 i, given that p(i) = 0.
-1, 0, 1
Let a(q) be the third derivative of -q**6/720 - q**5/180 + q**4/144 + q**3/18 - 17*q**2. Factor a(n).
-(n - 1)*(n + 1)*(n + 2)/6
Let b(a) = 15*a**5 + 45*a**4 + 45*a**3 - 2*a**2 + 17*a + 17. Let c(g) = 5*g**5 + 15*g**4 + 15*g**3 - g**2 + 6*g + 6. Let y(n) = -6*b(n) + 17*c(n). Factor y(q).
-5*q**2*(q + 1)**3
Let b(v) be the second derivative of v**4/3 + 4*v**3/3 + 27*v. Determine x so that b(x) = 0.
-2, 0
Let s(z) be the second derivative of -1/8*z**5 + 0*z**2 + 3*z - 3/20*z**6 + 1/12*z**7 + 3/8*z**4 + 0 - 1/6*z**3. Find l, given that s(l) = 0.
-1, 0, 2/7, 1
Let w(v) = v**3 + v**2. Let k(x) = 3*x**3 + 15*x**2 + 12*x. Let c(z) = -k(z) - w(z). Suppose c(q) = 0. Calculate q.
-3, -1, 0
Factor 3*k**5 + 22*k - 2*k**3 - 9*k**4 - 22*k + 11*k**3 - 3*k**2.
3*k**2*(k - 1)**3
Let h(m) be the first derivative of 2*m**3 + 4*m**2 + 2*m - 1. Solve h(v) = 0.
-1, -1/3
Let q(y) be the first derivative of 2*y**5/105 + y**4/21 - 2*y**3/21 - 4*y**2/21 + 8*y/21 + 54. Let q(c) = 0. What is c?
-2, 1
Let d(g) be the first derivative of 1/18*g**4 + 0*g + 0*g**2 + 2/27*g**3 + 2. Determine c, given that d(c) = 0.
-1, 0
Let f = -6 + 9. Factor -3*a + a**2 + 3*a + a - 1 - a**f + 0*a**3.
-(a - 1)**2*(a + 1)
Let z(g) be the second derivative of g**6/900 - g**5/150 + g**3/3 - g. Let i(o) be the second derivative of z(o). Determine r so that i(r) = 0.
0, 2
Let g(m) be the first derivative of -8/3*m**3 + 0*m**2 + 50/3*m**6 - 1 + 0*m + 14*m**4 - 26*m**5. Factor g(d).
2*d**2*(2*d - 1)*(5*d - 2)**2
Let t(w) = -9*w**4 - 11*w**3 + 10*w**2 - 3*w - 5. Let r(g) = g**4 + g**2 - g - 1. Suppose -5*h - 22 = 3. Let v(o) = h*r(o) + t(o). What is m in v(m) = 0?
-1, -2/7, 0, 1/2
Let a(d) = -52*d**3 + 10*d**2 + 52*d - 8. Let f(j) = -j**2. Let t(b) = a(b) + 2*f(b). Factor t(k).
-4*(k - 1)*(k + 1)*(13*k - 2)
Suppose 26*m + 14 = 66. Factor c**3 + 1/3*c**4 + 1/3*c + c**m + 0.
c*(c + 1)**3/3
Let j(h) be the first derivative of 25*h**6/27 - 2*h**5/9 - 3*h**4/2 + 10*h**3/27 + 2*h**2/9 - 4. Determine n, given that j(n) = 0.
-1, -1/5, 0, 2/5, 1
Let g(t) = t**2 - 16*t + 31. Let m be g(14). Let x(c) be the second derivative of 2/27*c**m + 1/54*c**4 + 0*c**2 - 2*c + 0. Find a such that x(a) = 0.
-2, 0
Let u(h) = 5*h**4 + 36*h**3 + 136*h**2 + 180*h + 73. Let y(b) = 11*b**4 + 72*b**3 + 271*b**2 + 360*b + 145. Let x(d) = -5*u(d) + 2*y(d). What is s in x(s) = 0?
-5, -1
Let m(s) be the third derivative of -1/210*s**5 + s**2 + 0*s + 0*s**4 - 1/294*s**8 - 1/70*s**6 + 0 - 3/245*s**7 + 0*s**3. Factor m(o).
-2*o**2*(o + 1)**2*(4*o + 1)/7
Let a(z) = -z**4 - z**3 + z**2 - z - 1. Let i(k) = 18*k**4 + 12*k**3 - 42*k**2 + 2*k + 10. Let u(x) = 20*a(x) + 2*i(x). Suppose u(o) = 0. What is o?
-2, -1/4, 0, 2
Let n(i) = -i**2 + 8*i - 9. Let c be n(6). Factor 6*q + 2*q**2 - 2 + 2*q**c - 5*q**2 + 0*q**3 - 3*q**2.
