r j.
-2, -1, -2/5, 0
Let q(l) be the second derivative of 9*l + 1/15*l**4 + 1/15*l**2 - 4/45*l**3 + 0 - 2/75*l**5 + 1/225*l**6. Solve q(r) = 0.
1
Let w(t) = 82*t**3 + 112*t**2 - 17*t + 21. Let v(q) = -27*q**3 - 37*q**2 + 6*q - 6. Let m(a) = 21*v(a) + 6*w(a). Let m(p) = 0. Calculate p.
-8/5, 0, 1/5
Let q(a) = a**3 - a - 1. Let w(z) = z**3 - 30*z**2 - 31*z + 54. Let c(v) = 6*q(v) - w(v). Factor c(y).
5*(y - 1)*(y + 3)*(y + 4)
Let l(u) = -u - 6. Suppose h - 3 = 0, 3*m = 6*m - 2*h + 30. Let j be l(m). Factor -6 + 4 - 3 - 4*t - 1 + 2*t**j.
2*(t - 3)*(t + 1)
Suppose 0 = 5*a - 150 - 630. Determine q so that -881*q - 326 - 232*q**2 - 28*q**2 - 25*q**3 + a*q + 76 = 0.
-5, -2/5
Let d(q) be the second derivative of 0 - 13*q + 1/21*q**3 + 0*q**2 + 1/70*q**5 + 1/21*q**4. Factor d(c).
2*c*(c + 1)**2/7
Suppose -2*k = 2*k - 2*v, 2*k = -5*v + 24. Factor -3 - 5 + 20*p + k - 5*p**2 - 9.
-5*(p - 3)*(p - 1)
Let v(w) be the first derivative of -w**3/3 - 65*w**2/2 - 64*w + 625. Solve v(y) = 0.
-64, -1
Suppose -12*q = 198 - 198. Find t such that q - 8/3*t**2 + 5/3*t**3 - 1/3*t**4 + 4/3*t = 0.
0, 1, 2
Let s(k) be the first derivative of -2*k**3/27 + 10*k**2/9 + 22*k/9 + 404. Suppose s(r) = 0. Calculate r.
-1, 11
Suppose 10/7*d**3 + 80/7*d - 24/7 - 54/7*d**2 = 0. Calculate d.
2/5, 2, 3
Let i(o) be the second derivative of -1/25*o**5 - 1/30*o**4 - 3*o + 0 + 0*o**3 + 0*o**2 - 1/75*o**6. Factor i(u).
-2*u**2*(u + 1)**2/5
Suppose -6 = -3*k - 3. Let i be 3 + (k + -1)/(-3). Let -5*u**2 - u**3 - u**3 + 2*u**2 - u**i = 0. Calculate u.
-1, 0
Let t = -16 + 20. Let m be 2/t - 117/(-18). Suppose m - 3*x**2 + 3*x - 5 - 2 = 0. What is x?
0, 1
Let o(w) be the third derivative of -w**7/42 + w**6/24 + 5*w**5/6 + 5*w**4/3 + 279*w**2. Factor o(k).
-5*k*(k - 4)*(k + 1)*(k + 2)
Let y(n) be the third derivative of n**6/280 - 3*n**5/14 + 9*n**4/2 - 28*n**3 - 231*n**2. Factor y(a).
3*(a - 14)**2*(a - 2)/7
Let n(f) be the third derivative of 0 - 1/720*f**5 + f**2 - 1/2160*f**6 + 0*f**4 + 0*f + 7/6*f**3. Let r(o) be the first derivative of n(o). Factor r(j).
-j*(j + 1)/6
Let n be 273/45 - (-2 + 8). Let i(t) be the third derivative of 0*t**3 + 0 + n*t**6 - 2*t**2 + 0*t + 1/6*t**4 - 1/105*t**7 - 1/6*t**5. Factor i(w).
-2*w*(w - 2)*(w - 1)**2
Let y(x) be the first derivative of 1/6*x**3 - 5 + 3/4*x**2 + x. Determine v so that y(v) = 0.
-2, -1
Suppose 1624 = 18*s - 16*s. Let h = 3275/4 - s. Factor 3/2*c**2 - h*c + 27/4*c**3 - 3/2.
3*(c - 1)*(c + 1)*(9*c + 2)/4
Suppose 0 = -2*a - 10, 0 = n - 2*a - 3*a - 54. Let s = n + -11. Suppose 16*q + 0*q + 11*q + 3*q**3 + s*q**2 = 0. What is q?
-3, 0
Let r(d) be the second derivative of -d**4/36 - 49*d**3/9 - 2401*d**2/6 - 23*d. Find u, given that r(u) = 0.
-49
Let f be (-8)/64*-8 + (-83)/84. Let a(u) be the third derivative of 0*u + 1/210*u**5 + 0*u**3 - f*u**4 + 0 + 6*u**2. Suppose a(i) = 0. What is i?
