t w = 6497/2 + -3245. Factor 1/2*n + w*n**2 + 0.
n*(7*n + 1)/2
Let b be 4/(-10)*19/(-76). Let g(x) be the third derivative of -4*x**2 + 0*x + 0 + b*x**5 + 1/12*x**4 - 2/3*x**3. Factor g(m).
2*(m + 1)*(3*m - 2)
Let r(u) be the second derivative of u**5/40 + u**4/6 + u**3/3 + 24*u. Factor r(p).
p*(p + 2)**2/2
Let w(h) = 5*h**2 + 130*h. Let y be w(-26). Factor z + y - 1/2*z**2.
-z*(z - 2)/2
Let y be 18 + -17 + 1679/(-420) + 3. Let g(d) be the third derivative of 1/240*d**6 + 0*d**5 + 0*d + 0*d**3 + 0*d**4 - 5*d**2 + 0 - y*d**7. Factor g(h).
-h**3*(h - 1)/2
Suppose 39 - 41 = 2*a. Let j be (-18)/(-16)*(a + 3). Factor -9/4*y + 3/4 - 3/4*y**3 + j*y**2.
-3*(y - 1)**3/4
Let x(h) = 16*h - 1. Let l be x(9). Solve -2 - 20*u + l*u**2 + 6*u - 155*u**2 = 0 for u.
-1, -1/6
Find x, given that -25/3*x**2 + 0 - 1/3*x**3 - 8*x = 0.
-24, -1, 0
Factor 16*q**4 - 18 + 5*q**5 + 8*q**3 + 2*q**2 - 7*q - 28*q + 21*q**3 + 7*q**3 - 6*q**5.
-(q - 18)*(q - 1)*(q + 1)**3
Let a(n) be the third derivative of 22*n**2 + 1/300*n**6 + 0*n**4 + 0*n + 0 + 0*n**3 + 1/300*n**5 + 1/1050*n**7. What is s in a(s) = 0?
-1, 0
Let h be -1*11/3*(-6)/(-1). Let d(b) = b**3 + 22*b**2 - b - 19. Let t be d(h). Find j such that 1/2 - 1/2*j**t - 1/2*j**2 + 1/2*j = 0.
-1, 1
Let m(s) be the first derivative of s**6/1260 - s**5/140 - 14*s**3/3 - 11. Let o(i) be the third derivative of m(i). Let o(f) = 0. Calculate f.
0, 3
Let l = 932 + -930. Let f(v) be the third derivative of 1/45*v**5 + 1/360*v**6 + 0 + 0*v + 1/18*v**4 + l*v**2 + 0*v**3. Factor f(o).
o*(o + 2)**2/3
Suppose 0 - 17/2*l**2 - 1/4*l**3 + 35/4*l = 0. Calculate l.
-35, 0, 1
Suppose 6/11*j**2 + 306/11 - 312/11*j = 0. What is j?
1, 51
Let k = -571/225 - -69/25. Factor 0 + k*y + 2/9*y**2.
2*y*(y + 1)/9
Let m be 3/45*47 - 4/30. Find u such that -12*u - 4*u**3 - 24*u**2 + m*u**5 + 0*u**5 - 5*u**3 - 68*u**4 + 74*u**4 = 0.
-2, -1, 0, 2
Let v(d) = 2*d**3 - 4*d**2 - d + 4. Let h be v(2). Factor -66*f - 2*f**h - 405 - 69*f - 3*f**2 + 45*f.
-5*(f + 9)**2
Let l(c) be the third derivative of -c**8/50400 + c**7/2100 - c**6/360 - c**5/15 - 20*c**2. Let t(p) be the third derivative of l(p). Factor t(s).
-2*(s - 5)*(s - 1)/5
Suppose 208 = 38*f - 20. Let l(s) be the third derivative of 1/1512*s**8 + 0*s**f + 0 + 1/945*s**7 + s**2 + 0*s**4 + 0*s**5 + 0*s**3 + 0*s. Factor l(b).
2*b**4*(b + 1)/9
Factor 0*x + 0 + 0*x**2 + 6/17*x**4 - 2/17*x**3.
2*x**3*(3*x - 1)/17
Suppose -5*j + 0*z = z - 25, 27 = 3*j + 3*z. Let v be (-15)/j + (-6)/(-4) - -3. Determine m, given that -9/4*m + v*m**2 + 3/2 = 0.
1, 2
Let f = -5921/3220 + 209/84. Let j = f + 2/115. Suppose -2/3*s**2 - j + 4/3*s = 0. Calculate s.
1
Suppose f = -4*v + 10 - 0, -4*f - 3*v = -14. Suppose -y**2 + 2*y**2 + 17*y**2 + 3*y**3 + 0*y**f + 24 + 36*y = 0. What is y?
