econd derivative of -1/21*u**4 + 2*u + 1/147*u**7 - 1/7*u**2 + 1/35*u**6 + 1/35*u**5 - 1/7*u**3 + 0. Suppose s(z) = 0. What is z?
-1, 1
Factor 1/2 + 1/2*x**4 - x**2 + 0*x**3 + 0*x.
(x - 1)**2*(x + 1)**2/2
Let s(a) = -5*a**3 + 14*a**2 - 3*a - 3. Let v(z) = -z**2 - z - 1. Let q(b) = s(b) + v(b). Factor q(j).
-(j - 2)*(j - 1)*(5*j + 2)
Let v = 1 + 2. Suppose 0*q + 12 = v*q. Factor 2*f**q + 0*f**2 + 2*f**5 + 3*f**2 - 3*f**2 - 2*f**3 - 2*f**2.
2*f**2*(f - 1)*(f + 1)**2
Let s(k) be the second derivative of k**7/210 - k**6/60 + k**5/60 - k**3/2 - 4*k. Let i(z) be the second derivative of s(z). Let i(a) = 0. Calculate a.
0, 1/2, 1
Let d be ((-696)/(-30))/(2/5). Factor -y**3 + 2*y - 56*y**4 + d*y**4 - 2*y**2 - y**3.
2*y*(y - 1)**2*(y + 1)
Let p(j) be the second derivative of j**8/3360 + j**7/840 - j**5/120 - j**4/48 + j**3/6 - 4*j. Let k(r) be the second derivative of p(r). Solve k(o) = 0 for o.
-1, 1
Let i(n) be the first derivative of 0*n - 4 + 3/14*n**2 - 1/7*n**3. Determine t so that i(t) = 0.
0, 1
Let c be (3 + (-40)/12)/(1/(-6)). Let z = 19/10 - 7/5. Solve 0*u + z*u**c + 0 = 0.
0
Solve 0*m**3 + 0 + 2/11*m - 4/11*m**4 + 4/11*m**2 - 2/11*m**5 = 0 for m.
-1, 0, 1
Let i be -6 + 2 - (-5 + 1). Let c(t) be the first derivative of -2 + i*t - 1/6*t**3 + 0*t**2 - 1/8*t**4. Find v such that c(v) = 0.
-1, 0
Suppose 3*a + 36 = 4*j + 12, -5*a = 2*j + 14. Factor 2*r**j - r**2 - 5*r**2 - 5*r**3 - 3*r.
-3*r*(r + 1)**2
Let i(n) be the first derivative of n**7/4200 - n**6/900 - 5*n**3/3 - 5. Let m(u) be the third derivative of i(u). Factor m(d).
d**2*(d - 2)/5
Let g = 23/24 + -5/8. Let y(f) be the second derivative of f - 1/12*f**4 - 1/2*f**2 + 0 + g*f**3. Determine z, given that y(z) = 0.
1
Let a(u) = u**2 + 8*u - 4. Let w be a(-9). Find c, given that -1/2*c**3 + 0 + 3/2*c**4 + 0*c**2 + 0*c + 2*c**w = 0.
-1, 0, 1/4
Let s(g) be the third derivative of g**6/360 - 7*g**5/180 + g**4/9 + 8*g**3/9 - 10*g**2. Factor s(f).
(f - 4)**2*(f + 1)/3
Let q(p) be the second derivative of -p**6/24 + 5*p**5/16 - 15*p**4/16 + 35*p**3/24 - 5*p**2/4 + 23*p. Find v such that q(v) = 0.
1, 2
Let d be (-20)/170 - (-203)/1292. Let x = d + 4/19. Factor -x*l**2 - 1/2 - 3/4*l.
-(l + 1)*(l + 2)/4
Let t = 633 - 1897/3. Factor -t*y - 1/3*y**2 - 1/3.
-(y + 1)**2/3
Let v(z) = -z + 13. Let n be v(10). Factor -n + 2*d + 2*d + 1 - 2*d**2.
-2*(d - 1)**2
Let s(d) be the first derivative of d**3 - 5/12*d**4 - 2 - 7/6*d**2 + 2/3*d + 1/15*d**5. Find g, given that s(g) = 0.
1, 2
Let u = -7 + 9. Factor 4*j**2 + 0*j**5 - 7*j**u + 3*j**5 - 9*j**4 + 9*j**3.
3*j**2*(j - 1)**3
Let q(g) be the first derivative of -g**5/20 - g**4/8 + g**3/12 + g**2/4 - 9. Factor q(p).
-p*(p - 1)*(p + 1)*(p + 2)/4
Let s(l) = -l**2 + 5*l + 2. Let j be s(5). Let f be 2 - (0 + 1)*(-6)/6. Factor 2 + 12*g - 49/2*g**f + 21/2*g**j.
