215 + 2*i + 8*i + 7*i - 2*i + 3*i**2 - 203 = 0.
-4, -1
Let f(k) = -22*k - 107. Let c be f(-5). Factor -7*r + 293 + r**c - 581 - 6*r**2 + 288.
r*(r - 7)*(r + 1)
Let z(f) be the first derivative of 19 - 4/3*f**3 + 76*f**2 + 0*f. Factor z(s).
-4*s*(s - 38)
Let w(a) be the second derivative of -3*a**5/20 - 5*a**4/2 + 143*a**3/2 + 2178*a**2 + 479*a. Factor w(c).
-3*(c - 12)*(c + 11)**2
Solve -1235/3*n**2 + 35/3*n**4 + 1/3*n**5 - 1444/3*n + 81*n**3 + 0 = 0 for n.
-19, -1, 0, 4
Factor -4099 - 5*h**2 + 7996 - 4647 - 385*h + 0*h**2.
-5*(h + 2)*(h + 75)
Let z(v) be the first derivative of 4768*v**3 + 147/5*v**5 - 231 - 24576*v - 3840*v**2 - 1221/2*v**4 - 1/2*v**6. Find b, given that z(b) = 0.
-1, 2, 16
Let r(k) be the first derivative of 8/5*k + 5/4*k**4 + 4/25*k**5 + 22/5*k**2 + 17 + 18/5*k**3. Factor r(a).
(a + 2)**3*(4*a + 1)/5
Let c(p) be the first derivative of -3*p**4/20 + 234*p**3/5 + 2847*p**2/10 + 2142*p/5 - 2236. Find u, given that c(u) = 0.
-3, -1, 238
Let m(r) = -25 - 85*r**2 - 57*r - 6*r - 82*r. Let s be -6*11/66*-25. Let w(q) = -7*q**2 - 12*q - 2. Let t(d) = s*w(d) - 2*m(d). Factor t(p).
-5*p*(p + 2)
Let r(n) be the first derivative of -37*n**5/20 - 35*n**4/16 + 19*n**3/3 - n**2/2 + 3280. What is z in r(z) = 0?
-2, 0, 2/37, 1
Let r(b) be the first derivative of 16/5*b - 73 - 4/5*b**2 + 1/15*b**3. Suppose r(z) = 0. What is z?
4
Let q(a) = a**2 + 6*a - 1. Let m be q(-7). Suppose 61*r = 14*r + 235. Factor -m*j**4 + r*j**4 + 6*j**3 + 3 - 6*j - 2*j**4.
-3*(j - 1)**3*(j + 1)
Let g(f) be the third derivative of -f**7/70 + 3*f**6/40 - 73*f**2 + 6*f. Find z such that g(z) = 0.
0, 3
Factor 1/6*m**2 - 116*m + 20184.
(m - 348)**2/6
Factor 289 + 1/4*j**4 - 1581/4*j + 463/4*j**2 - 39/4*j**3.
(j - 17)**2*(j - 4)*(j - 1)/4
Solve -15390/11*f**2 + 338/11*f**3 - 2/11*f**4 + 0 + 91854/11*f = 0.
0, 7, 81
Let h(i) be the first derivative of -20*i**3/3 - 1346*i**2 + 1080*i - 1743. Factor h(z).
-4*(z + 135)*(5*z - 2)
Determine i so that -21*i**5 - 120*i + 83*i**3 - 388*i**3 - 95*i**4 - 490*i**2 + 11*i**5 + 120*i**2 = 0.
-4, -3, -2, -1/2, 0
Let b(h) be the third derivative of h**8/201600 - h**7/450 + 98*h**6/225 + 7*h**5/20 + 26*h**2 + 2*h. Let g(f) be the third derivative of b(f). Factor g(x).
(x - 56)**2/10
Let q = -550/73 + 6575/146. Suppose -q - 45*z**3 - 120*z**2 - 5/2*z**4 - 115*z = 0. What is z?