-2
Let q(s) = -s + 4. Let h(b) = -2*b**2 + 298*b - 10960. Let g(i) = h(i) + 2*q(i). Factor g(r).
-2*(r - 74)**2
Let h(x) be the first derivative of -9*x**6/160 + x**5/4 - x**4/8 + 15*x**2/2 + 10. Let g(m) be the second derivative of h(m). Solve g(f) = 0 for f.
0, 2/9, 2
Let v = 18287/75 - 731/3. Let q(p) be the first derivative of 1/5*p**2 - 2 + 0*p + 3/5*p**3 + v*p**5 + 3/5*p**4. Let q(i) = 0. What is i?
-2, -1/2, 0
Solve -12*o**2 - 14*o**2 - 6*o**2 - 4*o + 36*o**2 = 0.
0, 1
Suppose 5*h - n - 2*n = 2, 0 = 32*h - 4*n - 104. Factor 0*r**3 + 0*r + 0 - 3/4*r**h + 3/4*r**2.
-3*r**2*(r - 1)*(r + 1)/4
Let s(z) = -z**3 - 4*z**2 + 5*z + 2. Suppose 33*k = 34*k + 5. Let g be s(k). Factor 4/11*f + 0 - 6/11*f**g.
-2*f*(3*f - 2)/11
Let h(l) be the first derivative of 14*l**3/27 + 13*l**2/9 - 16*l/3 + 300. Factor h(o).
2*(o + 3)*(7*o - 8)/9
Let x = 236 - 111. Factor 8 + 7 - x*r**3 - 60*r + 144*r**2 - 7 + 6*r**2.
-(5*r - 2)**3
Let a(v) be the first derivative of -2*v**3/33 + 101*v**2/11 + 291. Factor a(r).
-2*r*(r - 101)/11
Let i = -168/11 - -347/22. Let j(z) be the third derivative of -3*z**2 - i*z**4 - 2*z**3 + 0 - 1/20*z**5 + 0*z. Find n, given that j(n) = 0.
-2
Let j(t) be the third derivative of -t**5/30 - 17*t**4/6 - 289*t**3/3 + 2*t**2. Suppose j(h) = 0. What is h?
-17
Factor 10/11 - 2/11*r**2 + 8/11*r.
-2*(r - 5)*(r + 1)/11
Let q(r) = -2*r**3 - r**2 - 3*r - 3. Let c be (-5 - 0)/(4/(-4)). Let y(x) = -3*x - c*x**3 + 0 - 2 - 2*x**3 + 6*x**3. Let u(g) = -2*q(g) + 3*y(g). Factor u(j).
j*(j - 1)*(j + 3)
Suppose s - 10 = 2*f + 19, 0 = 3*s - 4*f - 77. Suppose -17*b = -s*b. Find j, given that -5*j + j**4 + j + 2*j + b*j**4 - 3*j**2 = 0.
-1, 0, 2
Suppose -1206 - 36*m**5 - 432*m**2 + 1191 - 546*m**3 - 138*m - 173*m**4 - 100*m**4 = 0. What is m?
-5, -1, -1/3, -1/4
Let q = -5 + 0. Let b be (-1)/q - -3*12/90. Factor -3/5*k**2 - b*k + 3/5 + 3/5*k**3.
3*(k - 1)**2*(k + 1)/5
Let k(g) = 22*g**2 - 44*g + 136. Let s(z) = -17*z**2 + 43*z - 134. Let c(r) = 3*k(r) + 4*s(r). Suppose c(d) = 0. Calculate d.
4, 16
Let f = 31 + -27. Let x be (-4 - (-28)/f) + -1. What is v in 4*v**2 - 6*v - 2*v**4 + 4*v - 2*v**4 + x*v**5 = 0?
-1, 0, 1
Let i = 23 + -6. Factor -i + 12 + 10 + 5*c**3 - 5*c**2 - 5*c.
5*(c - 1)**2*(c + 1)
Let h(i) = -6*i**2 + 2*i - 4. Let k = 21 + -17. Let x(r) = 7*r**2 - r + 4. Let d(j) = k*x(j) + 5*h(j). Suppose d(u) = 0. Calculate u.
1, 2
Let u(p) be the first derivative of -1/4*p**4 - 7 + 1/2*p**2 + 0*p + 0*p**3. Suppose u(s) = 0. Calculate s.
-1, 0, 1
Solve 80/3*l**2 - 8/3*l**4 + 34/3*l**3 - 4 + 26/3*l = 0.
-1, 1/4, 6
Let q(k) be the second derivative of 3/4*k**3 + 46*k + 0 + 1/2*k**2 - 1/12*k**4 - 9/40*k**5. Determine u, given that q(u) = 0.
-1, -2/9, 1
Let a be (14/4)/(25/(-10) - -4). Factor a*u + 5/3*u**2 + 1/3*u**3 + 1.
