**2.
-2*d*(d - 1)*(d + 2)/11
Factor -5000/3 - 2/3*v**2 + 200/3*v.
-2*(v - 50)**2/3
Suppose 4*w - 33 = 5*p, 3*w + 4*p = 5*p + 11. Let d(z) be the first derivative of -2/9*z + w + 1/3*z**2 + 8/27*z**3. Factor d(k).
2*(k + 1)*(4*k - 1)/9
Let g(b) be the first derivative of 36/7*b**3 + 15/14*b**4 + 15 - 48/7*b + 36/7*b**2. Find t, given that g(t) = 0.
-2, 2/5
Let j = -408 + 4494/11. Suppose 0*u + 3*u = 0. Solve -j*s**2 + u + 4/11*s + 2/11*s**3 = 0 for s.
0, 1, 2
Let f = -643 - -121528/189. Let w(n) be the second derivative of 0*n**4 - 3*n + 0*n**3 + 0*n**6 + 0*n**5 + 0*n**2 + 0 - f*n**7. Let w(c) = 0. Calculate c.
0
Let m = -4 + 5. Let a(s) = -s**5 + s**3 + 1. Let v(p) = -p + 12 - 4 - 10 + p**5. Let f(b) = m*v(b) + 2*a(b). Factor f(y).
-y*(y - 1)**2*(y + 1)**2
Let i = -178 - -216. Suppose 10 = -4*l - 5*z + i, 3*z - 14 = -l. Find q, given that 6/5*q**3 - 3/5*q**l + 3/5*q**4 - 6/5*q + 0 = 0.
-2, -1, 0, 1
Let a(l) be the first derivative of -19 - l**4 + 2*l**3 - 1/5*l**5 - 5*l + 2*l**2. Determine o so that a(o) = 0.
-5, -1, 1
Let w(a) be the second derivative of 0 + 31*a - 1/6*a**2 + 1/36*a**4 + 0*a**3. Determine s, given that w(s) = 0.
-1, 1
Let i(z) be the second derivative of -2*z**7/105 + 2*z**5/25 - 2*z**3/15 + 74*z. What is b in i(b) = 0?
-1, 0, 1
Let r(t) be the third derivative of 8/35*t**6 + 15/14*t**4 + 36/35*t**5 + 0*t - 2 - t**2 - 25/14*t**3. Let r(o) = 0. What is o?
-5/4, 1/4
Let y(x) be the first derivative of x**5/5 - x**3 + x**2 + 27. Solve y(u) = 0 for u.
-2, 0, 1
Let y be (-1 + 12)/(2/6). Let -y*t**4 - 39*t**4 + 315*t**3 - 13*t**4 + 391*t**5 - 386*t**5 + 405*t**2 = 0. Calculate t.
-1, 0, 9
Factor -1/3*c**2 - 29*c - 170/3.
-(c + 2)*(c + 85)/3
Let f be 6 + 25/175*-40. Let 10/7*t + 0 + f*t**2 = 0. What is t?
-5, 0
Let h(m) be the second derivative of 3/10*m**5 + 0*m**3 - 36*m - 1 + 1/10*m**6 + 0*m**2 - 1/28*m**7 - m**4. Factor h(o).
-3*o**2*(o - 2)**2*(o + 2)/2
Let k(l) = -16*l**2 - 151*l + 6. Let i(b) = -43*b**2 - 453*b + 16. Let v(m) = -3*i(m) + 8*k(m). Determine o so that v(o) = 0.
-151, 0
Let g be 23 + -27 - (-81)/20. Let t(l) be the third derivative of -g*l**6 - 2/15*l**5 + 0*l**3 - 2*l**2 + 1/9*l**4 + 0 + 1/45*l**7 + 0*l. What is y in t(y) = 0?
-1, 0, 2/7, 2
Let c(l) be the first derivative of -2*l**5/5 - 17*l**4/2 + 2*l**3 + 49*l**2 - 68*l - 155. Find s such that c(s) = 0.
-17, -2, 1
Let c(m) = -20*m**4 + 24*m**3 + 4*m**2 - 32*m - 8. Let b(q) = 3*q + 1 + 2 + 7*q**4 - q**2 + 4*q + 4*q - 8*q**3. Let u(h) = 8*b(h) + 3*c(h). Factor u(g).
-4*g*(g - 2)*(g - 1)*(g + 1)
Let g = 65 - 63. Suppose -6 - 5 + 5 - 4*d - 2*d**g + 11*d = 0. What is d?
3/2, 2
Let w(k) be the first derivative of 4/3*k + 10 + 2/3*k**2 + 1/9*k**3. Suppose w(u) = 0. Calculate u.
-2
Let b(a) be the third derivative of 0 + 0*a - 1/27*a**3 - 1/72*a**4 - 1/540*a**5 - 7*a**2. Determine j, given that b(j) = 0.