-15, -1
Let q(l) = -l**2 - 6*l + 2. Let s be q(-6). Let d be (-5)/(-1) + s/(-2). Factor -36*f**2 - 29 + 29 + d*f**4.
4*f**2*(f - 3)*(f + 3)
Let i be (2/7)/(83/581). Factor 0 + 9/8*x - 3/8*x**i.
-3*x*(x - 3)/8
Let r(o) = -2*o**4 + 32*o**3 - 46*o**2 - 74*o - 8. Let u(f) = -2*f**4 + 33*f**3 - 46*f**2 - 72*f - 12. Let l(y) = 3*r(y) - 2*u(y). What is h in l(h) = 0?
-1, 0, 3, 13
Let -194/9*z**2 + 2/9*z**3 - 2848/9 + 1456/9*z = 0. What is z?
4, 89
Suppose 3 = -2*n - 5*d + 7, 0 = -4*d. Suppose n*l = 2*j - 18 + 2, -5*j - l + 16 = 0. Find g such that -7*g + 13*g**2 - 13*g**2 + 4 - j*g**4 + 8*g**3 - g = 0.
-1, 1
Let h(s) be the first derivative of s**4/8 + 32*s**3/3 - 269*s**2/4 + 102*s - 1867. Factor h(z).
(z - 3)*(z - 1)*(z + 68)/2
Let l(i) = 3*i**4 - 18*i**3 + 21*i**2 - 12*i. Let f(x) = -3*x**4 + 18*x**3 - 22*x**2 + 12*x. Let v(j) = 6*f(j) + 5*l(j). Solve v(c) = 0.
0, 1, 4
Let z(y) be the first derivative of y**6/30 + 6*y**5/25 + 9*y**4/20 + 609. Factor z(p).
p**3*(p + 3)**2/5
Let z be 407/(-370) - (-6)/(-10) - -2. Let g(f) be the first derivative of 8/15*f**3 - 2 + 1/15*f**6 - z*f**4 + 4/5*f**2 + 0*f - 4/25*f**5. Factor g(n).
2*n*(n - 2)**2*(n + 1)**2/5
Determine d so that 356*d**2 - 314*d - 578*d**2 + 4*d**3 + 688 - 38*d - 118*d**2 = 0.
-2, 1, 86
Suppose -135/2 - 137/4*c - 1/4*c**2 = 0. Calculate c.
-135, -2
Suppose 3*v + 0*v + 3*p = 102, -4*p = -12. Let f = 1376 - 1374. Let -16*l**2 + 11*l + 8*l - 20 + v*l**f + l + 5*l**4 - 20*l**3 = 0. Calculate l.
-1, 1, 2
Let h(p) be the first derivative of 2/9*p**2 - 2/45*p**5 + 2/9*p**4 + 0*p - 10/27*p**3 + 37. Factor h(t).
-2*t*(t - 2)*(t - 1)**2/9
Let i(v) be the first derivative of 3*v**4/4 + 25*v**3 - 888*v**2 + 7872*v - 2759. Factor i(x).
3*(x - 8)**2*(x + 41)
Let h(l) be the first derivative of -3*l**5/5 - 135*l**4/2 + 1923. Solve h(g) = 0 for g.
-90, 0
Let n be (88/6)/(2/(-9)). Let c be ((-252)/n - 6/(-33)) + 1. Find o such that o**2 - 3*o**3 + 3*o**c + 12*o**2 - 6*o**4 - 7*o**2 = 0.
-1, 0, 1, 2
Let t(p) be the second derivative of 1/30*p**6 + 1/30*p**5 + 1/126*p**7 + 0*p**2 + 0*p**4 + 0*p**3 - 166*p + 0. Suppose t(k) = 0. Calculate k.
-2, -1, 0
Suppose 5*t + 21 = 2*t. Let o be t + (-8)/(224/(-371)). Suppose 15/4*n**2 - 5*n**4 + 25/4*n + 5/4 - o*n**3 = 0. Calculate n.
