t l be 160/(-140)*(-7)/2. Let -27/4*u**l - 39/4*u**3 + 27/4*u**2 + 3/2*u + 33/4*u**5 + 0 = 0. Calculate u.
-1, -2/11, 0, 1
Suppose -2*y + 13 = -3*p + 8, 4*y + 4*p - 20 = 0. Suppose -4*j + 6*j**2 - 3*j**3 + 1/2*j**y + 0 = 0. Calculate j.
0, 2
Suppose j + k = -1, -3*j + 3*k - 6 = -9. Factor 0*w + 2/7*w**3 + j + 2/7*w**2.
2*w**2*(w + 1)/7
Let u(p) = -38*p**4 - 112*p**3 - 104*p**2 + 6*p. Let i(x) = x**4 + x**2 - x. Let k(o) = -12*i(o) - 2*u(o). Suppose k(w) = 0. What is w?
-7/4, 0
Let r = 80 - 94. Let s = 16 + r. What is a in a**s + 0 + 2/3*a + 1/3*a**3 = 0?
-2, -1, 0
Let v = -13361/3 + 4455. Let u(j) = -2*j + 2. Let z be u(1). Factor z + 0*w - v*w**2.
-4*w**2/3
Let u(m) = -10*m**2 - 300*m + 10380. Let y(q) = -q**2 - q + 1. Let c(k) = u(k) - 12*y(k). Suppose c(z) = 0. Calculate z.
72
Let p(c) be the second derivative of c**7/336 + c**6/240 - c**5/160 - c**4/96 + 11*c + 3. Factor p(l).
l**2*(l - 1)*(l + 1)**2/8
Suppose 3*n = -2*q - 3*q + 11, -2*n + 1 = -3*q. Let 3*t**2 - 3 + 3*t**n - t**3 - 3*t**2 - 1 = 0. What is t?
-1, 2
Suppose 80*a - 128 - 32 = 0. Let -4/13 + 2/13*n**a + 2/13*n = 0. Calculate n.
-2, 1
Let n = 108301/3 - 36099. Suppose -n*l**2 + 4/3*l**4 - 1/3*l + 1/3*l**3 + 0 = 0. What is l?
-1, -1/4, 0, 1
Factor 18*v - 18*v**2 + 10*v**2 + 5*v**2 - 3*v - 18.
-3*(v - 3)*(v - 2)
Let h(d) = d**2 - 17*d + 74. Let x be h(9). Factor -b + 3*b**x + 0 - 13/4*b**3 + 3/2*b**4 - 1/4*b**5.
-b*(b - 2)**2*(b - 1)**2/4
Suppose -244*k**2 - 332/3*k - 160/3*k**3 + 64/3*k**4 - 40/3 = 0. Calculate k.
-2, -1/4, 5
Factor -6*s**2 - 25*s - 28*s**2 - 60 + 0*s + s + 37*s**2.
3*(s - 10)*(s + 2)
Let a(b) = -6*b**3 - 11*b**2 + 213*b - 383. Let j(s) = -3*s**3 - 6*s**2 + 108*s - 192. Let q(p) = 3*a(p) - 5*j(p). Determine f, given that q(f) = 0.
-7, 3
Let o(j) be the first derivative of j**4/22 + 20*j**3/33 - j**2/11 - 20*j/11 - 119. What is h in o(h) = 0?
-10, -1, 1
Let n(r) = -8*r**3 + 5*r**2 - 6*r - 40. Let q be n(-4). Factor -36*p**2 - 3072 - 3/4*p**3 - q*p.
-3*(p + 16)**3/4
Let h(k) be the first derivative of k**4/8 + 43*k**3 + 5547*k**2 + 318028*k - 300. Find t such that h(t) = 0.
-86
Let i(c) be the first derivative of -5*c**3/18 - 5*c**2/12 - 117. Find q such that i(q) = 0.
-1, 0
Let i(z) = 5*z**4 + 25*z**3 + 33*z**2 + 15*z + 2. Let h(l) = 110*l**4 + 550*l**3 + 725*l**2 + 330*l + 45. Let y(k) = 2*h(k) - 45*i(k). Factor y(r).
-5*r*(r + 1)**2*(r + 3)
Let i(a) be the second derivative of a**6/240 + a**5/40 + a**4/16 + a**3/12 - 2*a**2 - 13*a. Let x(h) be the first derivative of i(h). Factor x(m).
(m + 1)**3/2
Let l be 2/17 + -6*(-2)/(-102). Let f(k) be the third derivative of 0 + 1/180*k**5 - 1/72*k**4 - 4*k**2 + l*k + 0*k**3. Find h, given that f(h) = 0.
0, 1
Let m be ((-12)/(-8))/(2*(8 + 1)). Let f(l) be the third derivative of -7*l**2 + 0*l - 1/40*l**6 + 2/105*l**7 - m*l**5 + 1/6*l**3 + 0 + 1/8*l**4. Factor f(i).