-2, -1
Factor 6/11*w + 5/11 + 1/11*w**2.
(w + 1)*(w + 5)/11
Let s be (10/(-450)*12)/((-8)/18). Let d(q) be the third derivative of 0*q - 1/4*q**6 - 3/4*q**4 + 0 - s*q**5 - 4*q**2 - 3/70*q**7 - 1/2*q**3. Factor d(v).
-3*(v + 1)**3*(3*v + 1)
Let o(k) be the first derivative of 2*k**3/69 + 11*k**2/23 + 4. Factor o(c).
2*c*(c + 11)/23
Let b be (-40)/(-42) + -1*(-4)/(-14). Let j(m) be the first derivative of -2*m**2 - 9 - 6*m + b*m**3. Factor j(s).
2*(s - 3)*(s + 1)
Let o(l) be the third derivative of -l**6/720 + l**5/40 - 3*l**4/16 + 3*l**3/2 - l**2. Let w(a) be the first derivative of o(a). Suppose w(f) = 0. Calculate f.
3
Factor 68*q**3 + q**2 - 8 + 16*q - 70*q**3 - 5*q**2 - 2*q.
-2*(q - 1)**2*(q + 4)
Let t(g) be the second derivative of 0*g**2 + 1/336*g**7 - 12*g + 0 + 1/48*g**4 + 0*g**5 - 1/48*g**3 - 1/120*g**6. Let t(z) = 0. Calculate z.
-1, 0, 1
Factor -32/13 - 20/13*r - 2/13*r**2.
-2*(r + 2)*(r + 8)/13
Let l = 211 + -204. Let a be -6*(-2)/15*l. Factor -32/5*m**2 + a*m**3 + 2/5*m**5 + 18/5*m - 4/5 - 12/5*m**4.
2*(m - 2)*(m - 1)**4/5
Factor 12*z - 42 - 22*z**3 + 4*z**2 - 4*z**4 + 42 + 10*z**3.
-4*z*(z - 1)*(z + 1)*(z + 3)
Let u(k) = 6*k**3 - k**2 - k + 2. Let h be u(1). Factor -h*j**2 - 8*j - 582 + 582 + 2*j**3.
2*j*(j - 4)*(j + 1)
Let j(w) be the second derivative of 2*w**2 + 10/3*w**3 + 2/21*w**7 + 2/3*w**6 + 0 + 2*w**5 + 10/3*w**4 - 19*w. Factor j(t).
4*(t + 1)**5
Let q(y) be the first derivative of -y**4 + 16*y**3/3 + 42*y**2 + 413. Factor q(z).
-4*z*(z - 7)*(z + 3)
Let m = -20 - 16. Let s be 2/m*-4*9. Factor -4*d**3 + 11*d**3 + 3*d**3 - 4*d - 6*d**s.
2*d*(d - 1)*(5*d + 2)
Let s(i) be the third derivative of i**7/70 + 13*i**6/120 - 49*i**5/60 + 47*i**4/24 - 7*i**3/3 + 88*i**2. Factor s(u).
(u - 1)**2*(u + 7)*(3*u - 2)
Let x be (-25)/(-2) + 22/(-2). Factor 3/8*z**2 + 3/2 + x*z.
3*(z + 2)**2/8
Suppose -14*m + 19*m = 30. Factor -3*w**3 - 35*w + m*w**3 + 35*w.
3*w**3
Determine w, given that -3/2*w + 15/2 - 15/8*w**2 + 3/8*w**3 = 0.
-2, 2, 5
Let j(u) be the third derivative of -4/315*u**7 + 1/72*u**6 + 0*u + 0*u**3 + 0*u**4 + 1/252*u**8 + 0 - 1/180*u**5 + 18*u**2. What is l in j(l) = 0?
0, 1/2, 1
Let j = 85 - 59. Let v be j/4*(-8)/(-16). Solve -v*a**2 - 1 - 3*a - 1/4*a**4 - 3/2*a**3 = 0 for a.
-2, -1
Solve 45*u**3 + 5*u**5 - 375*u + 50*u**4 + 375*u = 0.
-9, -1, 0
Let s(q) = -73*q**3 + 585*q**2 - 7*q - 5. Let r be s(8). Find y, given that 3/4*y**r + 0 - 9*y + 33/4*y**2 = 0.
-12, 0, 1
Factor 4/3*a**2 + 0 + 8*a - 4/3*a**3.
-4*a*(a - 3)*(a + 2)/3
Let z(a) = -a**3 + 5*a**2 + 6*a - 10. Let n be z(4). Suppose 9*f - n = -6*f. What is t in 0 + 2/11*t**f + 50/11*t**4 + 0*t - 20/11*t**3 = 0?
0, 1/5
Factor 12*b**4 + 1099*b**5 + 48*b**2 + 16*b**4 - 1095*b**5 + 64*b**3.
