 a(u) be the first derivative of 2*u**5/5 - u**4/2 - 2*u**3/3 + u**2 - 10. Determine i, given that a(i) = 0.
-1, 0, 1
Factor 5/2*d**3 + 5 + 5/2*d**4 - 5/2*d - 15/2*d**2.
5*(d - 1)**2*(d + 1)*(d + 2)/2
Suppose -6*q = -q + 315. Let s be (-60)/q + 6/(-21). What is w in 0*w**2 - s*w + 0 - 2/3*w**5 + 0*w**4 + 4/3*w**3 = 0?
-1, 0, 1
Let j = -3/107 - -223/321. Factor -5/3*b**2 - 1/3*b**3 + j + 1/3*b + b**4.
(b - 1)**2*(b + 1)*(3*b + 2)/3
Let j(p) = -3*p**3 + 6*p**2 + 3*p + 24. Let l(a) = 2. Let s(d) = j(d) - 15*l(d). Factor s(v).
-3*(v - 2)*(v - 1)*(v + 1)
Let v(g) be the second derivative of -g**4/6 + 3*g**3 - 8*g**2 + 44*g. Factor v(j).
-2*(j - 8)*(j - 1)
Let s = 6 + -4. Suppose -s*p + 8 = 2*p. Solve 0 + 1/4*c**p + 0*c = 0.
0
Let o(g) = g**2 + 11*g + 7. Let y be o(-12). Let u = y + -19. Factor 0*n**2 - 1/2*n + 1/2*n**3 + u.
n*(n - 1)*(n + 1)/2
Factor 4/15*z + 2/15*z**4 + 0 - 4/15*z**3 - 2/15*z**2.
2*z*(z - 2)*(z - 1)*(z + 1)/15
Suppose -5*m = -f - 6*m - 2, 2*f = 2*m + 4. Factor f - 1/3*y**2 + 1/3*y.
-y*(y - 1)/3
Let v = 60 - 60. What is f in 1/4*f**5 + 0*f**4 + 1/4*f + v*f**2 - 1/2*f**3 + 0 = 0?
-1, 0, 1
Let i be 12/105 - (-2)/6. Let a = i - 1/21. Find b, given that -4*b**3 + a + 4*b**2 - 2*b - 2/5*b**5 + 2*b**4 = 0.
1
Factor -2/7*v**2 - 8/7 - 10/7*v.
-2*(v + 1)*(v + 4)/7
Let x(n) = -n**5 - 35*n**4 - 76*n**3 - 44*n**2 + 76*n + 84. Let k(q) = 35*q**4 + 75*q**3 + 45*q**2 - 75*q - 85. Let t(f) = -4*k(f) - 5*x(f). Factor t(b).
5*(b - 1)*(b + 2)**4
Let s be (2 - 2)*(1 - (-1)/(-2)). Factor s + 2/13*i**2 - 2/13*i**4 + 0*i + 2/13*i**5 - 2/13*i**3.
2*i**2*(i - 1)**2*(i + 1)/13
Let n = 963001/300 - 3210. Let d(c) be the third derivative of 0*c + 0 - 1/600*c**6 + 1/120*c**4 + n*c**5 - 1/30*c**3 - 2*c**2. Factor d(o).
-(o - 1)**2*(o + 1)/5
Let h(b) = -b**2 + 2*b. Let i(d) be the first derivative of 2*d**3/3 - 2*d**2 - 7. Let k(l) = 5*h(l) + 3*i(l). What is v in k(v) = 0?
0, 2
Let v(b) = b**3 + b**2 + b + 1. Let f(n) = -n**3 + 12*n**2 - 2*n - 6. Let t(c) = f(c) - 2*v(c). Suppose t(h) = 0. Calculate h.
-2/3, 2
Factor 5*a + 9*a**2 + 15*a**3 + 11*a**2 + 0*a**2.
5*a*(a + 1)*(3*a + 1)
Let n(g) be the second derivative of 1/27*g**3 + 2/63*g**7 + 7/54*g**4 + 0*g**2 + 17/135*g**6 - 2*g + 0 + 17/90*g**5. Find a such that n(a) = 0.
-1, -1/2, -1/3, 0
Let z = -9 - 6. Let f = -12 - z. What is q in 0*q**f + 0*q + 2/9*q**4 - 2/9*q**2 + 0 = 0?
-1, 0, 1
Let m(f) = -f**2 - 3*f - 5. Let n(y) = -y**2 - y - 3. Let j = 3 - 0. Let i(l) = j*m(l) - 5*n(l). Factor i(b).
2*b*(b - 2)
Let 4/7*k**3 - 2/7*k**5 + 4/7*k**4 - 2/7*k + 4/7 - 8/7*k**2 = 0. What is k?
