**3.
-3*l**3*(l + 1)
Let l(t) be the third derivative of t**6/960 + t**5/40 + t**4/4 + 4*t**3/3 + 2*t**2. Factor l(s).
(s + 4)**3/8
Let o(s) be the first derivative of -4*s**5/5 + 3*s**4 - 4*s**3 + 2*s**2 + 4. Solve o(u) = 0 for u.
0, 1
Let o(q) be the first derivative of 2*q**3/33 - 8*q**2/11 + 32*q/11 + 5. Factor o(l).
2*(l - 4)**2/11
Suppose -o - 3*c - 3 = 0, 2*c = -o - 0*c + 2. Let p be (o/(-15))/(-1*2). Solve -p*s**2 - 2/5 - 4/5*s = 0.
-1
Let o(b) be the third derivative of 1/48*b**4 - 1/6*b**3 + 0*b + 1/120*b**5 + b**2 + 0. Factor o(n).
(n - 1)*(n + 2)/2
Let i(n) be the third derivative of -n**5/150 - n**4/60 + 2*n**3/15 - 3*n**2. Factor i(s).
-2*(s - 1)*(s + 2)/5
Let i(k) be the third derivative of -k**7/210 + k**6/45 - k**5/60 - k**4/36 + 10*k**2. Solve i(o) = 0 for o.
-1/3, 0, 1, 2
Let i(d) be the second derivative of 0 + 1/9*d**4 + 0*d**3 + 11/30*d**5 - d + 0*d**2 + 1/5*d**6. Find g such that i(g) = 0.
-1, -2/9, 0
Let a(c) be the first derivative of -c**7/630 + c**5/180 + c**2/2 - 1. Let d(k) be the second derivative of a(k). Factor d(w).
-w**2*(w - 1)*(w + 1)/3
Let a(d) be the third derivative of -d**5/12 - 5*d**4/8 - 5*d**3/3 + 4*d**2. What is u in a(u) = 0?
-2, -1
Let x = 22 + -21. Let g(s) = -9*s**4 - 4*s**3 + 13*s**2 + 5*s + 5. Let b(w) = -w**4 + w**2 + w + 1. Let f(r) = x*g(r) - 5*b(r). Find y, given that f(y) = 0.
-2, 0, 1
Let z = 5 - 0. Let p(o) be the second derivative of -1/30*o**6 + 1/20*o**z + 2*o + 0 - 1/36*o**4 + 0*o**3 + 1/126*o**7 + 0*o**2. Factor p(k).
k**2*(k - 1)**3/3
Let m(j) be the first derivative of -15*j**5 + 0*j**2 - 9*j**3 + 9 + 0*j + 45/2*j**4. Factor m(b).
-3*b**2*(5*b - 3)**2
Let f(q) be the second derivative of 9*q**7/14 + 3*q**6/10 - 3*q**5/4 + q**4/4 + 2*q. Factor f(o).
3*o**2*(o + 1)*(3*o - 1)**2
Let c(s) be the second derivative of s**7/21 + s**6/15 - s**5/5 - s**4/3 + s**3/3 + s**2 + 3*s. Determine b so that c(b) = 0.
-1, 1
Let w(j) = -21*j**4 - 36*j**3 - 19*j**2 + j. Let b(t) = 20*t**4 + 36*t**3 + 20*t**2. Let g(a) = 5*b(a) + 4*w(a). Determine v, given that g(v) = 0.
-1, -1/4, 0
Let r(f) be the third derivative of f**5/60 + 11*f**4/12 + 121*f**3/6 - 29*f**2. Determine n, given that r(n) = 0.
-11
Let o(i) be the first derivative of -2*i**3/9 - 14*i**2/3 + 10*i + 4. Find k, given that o(k) = 0.
-15, 1
Let 4 - 2 - 2*p**4 + p**3 + 4*p - 5*p**3 = 0. What is p?
-1, 1
Suppose 0 = 5*s - 15, -4*t - 15 - 26 = s. Let u be (-2)/t - (-22)/(-121). Factor u + 2/9*r + 2/9*r**2.
2*r*(r + 1)/9
Let l(k) be the second derivative of -k**5/10 + 5*k**4/18 + 4*k**3/9 - 4*k**2/3 - k. Suppose l(a) = 0. What is a?
-1, 2/3, 2
Let u(w) be the first derivative of 9*w**4/8 + w**3 + 25. Factor u(c).
3*c**2*(3*c + 2)/2
Factor 7/3*x**2 + 0 + 2*x - x**3.
-x*(x - 3)*(3*x + 2)/3
Let y(f) be the third derivative of f**8/1680 - f**6/120 - f**5/60 - f**3/2 - 11*f**2. Let t(u) be the first derivative of y(u). Solve t(n) = 0 for n.
