(a).
-3*(a - 3)**3
Let t(m) be the third derivative of m**2 + 1/15*m**3 + 0 + 1/30*m**4 + 0*m + 1/150*m**5. Find x, given that t(x) = 0.
-1
Let q(x) be the first derivative of 1 + 1/3*x**3 + 0*x + 0*x**2. Solve q(n) = 0 for n.
0
Let v = -7 + 12. Factor -11 + 2*q + q**4 + 11 - v*q**2 + 2*q**2.
q*(q - 1)**2*(q + 2)
Suppose 6/7*n**2 - 9/7*n + 0 + 3/7*n**3 = 0. Calculate n.
-3, 0, 1
Let x(g) = 10*g - 40. Let f be x(4). Let r(q) be the second derivative of 0*q**2 - 3/20*q**5 + 1/4*q**4 + 1/2*q**3 - 1/10*q**6 + f + 4*q. Factor r(u).
-3*u*(u - 1)*(u + 1)**2
Let k(m) = -m**3 + 7*m**2 + m - 3. Let w be k(7). Suppose 24 = 4*f + 3*i, 0 = 4*f + i - 6*i + 8. Find l such that -8*l + 23 + w + f*l**2 + 26*l = 0.
-3
Let g(k) be the third derivative of k**7/1365 + 7*k**6/390 + 61*k**5/390 + 7*k**4/13 + 12*k**3/13 - 48*k**2. Factor g(l).
2*(l + 1)**2*(l + 6)**2/13
Let q be 1/((1 + 2)/966). Let b = q - 1273/4. Find j, given that 1/2*j - j**5 - 4*j**3 - b*j**4 + 0 - 3/4*j**2 = 0.
-2, -1, 0, 1/4
Let w = 5 - 3. Let k be 1*((-3)/(-3))/w. Factor 0 + k*g + 1/2*g**2.
g*(g + 1)/2
Let a(t) be the third derivative of 0 + 1/120*t**6 - 1/30*t**5 + 0*t**3 + 0*t + 0*t**4 + t**2 + 1/70*t**7. Factor a(s).
s**2*(s + 1)*(3*s - 2)
Let g(s) = 2*s**5 + 2*s**4 - 12*s**3 + 2*s**2 + 14*s - 6. Let u(d) = -d**4 + d**3 + d**2 - d + 1. Let c(b) = g(b) + 6*u(b). Find k such that c(k) = 0.
-1, 0, 2
Let g(f) be the first derivative of -f**4/10 - 8*f**3/15 - f**2 - 4*f/5 - 8. Factor g(q).
-2*(q + 1)**2*(q + 2)/5
Suppose m - 4*g - 2 = 4*m, 12 = 4*m - 2*g. Factor -10/7*d**m - 2*d - 4/7.
-2*(d + 1)*(5*d + 2)/7
Solve -f**4 - 6*f**2 + 2*f**3 - 2*f**2 + 7*f**2 = 0.
0, 1
Let f(m) be the first derivative of -2*m**3/3 - 34*m**2 - 578*m + 1. Factor f(u).
-2*(u + 17)**2
Suppose -k = -2*k + 4*v - 12, 6 = -5*k + 2*v. Let o(u) = u**2 + u + 4. Let h be o(k). Factor -r**2 + 1/2*r**h - r**3 + 1/2 + 1/2*r + 1/2*r**5.
(r - 1)**2*(r + 1)**3/2
Let -1/2 - 1/2*q**2 - q = 0. Calculate q.
-1
Factor 7/9*k - 16/9*k**3 + 1/9 + 8/9*k**2.
-(k - 1)*(4*k + 1)**2/9
Find w, given that -27/2*w - 1/2*w**3 + 27/2 + 9/2*w**2 = 0.
3
Factor 1/9*m**3 + 0 + 0*m**2 - 4/9*m.
m*(m - 2)*(m + 2)/9
Let h(o) = -o**4 - o**2 + o + 1. Let q(t) = 8*t**4 - 40*t**3 + 44*t**2 - 20*t + 8. Let a(f) = -4*h(f) + q(f). Let a(r) = 0. Calculate r.
1/3, 1
Let h(z) = z**2 + 37*z + 72. Let v be h(-35). Factor -o**v - 1/2 - 1/4*o**3 - 5/4*o.
-(o + 1)**2*(o + 2)/4
Let b(m) = -m**2 - m. Let t(d) = 3*d**3 + 7*d + 13 + 14*d**2 - 3 - 4 + 10*d. Let u(x) = -2*b(x) - t(x). Factor u(o).
