**2*(s - 22)**2*(s + 1)/3
Find n such that -39/4*n**2 - 37/4*n - 3 - 1/4*n**4 - 15/4*n**3 = 0.
-12, -1
Determine r, given that 42716 + 2*r + r**2 - 42716 = 0.
-2, 0
Determine h, given that -1/9*h**2 + 10/9*h - 8/3 = 0.
4, 6
Let v be 40/45*9/2. Suppose -8 = -2*h - 4. Factor -2 - v*y**2 + 4 - h + 4*y.
-4*y*(y - 1)
Let v = 6471/1724 - 3/862. Factor -39/4*g**2 - 21/2*g**3 - v*g**4 - 3*g + 0.
-3*g*(g + 1)**2*(5*g + 4)/4
Let l(q) be the first derivative of 2*q**3/33 - 138*q**2/11 + 9522*q/11 + 223. Suppose l(k) = 0. Calculate k.
69
Let y = -107 - -63. Let g be (-11)/y - (-14)/40. Factor -4/5*n + 1/5*n**2 + g.
(n - 3)*(n - 1)/5
Let r(l) be the second derivative of -l**7/84 - l**6/60 + l**5/40 + l**4/24 + 115*l. What is j in r(j) = 0?
-1, 0, 1
Factor -24/5*u**2 + 0*u - 2/5*u**3 + 0.
-2*u**2*(u + 12)/5
Let d(j) = 2*j**2 - j + 4. Let l be d(0). Suppose -5 + 14 = 3*t - s, -3*t - l*s = -24. Factor 1/2*p**t - 1/2 + p**3 - p + 0*p**2.
(p - 1)*(p + 1)**3/2
Let w(g) be the second derivative of g**6/150 - 3*g**5/100 + 2*g**3/15 + 9*g. Determine s so that w(s) = 0.
-1, 0, 2
Let n be (8 - 0)/(-80)*10/(-4). Let m(o) be the second derivative of 1/30*o**3 + 0 + 3*o + 1/5*o**2 - n*o**4. Factor m(v).
-(3*v + 1)*(5*v - 2)/5
Let d be (-1)/7 - 53/(-273). Let c(j) be the first derivative of 5 + 0*j - d*j**3 + 2/13*j**2. Solve c(g) = 0 for g.
0, 2
Let r = 69 - 54. Let u be (1/r)/(26/65). Factor u*n**2 + 1/6*n + 0.
n*(n + 1)/6
Suppose -2*k - 4*z + 6 = 0, -5*k + 2*z = -0*k - 15. Factor -10*x + 9*x**3 + 5*x**4 - 5*x**2 + 10*x**3 - 8*x**3 - x**k.
5*x*(x - 1)*(x + 1)*(x + 2)
Let z(d) be the second derivative of 0 - 7*d + 1/24*d**4 - 1/4*d**3 + 0*d**2. Factor z(g).
g*(g - 3)/2
Let t(f) be the first derivative of -10*f**4 + 16*f**3 + 4*f - 12*f**2 - 4 + 12/5*f**5. Suppose t(r) = 0. Calculate r.
1/3, 1
Suppose 0 = 3*u + 2*u + 184 - 199. Factor 8/3 - 16/9*a - 2/9*a**2 + 2/9*a**u.
2*(a - 2)**2*(a + 3)/9
Let c be ((-6)/(-27) - (-52)/(-72))*-6. Let l(o) be the third derivative of 1/6*o**c + 8*o**2 + 0*o + 5/24*o**4 + 0 + 1/15*o**5. What is b in l(b) = 0?
-1, -1/4
Suppose 159 = 10*l - 231. Suppose 0 = 2*m + 33 - l. Solve -q**m + 0 - 1/2*q**4 + q + 1/2*q**2 = 0 for q.
-2, -1, 0, 1
Suppose 2*j - 18 = -5*p + 5*j, 0 = -5*p + 5*j + 20. Factor 13*l**2 + 6 + 15*l - p*l**2 + 3*l**3 + 2*l**2.
3*(l + 1)**2*(l + 2)
Determine r so that -32/15 - 2/15*r**4 + 2*r**3 - 2*r + 34/15*r**2 = 0.
-1, 1, 16
Suppose 0 = 2217*y - 2258*y + 82. Solve -12/5*f + 0 - 3/5*f**y = 0 for f.
-4, 0
Let v be 1*(1 - 12 - -13). Let q(r) be the second derivative of -2/45*r**6 + 0*r**v + 0 - 5/9*r**4 + 4/15*r**5 + 4/9*r**3 + 7*r. Let q(i) = 0. Calculate i.
0, 1, 2
Let v be 2*(-1 - 4/(-8)) + 3. What is x in 51*x**v - 24*x + 58*x**2 - 106*x**2 = 0?