-1, 1, 2
Let p(h) be the third derivative of -h**7/840 - h**4/12 + 2*h**2. Let t(x) be the second derivative of p(x). Solve t(u) = 0 for u.
0
Let c = -5 + 4. Let i be 28/(-12) + c + 4. Determine v so that -1/3*v**2 - v - i = 0.
-2, -1
Factor -42/11*d**3 + 0 - 40/11*d**2 - 8/11*d.
-2*d*(3*d + 2)*(7*d + 2)/11
Let n(d) = d**4 - d**3 - d**2 - 1. Let j(w) = 42*w**4 - 112*w**3 + 25*w**2 + 44*w + 15. Let h(o) = -2*j(o) - 14*n(o). Let h(q) = 0. What is q?
-2/7, 1, 2
Factor 3/7*g**5 + 0 + 3/7*g**4 + 0*g**3 + 0*g + 0*g**2.
3*g**4*(g + 1)/7
Let p be ((-42)/8)/(-3 + 1). Let s(x) be the first derivative of -p*x**4 + 1 + 0*x**2 + 7/4*x**6 + 0*x - x**3 + 3/5*x**5. Suppose s(u) = 0. Calculate u.
-1, -2/7, 0, 1
Let b(d) be the first derivative of d**6/3 + 12*d**5/5 + 11*d**4/2 + 4*d**3/3 - 12*d**2 - 16*d - 42. Suppose b(l) = 0. What is l?
-2, -1, 1
Let t(y) = -8*y**2 + 18*y + 23. Let w(x) = -9*x**2 + 19*x + 24. Let r(v) = -4*t(v) + 3*w(v). Factor r(g).
5*(g - 4)*(g + 1)
Let c = 5 - 3. Let i = 4 - c. Determine f so that 3*f**2 + 2*f**i - 4*f**2 - 1 = 0.
-1, 1
Suppose -23*n + 36 = -5*n. Solve 4/5*q - 1/5 + 4/5*q**3 - 1/5*q**4 - 6/5*q**n = 0 for q.
1
Let k(g) be the first derivative of g**9/16632 - g**7/4620 - 5*g**3/3 + 7. Let s(h) be the third derivative of k(h). Find v, given that s(v) = 0.
-1, 0, 1
Let w(t) = -t + 10. Let h be w(8). Suppose -5*g - 5 + 20 = 0, 2*p + h*g = 6. Factor 0*o**2 + 0*o - 1/5*o**4 + p - 2/5*o**3.
-o**3*(o + 2)/5
Let s(k) = 7*k**2 - 11*k - 16. Let l(p) = -11*p**2 + 17*p + 24. Let h = 5 + 2. Let b(j) = h*s(j) + 5*l(j). Let b(m) = 0. Calculate m.
-2/3, 2
Let b(k) be the second derivative of -k**6/165 + k**5/110 + k**4/66 - k**3/33 + 15*k. Factor b(o).
-2*o*(o - 1)**2*(o + 1)/11
Suppose -y - 5*k = -24, 4*y = 3*k + k. Suppose -3*h + 2*p + 20 = 0, -2*h = h - p - 16. Factor 2*l**y + l**4 - 3*l**3 - l**h - l**5 + 2*l**3.
-l**3*(l - 1)**2
Let c(d) = -d**3 - d**2 + d - 3. Let z(l) = -l**3 + l**2 + l + 1. Suppose -4*y - 9 = -7*y. Suppose -y*q + 4 = -q. Let t(h) = q*z(h) + c(h). Factor t(k).
-(k - 1)*(k + 1)*(3*k - 1)
Let o(f) = f**3 + 5*f**2 - 7*f - 4. Let i be o(-6). Determine v, given that 4 - 4*v**i + 4*v**2 - 6 - 2*v**2 - 4*v = 0.
-1
Factor -26/7*j**2 - 2/7*j**3 + 0 + 4*j.
-2*j*(j - 1)*(j + 14)/7
Let q = -1359/20 - -68. Let h(r) be the third derivative of 0 + 0*r - 3*r**2 - 1/15*r**3 + q*r**4 + 1/300*r**6 - 1/50*r**5. What is s in h(s) = 0?
1
Let u(b) be the first derivative of -b**7/14 + b**6/10 - 2*b + 3. Let n(k) be the first derivative of u(k). Solve n(h) = 0.
0, 1
Let b(z) = 4*z**2 - 2*z**2 + 4*z**2 - 2*z + 5*z. Let d(s) = -7*s**2 - 2*s + 1. Let t(k) = 4*b(k) + 3*d(k). Factor t(p).
3*(p + 1)**2
Let l be ((-22)/35)/(12/(-15)). Let o = l + -2/7. Factor 0*p + o*p**2 - 1/2.
(p - 1)*(p + 1)/2
Let h(f) be the first derivative of -f**6/360 - f**5/30 - f**4/6 - 4*f**3/3 + 2. Let a(j) be the third derivative of h(j). Factor a(s).