-3*(o + 1)**2*(o + 2)
Let p = -1474023/5 - -293577. Let b = p - -1234. Factor -8/5 + b*v - 14/5*v**2.
-2*(v - 2)*(7*v - 2)/5
Let i(b) be the third derivative of b**6/180 - b**5/270 - 2*b**4/27 - 4*b**3/27 + 4*b**2. Find n, given that i(n) = 0.
-1, -2/3, 2
Let s(g) = 2*g + 3. Let b be s(0). Suppose -b*c - c = 0. Factor -2/7*n**5 + 0*n + 2/7*n**3 - 2/7*n**4 + c + 2/7*n**2.
-2*n**2*(n - 1)*(n + 1)**2/7
Let x be -6*1/(-4)*2. Suppose 0 = -0*o + o - x. Suppose 3 + 12*s**o + 21*s**2 + 8*s**3 + 1 - 25*s**4 - 20*s = 0. What is s?
-1, 2/5, 1
Let n be 23/(-66) - (-4)/6. Let q = n + 2/11. Factor q*v**2 + v + 1/2.
(v + 1)**2/2
Let g(q) be the second derivative of q**7/840 - q**6/60 + 3*q**5/40 - q**4/12 + 4*q. Let y(r) be the third derivative of g(r). Solve y(w) = 0.
1, 3
Let u(o) be the first derivative of 2*o**3/3 + 38*o**2/7 + 30*o/7 + 62. Solve u(p) = 0 for p.
-5, -3/7
Suppose -6 - 3/2*r**2 - 6*r = 0. Calculate r.
-2
Let v(m) be the second derivative of -m**8/6720 + m**6/240 + m**5/60 - m**4/3 - 2*m. Let f(k) be the third derivative of v(k). Suppose f(l) = 0. Calculate l.
-1, 2
Suppose 1 - 1 = 37*y. Suppose 0*q - 3/2*q**3 - 5/2*q**4 + y + q**2 = 0. Calculate q.
-1, 0, 2/5
Let z(d) be the first derivative of -243*d**4/16 + 63*d**3/4 - 6*d**2 + d + 1. Determine y so that z(y) = 0.
2/9, 1/3
Let g be (-9)/15 - (-55)/50. Factor u**2 + g - 3/2*u.
(u - 1)*(2*u - 1)/2
Let t(w) be the first derivative of -w**4/4 - 5*w**3/3 - 4*w**2 - 4*w + 5. Factor t(u).
-(u + 1)*(u + 2)**2
Let x(j) be the third derivative of j**6/540 - j**5/135 - j**4/108 + 2*j**3/27 - 4*j**2. Solve x(u) = 0 for u.
-1, 1, 2
Let v be 10/(-25) + 64/10. Suppose 4*b + 2*g = 50, 2*b - 33 + v = -3*g. Factor 7*x**2 - 2*x + b*x**3 + 0*x - 3*x**3.
x*(x + 1)*(9*x - 2)
Let a(w) be the first derivative of w**2 + w**3 - w - 4/5*w**5 - w**4 + 1. Determine t so that a(t) = 0.
-1, 1/2
Let f = 49 + -7. Let b be f/(-4)*(-12)/72. Factor b*z**2 - 1/4 + z**3 + 1/2*z.
(z + 1)**2*(4*z - 1)/4
Let b(y) be the third derivative of y**7/840 + y**6/80 - y**4/12 + 5*y**2. Let c(n) be the second derivative of b(n). Factor c(d).
3*d*(d + 3)
Let r(l) be the third derivative of -l**8/16800 + l**7/2100 - l**6/600 + l**5/300 - l**4/3 + l**2. Let k(p) be the second derivative of r(p). Factor k(y).
-2*(y - 1)**3/5
Let d(a) be the second derivative of -7*a**4/4 - 9*a**3/2 - 3*a**2 - 15*a - 1. Suppose d(y) = 0. What is y?
-1, -2/7
Suppose -x + 12 = m, 3*x - x + 3*m - 24 = 0. Let n be (-1 - x/(-8))*4. Find l, given that 4/3*l - 2/3*l**n - 2/3 = 0.
1
Let v = 88 - 86. Let r(m) be the third derivative of -v*m**2 - 2/21*m**3 + 1/210*m**5 - 1/84*m**4 + 0*m + 0. Factor r(f).
2*(f - 2)*(f + 1)/7
Let k(c) be the first derivative of -4*c**3/39 - c**2/13 + 2*c/13 + 3. Let k(r) = 0. Calculate r.
-1, 1/2
Let l be (-48)/(-15) - (-24)/30. Let q(g) be the second derivative of 1/9*g**3 + 0*g**2 - 1/18*g**l + 0 + 2*g. Solve q(m) = 0.