0, 1
Let u(p) = 2*p**2 + 4*p - 4. Let w be u(-4). Suppose 0 = 4*n + 3*g - w, 3 = -2*n + 3*n + g. Factor -9*i**3 + 3*i**5 + 0*i**2 + 3*i**2 + 6*i**n - 3*i**4.
3*i**2*(i - 1)**2*(i + 1)
Let z(u) be the second derivative of u**6/10 + 9*u**5/10 - u**4/4 - 3*u**3 - 86*u. What is a in z(a) = 0?
-6, -1, 0, 1
Let x = 3361/12 + -280. Let n(i) be the second derivative of 0*i**2 + 0 + 1/30*i**6 + 0*i**5 - x*i**4 - 2*i + 0*i**3. Suppose n(m) = 0. What is m?
-1, 0, 1
Let w = -12380 + 12380. Determine i so that 0*i + 2/3*i**3 + 0 + 1/3*i**5 + w*i**2 - i**4 = 0.
0, 1, 2
Let r = -13728 - -13730. Suppose 0 + 5/2*x**r + 15/4*x - 5/4*x**3 = 0. Calculate x.
-1, 0, 3
Let f = -2227/3 - -745. Let v(n) be the first derivative of 154/15*n**5 + 4 - f*n**3 + 4/3*n**2 + 0*n - 23/2*n**4. Solve v(k) = 0.
-2/7, 0, 2/11, 1
Determine p, given that 96/5 + 48/5*p + 6/5*p**2 = 0.
-4
Let 5/11*a - 2/11 - 1/11*a**3 - 3/11*a**2 + 1/11*a**4 = 0. Calculate a.
-2, 1
Let p(b) be the first derivative of b**5/10 + 23*b**4/4 + 42*b**3 + 122*b**2 + 160*b - 258. Factor p(m).
(m + 2)**3*(m + 40)/2
Let m be (135/(-891))/(35/(-42)). Suppose m*t**2 - 4/11 - 2/11*t = 0. Calculate t.
-1, 2
Let w(r) be the second derivative of 3/10*r**3 + 0 + 1/4*r**4 + 3/100*r**5 - 27/10*r**2 + 5*r. Suppose w(a) = 0. Calculate a.
-3, 1
Factor 5*h**2 - 173076 + 411959 + 139242 + 185156*h - 187906*h.
5*(h - 275)**2
Let s(p) = p + 17. Let t be s(-12). Suppose -t*c = -3*c - 10. Factor 2*d + 0*d**2 + 6*d**2 - c*d**2.
d*(d + 2)
Let l(g) be the second derivative of g**8/4480 + g**7/1120 + g**6/960 + 5*g**3 + 16*g. Let q(x) be the second derivative of l(x). Suppose q(s) = 0. What is s?
-1, 0
Let k(r) = 19 + r**3 - 13*r**2 + 37*r + 6 - 34. Let u be k(9). Factor -1/2*l**4 + u + 1/2*l**2 - l + l**3.
-l*(l - 2)*(l - 1)*(l + 1)/2
Let u(o) = -7*o**2 + 2*o - 13. Let s(d) = 18*d**2 - 5*d + 28. Let v(w) = -6*s(w) - 15*u(w). Let v(t) = 0. What is t?
-3, 3
Factor 0 - 2/11*q**4 - 96/11*q**2 + 26/11*q**3 + 72/11*q.
-2*q*(q - 6)**2*(q - 1)/11
Let m = -1099 - -60543/55. Let o(d) be the first derivative of 128/11*d**2 - 208/11*d**3 - 32/11*d + 112/11*d**4 + 3 - m*d**5. Factor o(r).
-2*(r - 2)**2*(7*r - 2)**2/11
Determine u so that -10/11*u**2 + 72/11*u + 2/11*u**4 - 8/11*u**3 - 72/11 = 0.
-3, 2, 3
Let g be 6 + 4*((-3)/2)/3. Factor 16*l**3 - 3*l - 17*l**4 + 5*l**2 - 4 + 16*l**g - 13*l**3.
-(l - 4)*(l - 1)*(l + 1)**2
Let o = -1955 + 3915/2. Factor -5/2*z**3 - 1/4*z**5 - 5/4*z - 1/4 - o*z**2 - 5/4*z**4.
-(z + 1)**5/4
Let m(z) be the third derivative of -z**5/20 - z**4 + 9*z**3/2 - 35*z**2 - 2*z. Find f such that m(f) = 0.
-9, 1
Determine h, given that 0*h**2 + 0 + 0*h**4 - 2/13*h**5 + 0*h**3 + 0*h = 0.