-(g - 1)*(7*g + 2)**2/2
Let t(s) = -25*s + 52. Let l be t(2). Factor 5/4*v**5 + 0 + 1/4*v**3 + 0*v + 1/2*v**2 - l*v**4.
v**2*(v - 1)**2*(5*v + 2)/4
Factor 2/5*b**3 + 0 - 4/5*b - 2/5*b**2.
2*b*(b - 2)*(b + 1)/5
Factor 0*i - 1/7*i**2 + 0.
-i**2/7
Let d = -9 + 12. Determine p so that -23*p**2 + 24*p - 81 + 0*p**2 - d*p**3 - 105*p - 4*p**2 = 0.
-3
Let a = -219 - -221. Let -1/5 - 2*w**2 - a*w**3 - w - w**4 - 1/5*w**5 = 0. What is w?
-1
Let r(z) = z**2 + 3*z - 6. Let a be r(-5). Factor -6*h + 6*h + 6*h**3 + h - a*h**2 - 2*h**3.
h*(2*h - 1)**2
Let w(t) be the second derivative of 4/7*t**2 - 2*t - 8/21*t**3 + 0 - 1/70*t**5 + 5/42*t**4. Find l, given that w(l) = 0.
1, 2
Let s(m) be the third derivative of m**7/315 - m**6/36 + m**5/10 - 7*m**4/36 + 2*m**3/9 - 2*m**2 + 24. Suppose s(p) = 0. What is p?
1, 2
Let l = 13 - 13. Let g(d) be the first derivative of 0*d**2 - 1 - 1/9*d**3 + l*d. Factor g(a).
-a**2/3
Suppose -4*b = -i - 11, 13 + 0 = 4*b + i. Factor 1/3*p**4 - 1/3*p - p**b + p**2 + 0.
p*(p - 1)**3/3
Let 4/9 + 2/3*z + 2/9*z**2 = 0. Calculate z.
-2, -1
Factor 3/7*k + 0 + 3/7*k**2.
3*k*(k + 1)/7
Let p(o) = 5*o - 1. Let j be p(1). Suppose 0 = -4*t - 0*f - f + 4, -j*t - 4*f + 16 = 0. Let 0*w + t*w**2 + 0 - 1/3*w**3 = 0. What is w?
0
Let x be 27/45 - 0/(-3 + 2). Factor x*u - 3/5*u**2 + 0.
-3*u*(u - 1)/5
Factor 0 - 1/3*h**5 - 2/3*h**3 + 0*h**2 + 0*h + h**4.
-h**3*(h - 2)*(h - 1)/3
Let a = 2 - 2. Let o(w) be the third derivative of -2/15*w**3 + w**2 + 0 - 1/60*w**4 + a*w - 1/60*w**6 + 4/75*w**5. Let o(i) = 0. Calculate i.
-2/5, 1
Let m(i) be the third derivative of i**7/1155 - i**6/660 - 11*i**2. What is l in m(l) = 0?
0, 1
Let a(r) = -r. Let q(j) = -8*j**2 - 2*j. Let h(v) = 6*a(v) + q(v). Let k(l) = l**3 - l. Let u(n) = h(n) - 6*k(n). Factor u(i).
-2*i*(i + 1)*(3*i + 1)
Let g(d) be the third derivative of -d**7/105 - 7*d**6/60 - d**5/6 + 7*d**4/12 + 2*d**3 - 14*d**2. Factor g(q).
-2*(q - 1)*(q + 1)**2*(q + 6)
Let k(g) be the third derivative of 5*g**8/84 + 16*g**7/105 - 19*g**6/30 - 14*g**5/15 + 14*g**4/3 - 16*g**3/3 - 30*g**2. Find z such that k(z) = 0.
-2, 2/5, 1
Let c(b) be the second derivative of 1/10*b**5 - 1/10*b**6 + 1/2*b**2 + 1/42*b**7 + 0 + 2*b + 1/6*b**4 - 1/2*b**3. Factor c(r).
(r - 1)**4*(r + 1)
Let n be 6/(-10) + 207/45. Suppose -s - 2*s**4 + 0*s + 2*s - s**2 - s**3 + 3*s**n = 0. What is s?
-1, 0, 1
Let l(z) = -z**3 + 2*z**2 + 4*z - 2. Let w be l(3). Let q(h) be the first derivative of w + 1/2*h**4 - 2/3*h**3 - h**2 + 2*h. Factor q(p).
2*(p - 1)**2*(p + 1)
Let h(y) = 5*y**2 + 40*y + 78. Let i(q) = -10*q**2 - 80*q - 155. Let o(c) = 5*h(c) + 2*i(c). Factor o(z).
5*(z + 4)**2
Let y(m) = -m**4 + 4*m**3 - 9*m**2 - 4*m + 5. Let a(h) = h**4 - 6*h**3 + 13*h**2 + 6*h - 7. Let b(q) = 5*a(q) + 7*y(q). Factor b(z).