(u + 1)**2*(u + 3)/3
Let q(f) = f + 1. Let t(i) = -i - 1. Suppose 6*m - 2 = 4*m. Let z(u) = -u**2 - 6*u - 5. Let v(y) = m*z(y) - 4*t(y). Let g(b) = 3*q(b) + v(b). Factor g(w).
-(w - 2)*(w + 1)
Let j(y) = 2*y**3 - 7*y**2 + 4*y - 14. Let n be j(4). Let o be 4/n*(-3)/(-4). Factor -2/3*i**2 + 0 - o*i**3 - 1/2*i.
-i*(i + 1)*(i + 3)/6
Suppose z - 27 = -25. Let h be (z/12)/((-21)/(-63)). Factor 0*x**2 - h*x**3 + 1/4*x**4 - 1/4 + 1/2*x.
(x - 1)**3*(x + 1)/4
Let j(b) = 27*b**2 + 161*b + 1114. Let n(r) = -5*r**2 - 32*r - 223. Let c(w) = 6*j(w) + 33*n(w). Factor c(m).
-3*(m + 15)**2
Let c(s) = -s**2 - 3*s - 3. Let p(w) = 2*w**2 + 8*w + 7. Let g(j) = -7*c(j) - 3*p(j). Determine k so that g(k) = 0.
0, 3
Let b(x) be the third derivative of 2*x**5/55 - x**4/4 - 3*x**3/11 - x**2 + 22. Find c, given that b(c) = 0.
-1/4, 3
Factor 0*p - 20/9*p**4 + 2/9*p**5 - 46/9*p**3 + 0 - 8/3*p**2.
2*p**2*(p - 12)*(p + 1)**2/9
Let c(v) = -318*v - 30. Let i be c(-3). Factor 1148*m**4 - i*m**4 + 100*m**2 + 263*m**3 + 49*m**5 + 4*m + 8*m.
m*(m + 1)*(m + 3)*(7*m + 2)**2
Let p be (1 + -3)*8/(-16). Let g be (-1 + 4)/(7*(0 + p)). Factor -9/7*o**2 - 9/7*o - 3/7 - g*o**3.
-3*(o + 1)**3/7
Let q(a) be the third derivative of 0*a - 1/40*a**6 + 0*a**3 + 0 - 1/4*a**4 - 3/20*a**5 - 20*a**2. Find r such that q(r) = 0.
-2, -1, 0
Let j(t) be the second derivative of -t**10/20160 + t**9/10080 + t**8/4480 - t**7/1680 - 7*t**4/6 - 3*t. Let a(m) be the third derivative of j(m). Factor a(v).
-3*v**2*(v - 1)**2*(v + 1)/2
Suppose -14*k - 175*k**3 + 165*k**3 + 34*k**2 - 2*k - 24 = 0. Calculate k.
-3/5, 2
Let h be (1 + (-595)/637)/(16/224). Let -6/13*i**2 - h + 22/13*i = 0. What is i?
2/3, 3
Suppose 2/3*f**2 - 218/9*f + 8 = 0. Calculate f.
1/3, 36
Let p(n) be the second derivative of -n**5/20 - n**4 + 9*n**3/2 - 13*n**2 - 18*n. Let g(l) be the first derivative of p(l). What is j in g(j) = 0?
-9, 1
Let n(r) = -2*r**2 - r + 1. Let h(a) = a**3 + a**2 + 34*a + 42. Let f(g) = h(g) - 6*n(g). Factor f(l).
(l + 2)**2*(l + 9)
Determine y so that 2/5*y**3 - 16/5*y**2 + 0 - 18/5*y = 0.
-1, 0, 9
Let -v**2 - 4 - 46*v + 3*v**2 + 44*v = 0. What is v?
-1, 2
Let c(m) be the first derivative of m**3/3 + 3*m**2/2 - 10*m - 126. Factor c(k).
(k - 2)*(k + 5)
Determine m, given that -10*m**4 - 16*m**3 + 8*m**5 - 13*m**5 + 11*m**3 = 0.
-1, 0
Let u(t) be the third derivative of -t**6/720 + t**5/20 - 2*t**4/3 + 32*t**3/9 - 2*t**2 - 17*t. Factor u(x).
-(x - 8)**2*(x - 2)/6
Suppose 5*l + 100 = 5*j + 20, -4*j - 2*l + 82 = 0. Suppose 0*m = -j*m. Factor m + 9/4*s + 3/4*s**2.
3*s*(s + 3)/4
Suppose 3*u + 21 = -0*q + 2*q, u = 5*q - 72. Factor q*v - 84*v**2 - 14*v - 10*v**3 - 124*v - 69*v - 64.
-2*(v + 4)**2*(5*v + 2)
Factor -1/6*n**3 - 2/3