-1, -1/4, 1
Let x(n) = 7*n - 47. Let v be x(7). Factor -2 - 22*i**v + 32*i**2 + 5*i**4 + 15*i**3 + 2.
5*i**2*(i + 1)*(i + 2)
Let f(u) be the second derivative of -32*u - 1/20*u**5 + 0*u**3 + 1/10*u**6 + 0 + 0*u**4 + 0*u**2 + 2/21*u**7. Solve f(y) = 0.
-1, 0, 1/4
Let d be -4 - 16*((-150)/(-20) + -8). Let g(c) be the first derivative of 2/5*c**d + 5 - 34/15*c**3 + 4/5*c**2 + 0*c. Factor g(w).
2*w*(w - 4)*(4*w - 1)/5
Let b(n) be the third derivative of -1/96*n**6 + 9*n + 0 + 5/6*n**3 - n**2 + 11/48*n**5 + 5/1344*n**8 - 5/8*n**4 - 1/56*n**7. Factor b(j).
5*(j - 2)*(j - 1)**3*(j + 2)/4
Suppose k = -0*k + 4. Let b = 22 + -19. Factor -58*s**5 + 3*s**3 + 64*s**5 - k*s**4 - 3*s**b.
2*s**4*(3*s - 2)
Let v = -1388027/1197 + -9084/133. Let k = 1228 + v. Find x, given that -k*x**2 - 8/9 + 2/3*x = 0.
2, 4
Suppose 0 + 1296*j + 48*j**2 + 4/9*j**3 = 0. Calculate j.
-54, 0
Let h(o) be the second derivative of -5/21*o**3 + 1/70*o**5 + 6/7*o**2 + 2*o - 1/21*o**4 - 2. Let h(d) = 0. What is d?
-2, 1, 3
Let u = 18951 - 18948. Factor 32/5*d + 16/5*d**2 + 0 + 2/5*d**u.
2*d*(d + 4)**2/5
Let o = 488 + -485. Solve 17*z**3 + 66*z**2 + 13*z**o + 20*z - 6*z**3 + 23*z**3 - 10*z**4 - 11*z**3 = 0.
-1, -2/5, 0, 5
Suppose -160*x - 4*a = -159*x + 1, a - 33 = -5*x. Let m(w) be the first derivative of -4*w + 32/3*w**3 - x - 4*w**2. Solve m(j) = 0 for j.
-1/4, 1/2
Let w(g) be the second derivative of -g**4/66 + 307*g**3/33 - 306*g**2/11 - 69*g - 25. Suppose w(a) = 0. What is a?
1, 306
Let s = 61415 - 61410. Suppose -35/3*w**2 - s*w**3 - 8/3 - 10*w - 2/3*w**4 = 0. Calculate w.
-4, -2, -1, -1/2
Suppose -6*b - 4*b = -250. Let w = b + -22. What is c in 5*c**w - 3*c**4 + c**2 - 2 - 3*c - 2*c**3 + 4*c**4 = 0?
-2, -1, 1
Let b = 16994 - 84966/5. Factor -19/5*v**2 + 8/5*v + 7/5*v**3 + b.
(v - 2)*(v - 1)*(7*v + 2)/5
Let c(b) = -6*b - b**2 + 16 + 0*b**2 - b + 7*b**3 - 12*b. Let g(l) = 48*l**3 - 8*l**2 - 132*l + 112. Let s(r) = -20*c(r) + 3*g(r). Suppose s(p) = 0. What is p?
-2, 1, 2
What is k in -1/7*k**5 + 0 - 9/7*k**2 + 20/7*k + 9/7*k**4 - 19/7*k**3 = 0?
-1, 0, 1, 4, 5
Factor 3/5*a**3 - 321/5*a**2 - 2739/5*a - 483.
3*(a - 115)*(a + 1)*(a + 7)/5
Let c(v) be the first derivative of 1/2*v**3 - 162 + 5046*v - 87*v**2. Suppose c(n) = 0. What is n?
58
Let m(w) be the first derivative of 0*w - 1/15*w**3 - 52 - 2/