0, 8
What is d in 30*d**2 - 6*d**2 + 44*d - 9*d**3 - 1549 + 1565 = 0?
-2/3, 4
Let s be -13 - -15 - 0/2. Let 41*m**2 + 8*m + 41*m**2 - 86*m**s - 4 = 0. What is m?
1
Suppose 2*l - 4 = 2*m, -4 = -3*m - 5*l + 6. Factor 4*d + 4388 - 2*d**2 - 4390 + m*d.
-2*(d - 1)**2
Let s(w) be the second derivative of w**4/6 + 66*w**3 + 9801*w**2 + 346*w. Determine j so that s(j) = 0.
-99
Let t(n) = -8*n**2 - 4*n + 6. Let j(p) = 12*p**2 + 10*p - 8. Let b(c) = 13*c**2 + 9*c - 9. Let a(h) = 3*b(h) - 2*j(h). Let g(r) = 6*a(r) + 11*t(r). Factor g(v).
2*v*(v - 1)
Let -18*x**3 + 0 - 9/2*x**2 - 21/2*x**4 + 3*x = 0. What is x?
-1, 0, 2/7
Let c = 81 + -328. Let r = c + 1239/5. Factor 2/5*y**2 + r*y + 0.
2*y*(y + 2)/5
Suppose 32 - 68*z**3 - 3*z**4 + 12*z - 18*z**2 + 80*z**3 - 35 = 0. Calculate z.
1
Let z(a) = a**2 - 4*a - 2. Let v be z(4). Let f = 4 - v. What is s in 3*s**4 - f*s**4 - s + 6*s**2 + 3*s**5 - 2*s - 3*s**4 = 0?
-1, 0, 1
Let l = 129 - 73. Determine v so that -6912 + 1728*v - l*v**2 - 105*v**2 - 3*v**3 + 17*v**2 + 7*v**3 = 0.
12
Let c(s) = -s + 23. Let r be c(11). Let k = r + -52/5. Factor 2/5*g**2 + 2/5*g**3 - k - 8/5*g.
2*(g - 2)*(g + 1)*(g + 2)/5
Let v(y) be the second derivative of -81*y**5/5 + 30*y**4 - 8*y**3 - 16*y**2 + 134*y. Suppose v(u) = 0. Calculate u.
-2/9, 2/3
Let r(l) be the second derivative of l**7/42 - 13*l**6/15 + 169*l**5/20 - 31*l. Determine n so that r(n) = 0.
0, 13
Let o = 4504/3745 + -2/749. Factor 0*z**2 - o*z + 4/5 + 2/5*z**3.
2*(z - 1)**2*(z + 2)/5
Let w = -1 - -1. Let i(n) = -4*n - 4. Let m be i(-1). Find d, given that w - d**2 - d + 3*d - 1 + m*d**2 = 0.
1
Let a be (1 + -5)/((-16)/20). Let 2*q - 7 - 3*q - a - q + 2*q**2 = 0. Calculate q.
-2, 3
Let p(v) be the first derivative of 3*v**4/22 + 50*v**3/33 - 84*v**2/11 + 8*v - 20. Let p(w) = 0. Calculate w.
-11, 2/3, 2
Let k(s) be the third derivative of -s**8/57120 - s**7/10710 + s**6/6120 + s**5/510 - s**4/4 + 8*s**2. Let m(q) be the second derivative of k(q). Factor m(t).
-2*(t - 1)*(t + 1)*(t + 2)/17
Let v be (-33)/44*(-26)/765. Let z(f) be the third derivative of 0 - 1/34*f**4 - v*f**5 + 0*f**3 + 0*f + 1/204*f**6 - 9*f**2. Suppose z(c) = 0. What is c?
-2/5, 0, 3
Solve o**5 - 59698*o**2 + 0*o**3 + 2*o**3 + 3*o**4 + 59698*o**2 = 0.
-2, -1, 0
Let p(f) be the second derivative of 3*f**5/140 - f**4/7 + 5*f**3/14 - 3*f**2/7 - 2*f - 9. Determine x so that p(x) = 0.
1, 2
Let a(v) = -v**2 - 11*v + 3. Let r be a(-8). Find t such that 0*t + 15*t**3 + 7*t + r*t**2 - t - 32*t**4 - 21*t**5 + 5*t**4 = 0.
-1, -2/7, 0, 1
Factor -29*r**3 + 5*r**3 - 136*r**2 - 20*r**3 - 3*r**4 - 96*r - r**4.
-4*r*(r + 1)*(r + 4)*(r + 6)
Let v(t) = -9*t**2 - 3*t - 1. Let f be v(-3). Let g = -4 - f. Factor -g*p**3 + 0*p**4 + 71*p**3 + p - 2*p**4 - 3*p + 2*p**2.