-1, 0, 2
Let w(t) be the third derivative of t**8/5040 + t**7/210 + t**6/20 + t**5/12 - 4*t**2. Let c(j) be the third derivative of w(j). Factor c(s).
4*(s + 3)**2
Let p = 41/6545 + 3/374. Let o(j) be the second derivative of p*j**5 + 0 - 8/7*j**2 + 4/7*j**3 - 1/7*j**4 - j. Factor o(c).
2*(c - 2)**3/7
Let -24*d + 75 - 3*d**2 - 171 + 75 = 0. What is d?
-7, -1
Factor 4*k**3 + 8 + k - 8*k**2 + 0*k + 2*k - 7*k.
4*(k - 2)*(k - 1)*(k + 1)
Suppose -71 + 80 = 3*d. Factor -3/2*q**2 - 1/2*q + 0 - 3/2*q**d - 1/2*q**4.
-q*(q + 1)**3/2
Let q(w) = -w**2 - 5*w - 1. Let j(h) = -2*h. Let a be j(2). Let s be q(a). Factor 16*m**5 + 10*m**3 - 24*m**4 - m**3 + 0*m**s - m**2.
m**2*(m - 1)*(4*m - 1)**2
Let i(p) = p**3 + p. Let h(y) = 2*y**3 - y**2 + 3*y. Suppose -4*k + 10 + 2 = 0. Let t(l) = k*i(l) - h(l). Factor t(r).
r**2*(r + 1)
Let m(w) be the second derivative of 5*w**7/21 + 17*w**6/15 + 11*w**5/10 - 13*w**4/6 - 16*w**3/3 - 4*w**2 - 18*w. Find z such that m(z) = 0.
-2, -1, -2/5, 1
Let z = 65 - 63. Factor 3*h - 6/5*h**3 + 3/5*h**z + 6/5.
-3*(h - 2)*(h + 1)*(2*h + 1)/5
Suppose 5*k + r - 3*r - 30 = 0, -2*k + 4*r = 4. Let o = -6 + k. Solve -3*h + 2 - 2*h**o - 6*h + 8*h**3 + 5*h - 4*h = 0 for h.
-1, 1/4, 1
Let z be 1/1 + (-192)/(-27) + -7. Factor -z*i**3 + 4/9 - 2/9*i - 16/9*i**2.
-2*(i + 1)**2*(5*i - 2)/9
Let d(t) be the first derivative of t**4/4 - t**3/9 - 56. Solve d(s) = 0.
0, 1/3
Let r(s) be the first derivative of 2*s**7/21 + 3*s**6/10 + 3*s**5/10 + s**4/12 - 3*s - 2. Let a(w) be the first derivative of r(w). Let a(m) = 0. Calculate m.
-1, -1/4, 0
Let n = 4110/7 + -586. Let m = 3 + -1. Determine y so that -8/7 + n*y - 2/7*y**m = 0.
2
Let h(q) be the second derivative of -13/30*q**4 - 1/75*q**6 - 4/5*q**3 - 3/25*q**5 + 0 + 3*q - 4/5*q**2. Factor h(p).
-2*(p + 1)**2*(p + 2)**2/5
Let q(s) be the second derivative of s**4/4 - 2*s**3 + 3*s**2 + 7*s. Let l(t) = 3*t**2 - 13*t + 6. Let f(j) = -3*l(j) + 4*q(j). Let f(n) = 0. What is n?
1, 2
Let g(h) be the second derivative of h**6/120 + h**5/20 + h**4/8 + h**3/6 - h**2 - 3*h. Let w(p) be the first derivative of g(p). Solve w(b) = 0.
-1
Suppose 0 = -3*c - c - 0*c. Let m(y) be the second derivative of 1/30*y**6 + y + 0*y**2 + 1/6*y**3 - 1/20*y**5 + c - 1/12*y**4. Determine a so that m(a) = 0.
-1, 0, 1
Suppose -s = -3*s - 2. Let k be (-4)/(-6) + (-1 - s). Solve 2/3 - 2/3*p**2 - k*p + 2/3*p**3 = 0.
-1, 1
Let s be ((-4)/10)/(5/150). Let n be (-6)/8 + (-15)/s. Factor -b + n*b**2 + 0.
b*(b - 2)/2
Let g(c) be the first derivative of -9*c**3 - 21*c**2/2 + 6*c + 13. Factor g(w).
-3*(w + 1)*(9*w - 2)
Let n(f) be the second derivative of -f**7/147 - 2*f**6/105 + f**4/21 + f**3/21 - 2*f. Find m, given that n(m) = 0.
