i**5/10 + 2*i + 2. Let r(k) be the first derivative of x(k). Find y, given that r(y) = 0.
0, 1
Let c(a) = a**2 - 4*a + 2. Let h be c(4). Suppose 0 = -4*x - 0*x + 28. Factor -2*u - 2*u**4 - x*u**5 + h*u.
-u**4*(7*u + 2)
Let b(k) be the first derivative of -k**7/70 - 3*k**6/40 - 3*k**5/20 - k**4/8 + k**2/2 + 4. Let t(g) be the second derivative of b(g). Factor t(v).
-3*v*(v + 1)**3
Factor -f**2 + 1/2 - 1/2*f.
-(f + 1)*(2*f - 1)/2
Let k = 2368361/11 - 215647. Let o = 342 + k. Factor 4/11 - o*v**3 + 16/11*v**2 - 14/11*v.
-2*(v - 1)**2*(3*v - 2)/11
Suppose -8 = -4*r + 4. Factor -3*w**5 + 3 + r*w**4 + 0*w**2 + 6*w**3 - 5*w**2 - 3*w - w**2.
-3*(w - 1)**3*(w + 1)**2
Let t(u) be the third derivative of -u**5/80 + 5*u**4/16 - 25*u**3/8 + 15*u**2. Factor t(i).
-3*(i - 5)**2/4
Let y(n) be the first derivative of n**3 - 27*n + 75. Factor y(m).
3*(m - 3)*(m + 3)
Let b be (-1)/(-2 + 15/9). Factor 3*z**2 - 4*z**3 + 2*z**3 - 3*z**4 + 2*z**b.
-3*z**2*(z - 1)*(z + 1)
Let o(l) be the first derivative of -l**6/24 + l**4/8 - l**2/8 + 1. Factor o(w).
-w*(w - 1)**2*(w + 1)**2/4
Suppose 0*o + 5*o = 25. Suppose 5*j + 5*t = -o, 5*t + 5 = 2*j + j. Factor -3 - 4*h**2 + 3*h - 18*h + j*h**2 - 8*h**2.
-3*(h + 1)*(4*h + 1)
Suppose -8*x - 2*x = -3*x. Let j be -2 + 3 + 2/(-4). Determine u so that x*u**2 + 0*u + 1/2*u**3 + j*u**4 + 0 = 0.
-1, 0
Find l such that 32/9*l**5 + 2/9*l - 4/3*l**2 + 2/9*l**3 + 16/3*l**4 + 0 = 0.
-1, 0, 1/4
Let p be 0/(-1) + (-12)/(-45)*3. Determine b so that 2/5*b**5 + 0*b**3 + 4/5*b**4 - 2/5*b + 0 - p*b**2 = 0.
-1, 0, 1
Let z(m) = -m**2 + m - 1. Let o(u) = u**4 + 4*u**3 + 7*u - 5. Let p(d) = -o(d) + 5*z(d). Factor p(w).
-w*(w + 1)**2*(w + 2)
Let a = -2 + 5. Let -3*m**3 + m**3 + m**4 - a*m**4 = 0. What is m?
-1, 0
Let x(h) be the first derivative of -h**3/15 - 3*h**2/10 - 9. Solve x(g) = 0.
-3, 0
Let j(w) = -450*w**3 - 945*w**2 - 605*w - 45. Let s(m) = 41*m**3 + 86*m**2 + 55*m + 4. Let z(x) = 6*j(x) + 65*s(x). Factor z(q).
-5*(q + 1)**2*(7*q + 2)
Let y(o) = 2*o - 2. Let c be y(7). Solve 12*p**2 + 6*p - 4 + c*p - 10*p = 0.
-1, 1/3
Let z be 4/(-10) + (-93)/(-120). Let g(l) be the first derivative of 1/4*l - 1/16*l**4 + 1/4*l**3 - z*l**2 - 3. Factor g(q).
-(q - 1)**3/4
Suppose r + r - 7 = -u, -4*u + r + 10 = 0. Find w, given that -1/2*w**u - 1/2 - 3/2*w**2 - 3/2*w = 0.
-1
Suppose 0 = 5*c - 24 + 4. Suppose 1 = -f + c. Factor -4*b**2 - 6*b**2 + 4 + 0*b**2 + 6*b**f - 2 + 2*b.
2*(b - 1)**2*(3*b + 1)
Let a = 13 - 15. Let k be (28 - 1)*a/(-21). Factor -2/7 - 12/7*o - k*o**2.
-2*(3*o + 1)**2/7
Let p = -5 - -7. Factor -4*j**3 + 6*j**5 + 4*j**p + 4*j**3 - 2*j**3 - 8*j**4.