-2*p*(p - 1)**2*(p + 1)
Let q be (-104)/(-234)*(18/20)/(18/30). What is t in 2/3*t - q*t**2 + 4/3 = 0?
-1, 2
Factor -8/3 + 2/9*w**2 + 2/9*w.
2*(w - 3)*(w + 4)/9
Factor -127/4 + 1/4*u**2 + 63/2*u.
(u - 1)*(u + 127)/4
Suppose 0 = 58*o + 12*o - 350. Let p(b) be the first derivative of -5*b**4 - 6 + o*b**2 - 3*b**5 + 25/3*b**3 + 0*b. Solve p(j) = 0 for j.
-2, -1/3, 0, 1
Let t(a) = a**3 + 12*a**2 - 26*a + 28. Let j be t(-14). Let p be 6*(20/8)/5. Suppose 4/5*d**p + 0*d - 8/5*d**2 + j = 0. What is d?
0, 2
Let u(j) be the third derivative of j**7/105 + j**6/30 - 25*j**2. Let n = -6 - -10. Let q(b) = -2*b**4 - 5*b**3. Let m(g) = n*q(g) + 5*u(g). Factor m(r).
2*r**4
Let a(h) = h + 29. Let g be a(-24). Let r(i) be the second derivative of 0*i**3 + 0*i**2 - 1/42*i**7 + 3*i + 0 + 0*i**6 + 0*i**4 + 1/20*i**g. Factor r(w).
-w**3*(w - 1)*(w + 1)
Let o(s) be the third derivative of s**7/10080 - s**6/576 + s**5/120 - s**4/24 - 14*s**2. Let l(d) be the second derivative of o(d). Let l(p) = 0. Calculate p.
1, 4
Let k(m) be the third derivative of 1/60*m**6 - 17*m**2 - 1/12*m**4 - 1/15*m**5 + 2/3*m**3 + 0*m + 0. Find x such that k(x) = 0.
-1, 1, 2
Let h = -4 + 6. Let y be (15/65)/(20/130). Factor 1/2*r**h + 3/2*r - 1/2 - y*r**3.
-(r - 1)*(r + 1)*(3*r - 1)/2
Let u be 6/4*-2 + 7. Suppose -u*r = -2*m + 12, -3 + 13 = 2*m - 3*r. Solve 6*a - 27 + 2*a - 3*a**m + a + 9*a = 0 for a.
3
Let p(t) be the second derivative of -t**7/42 - 16*t**6/15 - 33*t**5/2 - 242*t**4/3 + 1331*t**3/6 + 18*t. What is a in p(a) = 0?
-11, 0, 1
Let w(r) be the second derivative of 1/10*r**6 + 10*r - 1/14*r**7 + 0*r**2 + 0*r**3 + 0 - 1/4*r**4 + 3/20*r**5. Determine p so that w(p) = 0.
-1, 0, 1
Let a(f) be the third derivative of -f**8/3528 - f**7/315 - f**6/84 - f**5/70 - 26*f**2. Let a(r) = 0. What is r?
-3, -1, 0
Factor 3/4*z**3 + 9/4*z**2 + 0 - 21*z.
3*z*(z - 4)*(z + 7)/4
Let x(i) be the second derivative of -1/80*i**5 - 48*i + 0 + 1/24*i**4 + 1/24*i**3 - 1/4*i**2. Solve x(q) = 0.
-1, 1, 2
Determine l so that -192/7*l**2 + 160/7*l + 88/7*l**3 - 2*l**4 - 32/7 = 0.
2/7, 2
Let u be (-56)/2*45/(-9). Factor -n**3 - 136 - n**3 + 6*n + u.
-2*(n - 2)*(n + 1)**2
Let q = -1104 - -1109. Factor 2/11*o**q - 6/11*o - 4/11*o**2 - 2/11 + 6/11*o**4 + 4/11*o**3.
2*(o - 1)*(o + 1)**4/11
Let p = 53383/10011 + 3/3337. Let -p*b + 8/3*b**2 + 20/3*b**3 + 2*b**4 + 0 = 0. What is b?
-2, 0, 2/3
Let y = -2638 - -26381/10. Factor -1/10*c**2 - y - 1/5*c.
-(c + 1)**2/10
Let o(k) = -2*k - 34. Let r be o(-20). Let p(v) be the second derivative of -1/3*v**2 + 2/9*v**3 - 1/18*v**4 - r*v + 0. Let p(l) = 0. What is l?
1
Let m = 9 - 6. Suppose 2*f**2 + 5 - 1 + 141*f + f**m + 0 - 148*f = 0. What is f?
-4, 1
Find m such that 6/7*m + 26/7*m**3 - 34/7*m**2 + 6/7*m**4 - 8/7*m**5 + 4/7 = 0.