(i - 1)**2*(i + 1)*(4*i + 1)
Let u(d) = -d**4 + d**2. Let w(k) = -39*k**4 - 60*k**3 + 184*k**2 - 100*k + 15. Let c(s) = 6*u(s) + w(s). Solve c(y) = 0 for y.
-3, 1/3, 1
Let y(q) be the first derivative of 32/75*q**5 - 12/5*q**2 + 194/45*q**3 + 60 - 12/5*q**4 + 8/15*q. Factor y(t).
2*(t - 2)**2*(4*t - 1)**2/15
Let t(o) be the third derivative of -3*o**8/112 - o**7/14 + 19*o**6/60 + o**5/30 - 13*o**4/24 - o**3/2 + 197*o**2. Suppose t(r) = 0. What is r?
-3, -1/3, 1
Let o = -33 - 16. Let r = o - -51. Suppose 0 + 2/3*j - 2/3*j**4 + 2/3*j**r - 2/3*j**3 = 0. What is j?
-1, 0, 1
Let l(t) = t**2 + 14*t + 2. Let c be 4/((40/28)/(-5)). Let h be l(c). Factor 4*m + 3*m**5 - m**5 + 4*m**5 - 8*m**3 - h*m**5.
4*m*(m - 1)**2*(m + 1)**2
Let z(b) be the third derivative of -b**5/48 - 45*b**4/32 - 125*b**3/12 + 10*b**2 - 3. Factor z(w).
-5*(w + 2)*(w + 25)/4
Suppose 0 = -3*u + 17 + 1. Let n be u/(-8)*-1*2/3. Factor 0 - 1/4*k - 1/4*k**3 - n*k**2.
-k*(k + 1)**2/4
Let m(i) be the first derivative of i**5/20 + 5*i**4/4 + 59*i**3/6 + 45*i**2/2 + 81*i/4 + 47. Suppose m(t) = 0. Calculate t.
-9, -1
Suppose 7*q - 295 = -4*t + 2*q, -356 = -5*t - 2*q. What is x in 125 - 91 + 211 + 5*x**2 - t*x = 0?
7
Let j = -4482823/7098 + -155/1014. Let r = 633 + j. Factor -12/7 + 3/7*w**2 + r*w.
3*(w - 1)*(w + 4)/7
Let x(p) be the third derivative of p**7/1680 + p**6/720 - p**5/240 - p**4/48 + 11*p**3/3 - 15*p**2. Let n(h) be the first derivative of x(h). Factor n(w).
(w - 1)*(w + 1)**2/2
Let t be (895/4)/(-5) - (-3)/(-12). Let x be 3/2 - (3 + t/12). Factor -9/4*n**3 + x*n - 3/4 + 3/4*n**2.
-3*(n - 1)*(n + 1)*(3*n - 1)/4
Factor 2*b**2 - 2*b**4 + b**5 + 0*b**4 + 6*b**3 + b**5 - 8*b**3.
2*b**2*(b - 1)**2*(b + 1)
Suppose 2*i - 5*k = -16 - 1, 4*i + 5*k - 11 = 0. Let f be i*1/((-3)/27). Factor -f*d + 4 + 5 + 15*d + d**2.
(d + 3)**2
Let m(n) = -n**3 - 10*n**2 + 4*n + 28. Let x be m(-10). Let q be (-8)/3*x/8 + 1. Factor -16/3*u**3 + 0*u + 6*u**q + 8/3*u**2 - 2*u**4 + 0.
2*u**2*(u + 1)*(3*u - 2)**2/3
Let y(j) be the first derivative of -j**3/3 + 9*j**2/2 + 13*j + 7. Let v be y(10). Factor w**3 - 73*w**5 + 2*w**v + 40*w**5 + 30*w**5.
-3*w**3*(w - 1)*(w + 1)
Let q(r) be the third derivative of 0*r**5 + 0*r**3 + 1/12*r**6 - 16*r**2 + 0 + 0*r - 1/105*r**7 + 0*r**4. Factor q(n).
-2*n**3*(n - 5)
Let k = -17 - -13. Let u be (-204)/(-72) - 2/k. Factor -2*n - u*n**3 + 1/3 + 4*n**2 + n**4.
(n - 1)**3*(3*n - 1)/3
Let v(f) = 2*f - 3. Let j(h) = 6*h - 10. Let p(s) = -4*j(s) + 11*v(s). Let i be p(2). Find a such that 0 + 2/7*a - 4/7*a**2 + 2/7*a**i = 0.
0, 1
Suppose 4*w - 4 = -c + 3*c, c = -5*w + 5. Let t be (-1 - (0 + c))*-2. Factor -3*h**2 - t*h - 6 + 2*h - 2*h - 7*h.