2*(q - 1)**3
Let i(o) be the second derivative of -o**7/15120 + o**6/4320 + o**4/12 - 2*o. Let z(d) be the third derivative of i(d). Find p such that z(p) = 0.
0, 1
Let v(x) = -2 + 3 + 0. Let a(o) = 3*o**2 + 6*o - 3. Let r(g) = -a(g) - 6*v(g). Factor r(k).
-3*(k + 1)**2
Let t(u) be the first derivative of 0*u**2 - 2/15*u**3 + 1/20*u**4 + 0*u + 3. Factor t(m).
m**2*(m - 2)/5
Let k(l) be the first derivative of l**3/5 - 3*l**2/5 - 3. Factor k(y).
3*y*(y - 2)/5
Suppose 2*s - 2 = -0*s. Let b be s/5 - (-4)/(-20). Solve 0*p + 2/5*p**4 + 0 - 2/5*p**2 + b*p**3 = 0.
-1, 0, 1
Let b(a) be the second derivative of a**5/20 - a**4/2 + 5*a**3/3 - 5*a**2/2 + 4*a. Let n be b(4). Suppose 0*d + 0 - 1/3*d**n + 2/3*d**2 = 0. Calculate d.
0, 2
Let s(z) be the third derivative of -z**6/1620 + z**5/540 - 7*z**3/6 + 4*z**2. Let j(y) be the first derivative of s(y). Determine x so that j(x) = 0.
0, 1
Let n(y) = -7*y**2 - 16*y - 15. Let s(p) = -36*p**2 - 82*p - 78. Let o(g) = -g - 1. Let t(z) = -2*o(z) + s(z). Let k(j) = -16*n(j) + 3*t(j). Factor k(d).
4*(d + 1)*(d + 3)
Let u(j) be the second derivative of -j**4/30 + j**2/5 + j. Determine z so that u(z) = 0.
-1, 1
Suppose -20*x - 3 - 49*x**3 - 40*x**2 - 1 - 4*x**5 + 9*x**3 - 20*x**4 = 0. Calculate x.
-1
Let m(d) = d**5 - d**4 - 3*d**3 + d**2 + 5*d. Let v(p) = 8*p**5 - 10*p**4 - 26*p**3 + 10*p**2 + 44*p. Let n(r) = -52*m(r) + 6*v(r). Factor n(x).
-4*x*(x - 1)*(x + 1)**3
Let z(y) be the third derivative of y**8/4200 + y**7/700 + y**6/300 + y**5/300 + 5*y**3/6 + 7*y**2. Let a(h) be the first derivative of z(h). Factor a(q).
2*q*(q + 1)**3/5
Let r(o) = -13*o**2 - 17*o - 9. Let g(l) = -3*l**2 - 4*l - 2. Let u(f) = 9*g(f) - 2*r(f). Solve u(y) = 0.
-2, 0
Let y(n) = 8*n**3 + 6*n**2 - 5. Let f(i) = i**3 + i**2 - i. Let b(o) = -18*f(o) + 2*y(o). Factor b(k).
-2*(k - 1)**2*(k + 5)
Let d(r) be the third derivative of r**7/70 - r**6/20 - r**5/5 + r**4/4 + 3*r**3/2 + r**2. Solve d(z) = 0.
-1, 1, 3
Let b be (-2)/(-6)*(-2 + 8). Determine s, given that 16 - 16*s + 16*s**3 - 9*s**b - 4*s**4 - 7*s**2 + 4*s**2 = 0.
-1, 1, 2
Let i be ((-6)/28)/(6/(-8)). Find w, given that -i - 2/7*w**4 - 8/7*w - 8/7*w**3 - 12/7*w**2 = 0.
-1
Let v(i) = -12*i**4 - 64*i**3 - 66*i**2 + 14. Let d(z) = -4*z**4 - 21*z**3 - 22*z**2 + 5. Let h(o) = -20*d(o) + 6*v(o). Factor h(n).
4*(n + 1)*(n + 2)**2*(2*n - 1)
Let r(f) be the second derivative of f**7/14 - f**6/10 - 9*f**5/20 + f**4/4 + f**3 - 7*f. Solve r(p) = 0.
-1, 0, 1, 2
Let p(i) = -i**4 + 2*i**3 - 1. Let d(z) = 5*z**5 - z**3 - 5 - z**4 + 4 + 2*z**3 - 4*z**5. Let n(w) = 2*d(w) - 2*p(w). Solve n(l) = 0.
-1, 0, 1
Let o be (24/(-14))/(9*(-1)/14). Factor o*m - 10/9*m**2 - 8/9.