-2*z*(z - 1)*(z + 1)**2
Determine f so that 3/5*f**2 - 3/5*f - 3/5 + 3/5*f**3 = 0.
-1, 1
Suppose -2*y = -0*y - 6. Let s(i) = -2*i**2 + 4*i - 6. Let q(m) = -2*m**2 + 3*m - 7. Let f(z) = y*s(z) - 2*q(z). Factor f(k).
-2*(k - 2)*(k - 1)
Let y be 1/3 + 65/39. Let m(t) be the third derivative of 0*t**4 + 1/60*t**5 - 1/120*t**6 + 0*t**3 - y*t**2 + 0 + 0*t. Factor m(b).
-b**2*(b - 1)
Let b(c) be the first derivative of -2*c**3/21 - 6*c**2/7 - 18*c/7 - 14. Factor b(i).
-2*(i + 3)**2/7
Let o = -5/4 + 33/20. Find k, given that -8/5*k**4 - 12/5*k**3 + 0 - 8/5*k**2 - 2/5*k**5 - o*k = 0.
-1, 0
Let p(q) be the first derivative of -12*q**5/5 - 11*q**4 - 16*q**3 - 8*q**2 + 12. Factor p(m).
-4*m*(m + 1)*(m + 2)*(3*m + 2)
Let i be 4 + -6 + 76/30. Determine k, given that 2/15*k**3 + 2/3*k + i*k**2 + 4/15 = 0.
-2, -1
Factor 6*n**4 - 24*n**3 + 3*n + 15*n**3 - 27 + 27.
3*n*(n - 1)**2*(2*n + 1)
Let m(w) = w - 1. Let v(r) = -r**2 + 9*r - 8. Suppose 5*k + 5*g = 135, 3*k + 2*g - 75 = g. Let p(j) = k*m(j) - 3*v(j). Let p(x) = 0. Calculate x.
0, 1
Suppose 6*q = 2*q - 3*q. Factor 2/5*p**5 + q + 24/5*p**3 + 0*p + 16/5*p**2 + 12/5*p**4.
2*p**2*(p + 2)**3/5
Let v = 2/3 + -1/6. Find b such that 0 - v*b + 1/2*b**2 = 0.
0, 1
Let o(q) be the first derivative of 5*q**3/3 + 5*q**2 + 5*q + 2. Factor o(n).
5*(n + 1)**2
Let s(q) = -q**5 + q**4 - q**3 + q - 1. Let l(o) = 2*o**5 - 2*o**4 - 14*o**3 + 4*o**2 + 10*o - 2. Let v(c) = l(c) - 2*s(c). Let v(i) = 0. Calculate i.
-1, 0, 1, 2
Let w(d) be the second derivative of -d**5/20 + d**4/4 - 5*d. Factor w(f).
-f**2*(f - 3)
Factor 2037 - 2025 - 33*o + 14*o**2 - 5*o**2 - 6*o.
3*(o - 4)*(3*o - 1)
Let f(a) be the second derivative of 6*a**6/35 - 23*a**5/70 + a**4/14 + 2*a**3/21 - 31*a. Suppose f(j) = 0. What is j?
-2/9, 0, 1/2, 1
Factor -3/2*l**2 - 363/2 + 33*l.
-3*(l - 11)**2/2
Let p(r) = -r**3 - r. Let l(a) = 2*a**4 + 12*a**3 + 6*a**2 + 8*a. Suppose 2*b + 3 = -b. Let q(t) = b*l(t) - 6*p(t). Let q(o) = 0. What is o?
-1, 0
Suppose 0*h**2 + 2315 - 2315 - 20*h + 5*h**2 = 0. Calculate h.
0, 4
Let m = 2 + 0. Determine u so that 6*u - 4*u + u**2 - 4*u**2 + u**m = 0.
0, 1
Solve -3/8*m - 3/8*m**3 - 3/4*m**2 + 0 = 0 for m.
-1, 0
Let o(h) be the third derivative of -1/112*h**8 + 0*h**7 + 2*h**2 - 1/8*h**4 + 0*h**5 + 0*h + 1/20*h**6 + 0*h**3 + 0. Factor o(n).
-3*n*(n - 1)**2*(n + 1)**2
Let y(w) be the second derivative of -w**4/20 + w**3/10 + 9*w**2/5 + 5*w. Factor y(p).
-3*(p - 3)*(p + 2)/5
Let r(j) = -j**4 - 14*j**3 - 11*j**2 + 14*j + 10. Let h(f) = -f**4 + f**3 + f**2 - f + 1. Let w(n) = -2*h(n) - r(n). Factor w(o).
3*(o - 1)*(o + 1)*(o + 2)**2
Let b(y) = 4*y**3 + y - 1. Let u be b(1). Let d be (-11)/(-4) - 3/u