-1, 0, 1
Let k(x) be the third derivative of x**8/84 - x**7/21 + 5*x**6/96 + x**5/48 - 5*x**4/96 - x**3/24 - 6*x**2. Let k(t) = 0. What is t?
-1/4, 1
Let n(o) be the first derivative of 5*o**3/3 + 5*o**2/2 - 4. Factor n(m).
5*m*(m + 1)
Let t(i) = -i - 1. Let q be t(-4). Factor -9*w**2 - 3*w**3 + 5*w + 18*w**2 + 2 + 4*w**q - 5*w**2.
(w + 1)**2*(w + 2)
Determine i, given that 8/3*i**2 - 2/3 + 2*i = 0.
-1, 1/4
Suppose -b - 4 = -3*a - 0*a, 2*a = 4. Suppose -f + 0*f + b = 0. What is m in -4*m**f - 2 + 3*m**2 + 3*m**2 = 0?
-1, 1
Factor 32/9*r**5 - 352/3*r**2 + 2306/9*r**3 + 0 + 128/9*r - 176/3*r**4.
2*r*(r - 8)**2*(4*r - 1)**2/9
Let g = -5/29 + 49/116. Factor -5/4*n**2 + n + g.
-(n - 1)*(5*n + 1)/4
Let r(j) be the third derivative of j**6/120 + j**5/60 + 2*j**2. Factor r(f).
f**2*(f + 1)
Let f = -1 - -3. Solve 4 + 0*v**2 - 6*v - f*v**2 + 4*v**2 = 0 for v.
1, 2
Let b be 10/(-75)*-3 + 333/180. Factor b*l + 3/4 + 3/2*l**2.
3*(l + 1)*(2*l + 1)/4
Let z(y) = -18*y**4 - 44*y**3 + 36*y**2. Let v(j) = 2*j**4 + 5*j**3 - 4*j**2. Let u(p) = -52*v(p) - 6*z(p). Solve u(k) = 0 for k.
-2, 0, 1
Let m(w) be the first derivative of w**5/240 - w**4/48 + w**3/24 - 3*w**2/2 - 9. Let g(t) be the second derivative of m(t). Solve g(i) = 0.
1
Let q(x) = 2*x**4 + x**3 - 2*x**2 + 5*x + 3. Let l(n) = -n**4 + n**2 - 4*n - 2. Let d(k) = -3*l(k) - 2*q(k). Factor d(m).
-m*(m - 1)*(m + 1)*(m + 2)
Let d(h) be the first derivative of -3 + 3*h - 4*h**3 - 9/2*h**2. Factor d(x).
-3*(x + 1)*(4*x - 1)
Let b(p) = -p + 2. Let h be b(1). Let o(z) = 2*z + 1. Let c be o(h). Factor 8/7 + 14*w**4 - 6/7*w**2 - 20*w**c + 40/7*w.
2*(w - 1)**2*(7*w + 2)**2/7
Let g be 4/18 + 2/(-9). Suppose g*r + 0*r**2 - 4*r + r**2 + 5*r = 0. What is r?
-1, 0
Let x(n) = 4*n**3 + 2*n**2 + 2*n. Let p(v) = 13*v**3 + 5*v**2 + 7*v. Suppose 0 = -u + 3*u - 14. Let w(c) = u*x(c) - 2*p(c). Let w(a) = 0. What is a?
-2, 0
Factor -y - 2*y + 2 + 4 + y**2 - 4*y**2.
-3*(y - 1)*(y + 2)
Let r = -227 + 232. Find c, given that 4/9*c**4 - 2/9*c**3 + 0*c - 2/9*c**r + 0 + 0*c**2 = 0.
0, 1
Let u(a) be the second derivative of a**6/10 + a**5/3 + 13*a**4/36 + a**3/9 - 20*a. Factor u(x).
x*(x + 1)**2*(9*x + 2)/3
Factor 1 - 26 - 10 - 20*x + 11 - 4*x**2.
-4*(x + 2)*(x + 3)
Let o(c) = 15*c**3 - c. Let u be o(1). Suppose 4*z + 2 = u. Factor -3*w**5 + z*w**5 + 0*w**3 + w**3 + 2*w**4 + w**5.
w**3*(w + 1)**2
Let p(i) be the first derivative of -2*i**3/3 + 4*i**2 - 6*i + 22. Solve p(w) = 0 for w.
1, 3
Let a(u) = u**2 - u. Let h(q) = q**2 + q. Let g(t) = -t**2 + 6*t + 8. Let z be g(7). Let v(f) = z*a(f) - 3*h(f). Factor v(o).
-2*o*(o + 2)
Let g be 1*(-3 + -2)*-1. Suppose 3*s - g*s + 6 = 0.