-3*(h + 1)*(h + 2)
Let u(r) be the first derivative of 7*r**6 + 116*r**5/5 - 219*r**4/14 - 188*r**3/7 + 172*r**2/7 - 48*r/7 - 477. Suppose u(y) = 0. What is y?
-3, -1, 2/7, 2/3
Let i be -7 - -3 - -1 - -18. Determine q so that 38 + i*q**2 + 54 - 112 + 5*q**3 = 0.
-2, 1
Factor 605 - 6013 - 112*g**2 + 967*g + 678*g - 243*g + 366*g + 2*g**3.
2*(g - 26)**2*(g - 4)
Suppose 21*a - 10*a**3 + 26*a**2 - 55*a + 20*a - 2*a**4 = 0. What is a?
-7, 0, 1
Solve 2/11*c**3 - 2/11*c**2 - 16/11*c + 24/11 = 0 for c.
-3, 2
Let k be 40/15*(-9)/(-6). Factor 3*c**2 + 18*c - 5*c**k - 10*c**3 - 12*c + 20*c**4 - 14*c**3.
3*c*(c - 1)**2*(5*c + 2)
Let n = -145 + 167. Suppose -5*j - 2 + n = 0. Solve -3/2*w - 3*w**2 + 3/2*w**j + 3*w**3 - 3/2*w**5 + 3/2 = 0 for w.
-1, 1
Let d = -8 + 11. Suppose u + 2*a = 2*u, -d*u - a = 0. Suppose -3/4*h**4 + u + 3/4*h**2 + 0*h + 0*h**3 = 0. Calculate h.
-1, 0, 1
Let f(s) be the second derivative of -5*s + 5 + 1/36*s**4 - 1/3*s**3 + 3/2*s**2. Solve f(k) = 0 for k.
3
Let i(y) be the first derivative of y**4/24 - y**3/4 + y**2/2 - 11*y - 14. Let h(d) be the first derivative of i(d). Find s, given that h(s) = 0.
1, 2
Let r(x) be the third derivative of x**5/450 + x**4/60 - 4*x**3/45 - 321*x**2. Factor r(q).
2*(q - 1)*(q + 4)/15
Let m(w) be the third derivative of -2*w**7/21 + 11*w**6/30 - 7*w**5/15 + w**4/6 + 23*w**2. What is h in m(h) = 0?
0, 1/5, 1
Let l(r) = -r**3 + 4*r**2 + 381*r - 2214. Let o be l(6). Factor -8/7*w - 4/7*w**3 + 12/7*w**2 + o.
-4*w*(w - 2)*(w - 1)/7
Suppose -70*v = -65*v - 25. Suppose -4*w - 14*o = -9*o - 7, v = 2*w + o. Find p such that -2/7*p**w + 0*p**2 + 0 + 8/7*p = 0.
-2, 0, 2
Let h(m) be the third derivative of m**6/600 - 7*m**5/150 + 17*m**4/40 - 9*m**3/5 - 88*m**2. Factor h(o).
(o - 9)*(o - 3)*(o - 2)/5
Let q(h) = -h**3 - 60*h**2 + 133*h - 108. Let u(y) = 10*y**3 + 540*y**2 - 1195*y + 975. Let c(z) = -55*q(z) - 6*u(z). Suppose c(d) = 0. What is d?
1, 2, 9
Factor -16*n**2 + 6*n**4 - 144*n + 66*n - 2*n**3 + 0*n**2 + 70*n.
2*n*(n - 2)*(n + 1)*(3*n + 2)
Let y be -3 + -20 - (1 - -2). Let x = y - -26. Let -1/2*t**4 + 0*t**2 + 0*t**3 + x*t + 0 = 0. What is t?
0
Let h = 1310 + -5239/4. Let m be 3 + 0 + 2 - 3. Factor h*x**4 - 1/2*x**m + 0*x**3 + 1/4 + 0*x.
(x - 1)**2*(x + 1)**2/4
Let y(n) = -n**3 + 17*n**2 + 18*n + 25. Let u be y(18). Suppose -4*d + 5 = u, -2*d + 2 = 4*j. Factor 0 + 1/2*q - 1/4*q**2 - 1/4*q**j.
-q*(q - 1)*(q + 2)/4
Let j(t) be the third derivative of -5/24*t**4 - 18*t**2 + 1/120*t**6 + 0*t - 1/3*t**3 + 0 - 1/20*t**5 + 1/210*t**7. Let j(u) = 0. What is u?
-1, 2
Let g(r) be the second derivative of r**6/6 + 5*r**5/4 - 35*r**4/4 - 425*r**3/6 + 250*r**2 + 931*r. What is q in g(q) = 0?
-5, 1, 4
Let g(c) be the third derivative 