-2*(m - 2)*(5*m - 2)/9
Let f(y) be the third derivative of y**7/210 + y**6/40 + y**5/30 - 2*y**2. Suppose f(d) = 0. Calculate d.
-2, -1, 0
Solve -1/2*r - 2*r**4 + 0 - 2*r**2 - 1/2*r**5 - 3*r**3 = 0.
-1, 0
Let a be (-3)/9*-3 - -2. Suppose 4*o = a*i + o + 3, i + o = 5. Factor 2*y + 0*y + y**2 + 5*y**i + 4*y**2.
2*y*(5*y + 1)
Let d be 14/(-126) - (-13)/36. Let -d*h**4 + 0 + 0*h - 1/2*h**3 - 1/4*h**2 = 0. What is h?
-1, 0
Let y = 26 - 19. Let g(h) be the third derivative of 1/120*h**6 + 0*h - 1/48*h**4 + 0 - h**2 + 0*h**3 + 0*h**y + 0*h**5 - 1/672*h**8. What is d in g(d) = 0?
-1, 0, 1
Suppose 9*v = 12*v. Let m(f) be the first derivative of -1/2*f + 2 + v*f**2 + 1/6*f**3. Factor m(b).
(b - 1)*(b + 1)/2
Let b(w) be the third derivative of w**7/140 - w**6/20 + w**5/8 - w**4/8 - 7*w**2. Let b(r) = 0. What is r?
0, 1, 2
Let g(k) be the first derivative of 4*k**3/21 + 6*k**2/7 - 16*k/7 - 25. Factor g(w).
4*(w - 1)*(w + 4)/7
Let b = -9 + 6. Let z be b + 7/1 + -2. Factor -3*p**2 + 5*p**2 - 2*p**2 - 2*p**z.
-2*p**2
Let p(h) be the third derivative of h**7/168 - 5*h**6/96 + h**5/6 - 5*h**4/24 + 15*h**2. Factor p(k).
5*k*(k - 2)**2*(k - 1)/4
Let c(m) be the third derivative of -m**6/120 + m**5/15 - 5*m**4/24 + m**3/3 - 14*m**2. Find v, given that c(v) = 0.
1, 2
Factor 4*q**3 - 157*q**4 - 3 + 75*q**4 + 83*q**4 - 4*q + 2*q**2.
(q - 1)*(q + 1)**2*(q + 3)
Let a = 41 + -41. Let m(o) be the second derivative of 3*o + 0*o**2 - 1/6*o**4 + 1/20*o**5 + a*o**3 + 1/30*o**6 + 0. Factor m(w).
w**2*(w - 1)*(w + 2)
Let p be (2/(-6))/(3/(-36)). What is u in -10*u - 12 + 2*u + 8 - p*u**2 = 0?
-1
Factor -4/7 - 8/7*h**2 + 2/7*h**3 + 10/7*h.
2*(h - 2)*(h - 1)**2/7
Let w(x) be the first derivative of 3*x**6/40 + 2*x**5/5 + 3*x**4/8 - x**3 + x**2/2 - 5. Let y(p) be the second derivative of w(p). Factor y(l).
3*(l + 1)*(l + 2)*(3*l - 1)
Let m(b) be the second derivative of -1/18*b**4 + 1/9*b**3 + 1/3*b**2 + 0 - 3*b - 1/30*b**5. Factor m(y).
-2*(y - 1)*(y + 1)**2/3
Let p = 71/4 - 343/20. Let t(v) be the second derivative of 1/21*v**7 + 1/3*v**3 - 2*v + 2/3*v**4 + p*v**5 + 0*v**2 + 4/15*v**6 + 0. Factor t(f).
2*f*(f + 1)**4
Let o(t) be the first derivative of 1/20*t**4 + 5 + 0*t**2 + 0*t + 1/15*t**3 - 1/25*t**5 - 1/30*t**6. Factor o(x).
-x**2*(x - 1)*(x + 1)**2/5
Let w be (5 + 0)*(-8)/10. Let c be 10/(-8)*w/(-1). Let s(g) = -2*g**3 + 2*g. Let t(j) = -j**3 + j. Let d(b) = c*t(b) + 3*s(b). Determine z so that d(z) = 0.
-1, 0, 1
Let m = -2 + 4. Determine n so that -n**2 + 29 - m*n - 29 = 0.
-2, 0
Factor 3/4*p + 0 + 5/4*p**2.
p*(5*p + 3)/4
Suppose 0 = 4*l - 12. What is d in 2 - d**2 + d - l*d + 2*d**3 - d**2 + 0*d**2 = 0?
-1, 1
Let p(g) be the second derivative of -g**7/84 + g**6/60 + g**5/20 - g**4/12 - g**3/12 + g**2/4 - 3*g. 