2*j**2*(j - 1)**2*(3*j + 2)
Suppose 0 = -4*f + 20, 10 = 3*k + 5*f - 15. Let b(c) = -c**2 + c + 2. Let u be b(0). Determine t, given that -t**u - 1/2*t + k - 1/2*t**3 = 0.
-1, 0
Suppose -4*i + 3*f = -0*i - 26, -2*i = 5*f. Find g, given that i*g**2 - 3*g**4 - 3*g**2 + 2*g**4 - 1 = 0.
-1, 1
Factor -s**4 + 0*s**4 + 3*s**4 - s**2 - s**4.
s**2*(s - 1)*(s + 1)
Let g(s) = -2*s - 10. Let i be g(-7). Suppose i*w = 5*f - 30, -6*w - 31 = -3*f - w. Factor 3*t**3 - 2*t**f + 3*t**3 - 3*t**3.
t**2*(3*t - 2)
Let k = -3 + 5. Let q(u) be the second derivative of 1/6*u**3 + 1/15*u**6 - u + 0*u**k - 1/6*u**4 + 0*u**5 + 0 - 1/42*u**7. Suppose q(x) = 0. Calculate x.
-1, 0, 1
Let k(c) = 4*c**2 + 56*c + 5. Let s be k(-14). Suppose 0 + 0*y**2 + 2*y**s + 0*y + 4/3*y**4 + 0*y**3 = 0. Calculate y.
-2/3, 0
Let t(p) be the first derivative of -1/50*p**5 - 1/75*p**6 + p + 1/15*p**4 + 0*p**2 + 0*p**3 + 1. Let q(y) be the first derivative of t(y). Factor q(v).
-2*v**2*(v - 1)*(v + 2)/5
Let h be 1/(1*1*3/6). Factor 0*u + 2/3 + 0*u**3 + 2/3*u**4 - 4/3*u**h.
2*(u - 1)**2*(u + 1)**2/3
Let g = -4 - -5. Factor 2*w + g + 3*w**2 + 1 + 3*w.
(w + 1)*(3*w + 2)
Let v(n) be the first derivative of n**7/1260 + n**6/240 + n**5/120 + n**4/144 - n**2 + 1. Let q(d) be the second derivative of v(d). Solve q(x) = 0 for x.
-1, 0
Let s(p) = p**3 + 3*p**2 - p + 5. Let f be s(-3). Suppose -5*u + f*u = 0. Factor 0 - 1/4*x**3 - 1/2*x**2 + u*x.
-x**2*(x + 2)/4
Suppose 3*q = -q + 72. Let w = q - 13. Factor 0 + k - 2*k**3 + w*k - 4.
-2*(k - 1)**2*(k + 2)
Let z(j) be the third derivative of -j**6/40 - 3*j**5/40 + j**4/8 + 4*j**2. Determine n so that z(n) = 0.
-2, 0, 1/2
Let f(r) be the first derivative of -2*r**3/15 - 7*r**2/5 - 4*r - 12. Let f(j) = 0. What is j?
-5, -2
Let h(c) = c**3 - 2*c**2 - c. Let w be h(3). Solve -10*u**4 + w*u + 4*u**3 + 2*u + 7*u**2 + 23*u**2 - 4 - 4 = 0 for u.
-1, 2/5, 2
Let c = 392/597 - -2/199. Factor -c - 1/3*y**2 - y.
-(y + 1)*(y + 2)/3
Let y(o) = -o**2 - 8*o + 3. Let z be 1 - ((-3 - -13) + -1). Let q be y(z). Let -26*m + 4 + 0 + 16*m**2 + 24*m**2 - 4*m**q - 14*m**3 = 0. What is m?
2/9, 1
Let a(y) be the second derivative of y**9/22680 - y**8/5040 - y**7/3780 + y**6/540 - y**4/2 - 7*y. Let t(q) be the third derivative of a(q). Factor t(l).
2*l*(l - 2)*(l - 1)*(l + 1)/3
Let o(k) be the third derivative of -k**10/680400 + k**8/90720 + k**5/20 + k**2. Let g(i) be the third derivative of o(i). What is t in g(t) = 0?
-1, 0, 1
Let k(n) be the first derivative of 7 + 9/7*n**2 - 22/21*n**3 + 4/7*n. Suppose k(f) = 0. Calculate f.
-2/11, 1
Let x(j) be the first derivative of j**3/5 + 6*j**2/5 + 9*j/5 - 2. Factor x(u).
3*(u + 1)*(u + 3)/5
Let 6/5*f - 3/5 - 3/5*f**2 = 0. Calculate f.
1
Let h = 88 - 85. Let n(g) be the third derivative of -1/120*g**6 + 0*g**7 + 2*g**2 + 0*g**h + 1/336*g**8 + 0*g + 0*g**4 + 0*g**5 + 0. Solve n(a) = 0.