0, 1
Let v(c) be the second derivative of 1/12*c**4 - 1/6*c**3 + 0 + 0*c**2 + 3*c. Factor v(l).
l*(l - 1)
Determine l so that -9*l + 16*l**2 + 14*l**2 + 17*l**2 + 6 - 44*l**2 = 0.
1, 2
Let u(p) be the second derivative of 1/3*p**3 - 1/12*p**4 + 0 + 0*p**2 + p - 1/20*p**5. Determine q, given that u(q) = 0.
-2, 0, 1
Let h(r) be the third derivative of -r**7/10080 - r**6/2880 + r**5/240 + r**4/8 + 3*r**2. Let i(v) be the second derivative of h(v). Factor i(b).
-(b - 1)*(b + 2)/4
Let g be 23/46*0*2/(-4). Let -3/2*j**2 + g - 3/2*j = 0. Calculate j.
-1, 0
Let r(m) be the second derivative of -m**6/60 + m**5/20 + 7*m**4/24 + m**3/3 + 8*m. Factor r(t).
-t*(t - 4)*(t + 1)**2/2
Let b(l) be the second derivative of 1/42*l**7 + 2*l + 1/48*l**4 + 11/120*l**6 + 0*l**2 + 9/80*l**5 - 1/24*l**3 + 0. Let b(c) = 0. What is c?
-1, 0, 1/4
Let a(o) be the third derivative of 2*o**7/175 + o**6/40 - 7*o**5/100 - o**4/20 - 44*o**2. Let a(r) = 0. Calculate r.
-2, -1/4, 0, 1
Let b = -46985 + 207250837/4411. Let s = 141162/22055 - b. Factor 2/5 + s*h**2 - 16/5*h.
2*(4*h - 1)**2/5
Let v(x) be the first derivative of -2*x**6/15 - 4*x**5/25 + x**4/5 + 4*x**3/15 - 35. Factor v(y).
-4*y**2*(y - 1)*(y + 1)**2/5
Let m be ((-4)/502)/(2 - 3). Let r = m - -492/1255. Find h, given that r*h**2 + 8/5*h + 8/5 = 0.
-2
Factor -3*p**3 + 22*p + 4*p**3 - 17*p - 2 - 4*p**2.
(p - 2)*(p - 1)**2
Let u(s) be the first derivative of -s**5 - 7*s**4/4 - 2*s**3/3 + 4. Factor u(o).
-o**2*(o + 1)*(5*o + 2)
Let p(o) be the first derivative of 0*o**2 - 1/3*o**3 - 7 + o. Factor p(z).
-(z - 1)*(z + 1)
Let y(r) be the first derivative of r**9/9072 + r**8/1680 - r**6/270 + 2*r**3 - 8. Let m(f) be the third derivative of y(f). Determine n, given that m(n) = 0.
-2, 0, 1
Let m be (24/(-9))/((-6)/(-27)). Let x be (-4)/m - (-1)/9. Factor -x*r - 8/9*r**3 + 0 + 2/9*r**4 + 10/9*r**2.
2*r*(r - 2)*(r - 1)**2/9
Let g(y) be the third derivative of -y**8/20160 - y**7/2520 - y**6/720 - y**5/60 + 3*y**2. Let a(n) be the third derivative of g(n). Factor a(j).
-(j + 1)**2
Let k = -205/66 - -36/11. Let l(h) be the second derivative of -1/20*h**5 + 0 + k*h**3 + 1/30*h**6 + h**2 - 1/4*h**4 + 4*h. Suppose l(n) = 0. Calculate n.
-1, 1, 2
Let s(q) be the second derivative of q**6/135 - 2*q**5/15 + 5*q**4/9 - 28*q**3/27 + q**2 - 16*q. Determine y so that s(y) = 0.
1, 9
Factor 12 - 12*q + 9*q - 2*q**2 + 0*q**2 + 13*q.
-2*(q - 6)*(q + 1)
Let r be -5 + (-132)/(-18) + (-3 - -1). Factor 0*u - 1/3*u**2 + r.
-(u - 1)*(u + 1)/3
Let m = 4 + -6. Let n be m/(-2*(-3)/(-9)). Factor 2*h**4 - h**2 - n - h**2 + 3.
2*h**2*(h - 1)*(h + 1)
Let b(j) be the first derivative of -j**6/48 + j**5/8 - 5*j**4/16 + 5*j**3/12 + 9*j**2/2 - 6. Let h(v) be the second derivative of b(v). Factor h(w).
-5*(w - 1)**3/2
Let l be ((-2)/7)/((-1)/7). Let s(t) be the third derivative 