-(s + 2)**2
Suppose -5*b + 22 - 7 = 0. Factor 3*w**3 + 0*w + 3*w**2 + w + 0*w**b + w**2.
w*(w + 1)*(3*w + 1)
Let k(i) = 5*i + 4. Let m be k(-4). Let g be 10/(-4)*m/4. Solve g*o**3 - 15*o**2 - 16*o**4 + 4*o**3 - 2*o + 1 + 18*o**3 = 0.
-1/4, 1/4, 1
Let p(f) be the third derivative of 3*f**7/7 - 11*f**6/80 - 9*f**5/40 + f**4/8 - 7*f**2 + 1. Suppose p(c) = 0. What is c?
-2/5, 0, 1/4, 1/3
Suppose -16*r**2 - 6*r**4 + 12*r**5 + 0*r**5 + 34*r**4 + 0*r**2 = 0. Calculate r.
-2, -1, 0, 2/3
Find k such that -4/3*k**3 + 4/3*k**5 + 0*k + 2/3*k**4 - 2/3*k**2 + 0 = 0.
-1, -1/2, 0, 1
Let x be 1 - 0 - (-3 - -3). Let m be (x - 1)*(2 + -1). Factor -3*k**4 + m*k**2 + k - k**3 + k**2 + 2*k**4.
-k*(k - 1)*(k + 1)**2
Let g(q) = 3*q**2 + 6*q - 5. Let l(y) = -7*y**2 - 13*y + 11. Let j(f) = 9*g(f) + 4*l(f). Factor j(w).
-(w - 1)**2
Solve 0 - p**2 - 2/3*p - 1/3*p**3 = 0.
-2, -1, 0
Let 3/2*u - 1/2*u**2 - 1 = 0. What is u?
1, 2
Let u(f) be the second derivative of -f**8/3360 + f**7/1260 - f**4/12 - 3*f. Let p(t) be the third derivative of u(t). Suppose p(l) = 0. What is l?
0, 1
Let k be 6/21*1/3. Let l(i) be the first derivative of 0*i**2 - 6/35*i**5 + 0*i + 1/21*i**6 - k*i**3 + 3 + 3/14*i**4. Solve l(f) = 0 for f.
0, 1
Let m be 1/1*(2 - 11). Let l = m + 18. Find b such that 13/2*b**2 + l*b**3 - 13/2*b**4 + 0 - 10*b**5 + b = 0.
-1, -2/5, -1/4, 0, 1
Let r(g) be the first derivative of -3/5*g**2 + 1/5*g**3 + 7 + 3/5*g. Find q such that r(q) = 0.
1
Let c be (2 + 0)*-2 + 4. Let q be -1 - 21/(-15) - c. Factor -6/5*b**3 + q*b**4 + 0*b + 0 + 4/5*b**2.
2*b**2*(b - 2)*(b - 1)/5
Let r(v) = v**3 + 30*v**2 + 243*v + 726. Let a(p) = -p**2 + 1. Let k(i) = 3*a(i) + r(i). Find l such that k(l) = 0.
-9
Let r(s) = s**2 - 9*s + 5. Let y be r(9). Suppose y*z = -0*z. Factor 7/4*h**3 + 0 - 1/2*h**2 + z*h.
h**2*(7*h - 2)/4
Let w(f) be the second derivative of 0*f**3 + 0*f**5 + 0*f**4 + 1/240*f**6 - f**2 + 0 + f. Let n(o) be the first derivative of w(o). Factor n(d).
d**3/2
Let y be (8038/6)/((-22)/(-6)). Let k = y - 365. Factor -k*j + 2/11*j**2 + 0.
2*j*(j - 2)/11
Let q(i) be the third derivative of 1/735*i**7 + 0 + 0*i**3 - i**2 - 1/210*i**5 + 0*i**4 + 0*i**6 + 0*i. Solve q(o) = 0 for o.
-1, 0, 1
Let g(o) be the second derivative of -3*o**5/100 - 2*o**4/15 - 7*o**3/30 - o**2/5 - 7*o. What is y in g(y) = 0?
-1, -2/3
Let p(o) be the second derivative of -o**10/166320 - o**9/27720 - o**8/12320 - o**7/13860 - o**4/3 - o. Let h(z) be the third derivative of p(z). Factor h(x).
-2*x**2*(x + 1)**3/11
Let n(l) be the third derivative of l**8/1680 - l**7/525 - l**6/300 + l**5/75 + l**4/120 - l**3/15 + 4*l**2. Solve n(p) = 0.
-1, 1, 2
Let m(p) = 2*p**2 - 2*p + 1. Let t be m(2). Suppose s - 5*s + 8 = 0. Let 3*b**3 + b**2 - 4*b**t - 4*b**4 - b**2 - b + s*b**2 = 0. Calcul