0
Suppose 0*m + 3*x - 17 = -2*m, m - 2*x + 2 = 0. Factor 162*c**2 - 34*c**2 - 2*c**5 + 773*c**3 - 933*c**3 + 34*c**m.
-2*c**2*(c - 8)**2*(c - 1)
Let t be (-4)/6 + 126/27. Find k such that 28*k - 15*k - 36*k**2 + 33*k**t - 18*k**3 - 9*k**5 + 11*k = 0.
-1, 0, 2/3, 2
Let g = -5 + 12. Suppose u + 8 = 4*o, -3*o + 9*u = 4*u - 6. Factor 2 - 2 - 6*b**2 + g*b**2 - b - o.
(b - 2)*(b + 1)
Let a(d) be the third derivative of 4*d**7/1155 + 3*d**6/220 + d**5/55 + d**4/132 + 70*d**2. Suppose a(s) = 0. What is s?
-1, -1/4, 0
Let y(w) be the second derivative of -1/180*w**5 + 0 - 1/108*w**4 + 5/54*w**3 - 1/6*w**2 - 7*w. Factor y(o).
-(o - 1)**2*(o + 3)/9
Factor -18 - 184*r**2 + 82*r**2 + 70*r**2 + 48*r.
-2*(4*r - 3)**2
Let l(u) be the second derivative of -2/3*u**4 - 1/5*u**5 - 5*u + 0*u**3 + 2/21*u**7 + 0*u**2 + 4/15*u**6 + 0. Factor l(f).
4*f**2*(f - 1)*(f + 1)*(f + 2)
Suppose 5*r = -0*r. Let w(u) = 7*u + 44. Let l be w(-5). Determine v, given that -4*v**2 - v + l*v**3 - 11*v**4 + r*v**2 + 4*v**5 + 3*v**2 = 0.
-1/4, 0, 1
Let v(z) = 0*z + z + 0 + 2 + 1. Let k be v(3). Factor k + 3*y**2 + 2 - 8.
3*y**2
Let w be 57/(-532)*16 - 66/(-14). Factor -1/3*v - 1/3*v**2 + 1/3 + 1/3*v**w.
(v - 1)**2*(v + 1)/3
Let x(c) be the first derivative of 2*c**3/45 + 2*c**2/3 - 194. Let x(w) = 0. What is w?
-10, 0
Find r, given that -8/5*r**2 + 1/5*r**3 + 12/5*r + 0 = 0.
0, 2, 6
Factor -128*x + 9*x**3 + 16*x**2 + 144 - 5*x**3 + 4*x**2.
4*(x - 2)**2*(x + 9)
Let z be -9*(-3)/(-45)*(-185)/37. Factor 7/5*p**2 - 2/5*p - 1/5*p**5 + 0 - 9/5*p**z + p**4.
-p*(p - 2)*(p - 1)**3/5
Suppose 0 = -647*g + 340*g. Let b = 20 + -99/5. Solve b*r**4 + g + 1/5*r**3 + 0*r**2 + 0*r = 0.
-1, 0
Let n(c) be the second derivative of 1/20*c**5 - 1/60*c**6 - 20*c + 0*c**2 - 1/6*c**3 + 1/24*c**4 + 0. Factor n(d).
-d*(d - 2)*(d - 1)*(d + 1)/2
Let o be -1 - 1/(-6)*15. Let s(q) be the first derivative of -1/3*q**3 + o*q**2 - 2*q - 6. Factor s(n).
-(n - 2)*(n - 1)
Let a(z) be the third derivative of -z**6/360 - z**5/36 + 13*z**4/72 - 7*z**3/18 + 5*z**2 - 4*z. Solve a(b) = 0 for b.
-7, 1
Let x be (-684)/6061 + 2/11 - (-19)/145. Factor -x*f**3 + 25 + 3*f**2 - 15*f.
-(f - 5)**3/5
Let g(z) be the first derivative of z**3/3 + 15*z**2 - 64*z + 2. Factor g(q).
(q - 2)*(q + 32)
Let a(k) = 19*k**2 - 9*k + 5. Let u(w) = 2*w**2 - 1. Let l(g) = 2*a(g) - 18*u(g). Factor l(q).
2*(q - 7)*(q - 2)
Find f, given that 7*f - 107*f - 4116*f**2 + 98 + 4118*f**2 = 0.
1, 49
Let t(u) = 3*u**3 - 30*u**2 + 57*u - 26. Let m(j) = 10*j**3 - 90*j**2 + 171*j - 77. Let g(k) = 4*m(k) - 14*t(k). Factor g(d).
-2*(d - 28)*(d - 1)**2
Suppose 2*l + 790 - 793 = -3*m, 0 = -4*l + 4*m + 16. Solve -18*d**2 - 75/4*d**4 - l*d - 135/4*d**3 + 0 = 0.
-1, -2/5, 0
Factor -39*l