-1, 0, 1
Let y(f) = 76*f**3 + 314*f**2 + 266*f + 80. Let s(k) = 15*k**3 + 63*k**2 + 53*k + 16. Let w(r) = -28*s(r) + 6*y(r). Find x, given that w(x) = 0.
-2, -2/3
Let k be (-20)/132 - 2/(-6). Let c be -1 - (26/(-22) + 0). Factor k*v + c*v**2 + 0.
2*v*(v + 1)/11
Let d(o) = 4*o**3 + 20*o**2 + 56*o + 52. Suppose 0 = -5*b - 2 + 12. Let j(v) = -17*v**3 - 81*v**2 - 225*v - 207. Let l(h) = b*j(h) + 9*d(h). Factor l(t).
2*(t + 3)**3
Let l(m) be the first derivative of -4*m**3/15 - 8*m**2/5 - 16*m/5 - 4. Factor l(x).
-4*(x + 2)**2/5
Let f(b) be the second derivative of -b**6/30 + b**4/4 + b**3/3 + 11*b. Factor f(o).
-o*(o - 2)*(o + 1)**2
Let o(z) be the third derivative of -z**2 - 1/12*z**4 + 1/60*z**6 + 0*z + 0*z**3 + 0*z**5 + 0. Let o(y) = 0. What is y?
-1, 0, 1
Let m(r) be the third derivative of r**5/3 + 5*r**4/6 - 17*r**3/6 + 5*r**2. Let d(j) = -7*j**2 - 7*j + 6. Let o(f) = 17*d(f) + 6*m(f). Factor o(l).
l*(l + 1)
Let r(q) = q**4 + q**3 + q**2 + q. Let f(m) = 0*m**3 - 3*m + 6*m**4 - 7*m**5 - 3*m**4 - 3*m**2 - m**3 - m**4. Let t(z) = -2*f(z) - 6*r(z). Factor t(c).
2*c**3*(c - 1)*(7*c + 2)
Let h(j) be the first derivative of -j**3/9 - 2*j**2/3 - j + 6. Factor h(s).
-(s + 1)*(s + 3)/3
Let h(l) be the second derivative of l**5/35 - 2*l**3/7 - 4*l**2/7 - 7*l. Factor h(y).
4*(y - 2)*(y + 1)**2/7
Let i(m) = -m**2 - m. Let t be i(0). Suppose -4*s - s + 25 = t. Let -1/2*r**4 - 1/4*r**s + 0*r**3 + 0 + 1/4*r + 1/2*r**2 = 0. Calculate r.
-1, 0, 1
Let z(j) be the third derivative of j**5/150 + j**4/30 + j**3/15 + 13*j**2. What is f in z(f) = 0?
-1
Factor -12*v - 11*v**2 - 4*v**3 - 9/2 - 1/2*v**4.
-(v + 1)**2*(v + 3)**2/2
Let b = -88 + 361/4. Let q be (-15)/10*3/(-18). Factor q + b*c**2 - 3/2*c.
(3*c - 1)**2/4
Suppose -4*g = -2*x + 17 - 15, -g = 2*x - 12. Factor 0*o - 2/7 + 2/7*o**g.
2*(o - 1)*(o + 1)/7
Let n(o) = o - 5. Let r be n(7). Factor r*s**3 - 32 + 6*s - 4*s**2 - 2*s**2 + 30.
2*(s - 1)**3
Suppose 0 = -w + p, -5*w + 2*p - 3 = -9. Factor -6/5 + 9/5*s - 3/5*s**w.
-3*(s - 2)*(s - 1)/5
Let g be (0/1 - 1)/(4/(-16)). Let m(h) be the first derivative of -2 + 0*h**2 + 0*h**3 + 0*h**g + 0*h - 1/21*h**6 + 2/35*h**5. Factor m(j).
-2*j**4*(j - 1)/7
Suppose 0 = -0*g - 5*g. Suppose l - 2 - 2 = g. Determine w, given that 66*w**4 + 65*w**l - 40*w**2 - 8*w + 6*w**3 + 9*w**4 - 98*w**5 = 0.
-2/7, 0, 1
Let y(b) be the second derivative of 0*b**5 + 1/9*b**3 + 0*b**2 + 2/45*b**6 - 1/9*b**4 + 0 + 2*b - 1/63*b**7. Factor y(n).
-2*n*(n - 1)**3*(n + 1)/3
Let g(p) be the second derivative of 1/36*p**4 + 0 + 2/3*p**2 - 2/9*p**3 + 5*p. Solve g(z) = 0 for z.
2
Let n = 35/2 - 171/10. Factor 4/5 + 14/5*s + 2*s**3 + 18/5*s**2 + n*s**4.
2*(s + 1)**3*(s + 2)/5
Let w(n) be the third derivative of n**7/210 + n**6/20 + n**5/60 - n**4 + 8*n**3/3 - 27*n**2. 