4*b**2*(b + 2)**2*(b + 3)
Let c(u) = 3*u**3 - u**2. Let n be c(1). Let y(m) = 2*m - 16. Let f be y(9). Determine l so that 2*l**3 - 3*l**3 + 4 - 4 + n*l + l**f = 0.
-1, 0, 2
Let k = 11193 + -45923/4. Let c = k + 288. Factor -1/2 + c*b**2 + 1/4*b.
(b - 1)*(b + 2)/4
Let n(m) = 12*m**2 - 3*m**2 + 260*m - 256*m. Let q(l) = 8*l**2 + 4*l. Let v be (-1)/2 + (-18)/(-4). Let u(h) = v*n(h) - 5*q(h). Let u(z) = 0. What is z?
-1, 0
Find v such that 1/3*v**3 - 197/3*v + 33 + 97/3*v**2 = 0.
-99, 1
Let b = 3156359/35 - 90167. Let q = -72/5 + b. Factor 0*p**2 - 2/7*p**3 + 0 + 0*p + q*p**4.
2*p**3*(p - 1)/7
Let y(z) be the second derivative of 5*z**5/4 - 145*z**4/12 + 100*z**3/3 - 40*z**2 - 313*z. Factor y(x).
5*(x - 4)*(x - 1)*(5*x - 4)
Let h = 121 + -41. Let 19 + 3*o**4 + 17*o**4 - 88*o**3 - h*o - 3 + 132*o**2 = 0. What is o?
2/5, 1, 2
Suppose 22*x = 38*x - 0*x - 96. Factor -1/2 + x*n**2 - 13/4*n**3 - 9/4*n.
-(n - 1)**2*(13*n + 2)/4
Let o(l) = 2*l**3 + 30*l**2 - 11*l - 69. Let w(k) = -k**3 - 2*k**2 - k + 1. Let h(p) = -4*o(p) - 20*w(p). Determine y, given that h(y) = 0.
-4/3, 4
Let p = 85 + -83. Determine b so that -8*b + 38*b**3 - p*b + 11*b**4 - 4 + 9*b**4 + 12*b**2 + 0*b = 0.
-1, -2/5, 1/2
Let c(x) be the second derivative of x**8/8400 + x**7/840 + x**6/600 - 3*x**5/200 + 2*x**3 - 22*x. Let v(b) be the second derivative of c(b). Factor v(u).
u*(u - 1)*(u + 3)**2/5
Let t be 48/32*2/2. Factor o + 0 + 1/2*o**3 - t*o**2.
o*(o - 2)*(o - 1)/2
Suppose 7*s - 239*d + 243*d - 4 = 0, -3*d = 5*s - 2. Factor 0 + 6/5*w**3 - 3/5*w**2 - 3/5*w**s + 0*w.
-3*w**2*(w - 1)**2/5
Let v(d) = d**3 + d + 1. Let n(z) = 4*z**4 + 19*z**3 + 32*z**2 - z - 15. Let x(u) = -2*n(u) - 6*v(u). Solve x(f) = 0 for f.
-3, -2, -1, 1/2
Let r(n) = -3*n - 17. Let o be r(-8). Suppose o*w - 32 = -18. Factor -2/5*g**w + 8/5*g - 6/5.
-2*(g - 3)*(g - 1)/5
Let f(t) be the first derivative of 3/2*t**2 - 11*t**3 - 9/5*t**5 + 33/4*t**4 - 55 + 6*t. Suppose f(v) = 0. Calculate v.
-1/3, 1, 2
Let c = -92 + 95. Factor c*m - 15*m**3 + 0*m**2 + 14*m**2 - 11*m**2 + 9*m**4.
3*m*(m - 1)**2*(3*m + 1)
Suppose -5*r + 5*h + 5 = 0, 2 = 4*r + 106*h - 111*h. Let c = -92/7 + 1238/91. Factor -2/13 - c*d**2 + 6/13*d + 2/13*d**r.
2*(d - 1)**3/13
Factor 0 + 0*g - 2/17*g**2 - 2/17*g**3.
-2*g**2*(g + 1)/17
Let m be (((-135)/(-378))/5)/(1/4). Find t, given that 0*t + 0 + m*t**3 - 2/7*t**5 + 0*t**4 + 0*t**2 = 0.
-1, 0, 1
Let n(t) be the third derivative of -5/2*t**6 - 12/35*t**7 - 71/15*t**5 - 25/6*t**4 + 0 + 0*t - 2*t**3 - 22*t**2. Find l, given that n(l) = 0.
-3, -1/2, -1/3
Let o be (-8)/56*(0 + 0). Let s(m) be the second derivative of -4*m + o - 27/70*m**5 - 9/14*m**4 + 0*m**3 + 4/7*m**2. Find x,