e (-258 - 9/(-1))/((-9)/12). Suppose -352*k + 240 = -c*k. Factor 1/3*u**2 + k - 4*u.
(u - 6)**2/3
Suppose -567/2 - 3/4*u**2 - 123/4*u = 0. What is u?
-27, -14
Let f(x) be the second derivative of -x**5/60 + 491*x**4/36 - 10004*x**3/3 - 10086*x**2 - 698*x + 1. Determine t so that f(t) = 0.
-1, 246
Let h(y) be the first derivative of -5*y**3/3 - 90*y**2 + 1760*y + 2335. What is j in h(j) = 0?
-44, 8
Let a(y) be the second derivative of 7 + 1/60*y**5 - 5*y + 1/16*y**4 + 27/2*y**2 + 0*y**3. Let t(u) be the first derivative of a(u). Factor t(o).
o*(2*o + 3)/2
Suppose 142 = 11*b - 2355. Factor 4*q**2 + 17*q - b*q - 14*q + 3136.
4*(q - 28)**2
Let w = 105 - 99. Determine r, given that -7615*r**3 - 36*r - 35*r**2 + w*r + 5*r**4 + 7615*r**3 = 0.
-2, -1, 0, 3
Let l(o) be the third derivative of 8*o**3 + 1/3*o**5 + o**2 - 63*o + 0 - 1/60*o**6 - 7/3*o**4. Find b, given that l(b) = 0.
2, 6
Let h(g) be the second derivative of -49*g**5/10 - 70*g**4 - 76*g**3 - 32*g**2 - 3*g + 82. Determine f so that h(f) = 0.
-8, -2/7
Let a(l) be the third derivative of l**8/2520 - l**7/1260 - l**6/270 + 40*l**3/3 - 64*l**2 + 2. Let f(u) be the first derivative of a(u). Factor f(v).
2*v**2*(v - 2)*(v + 1)/3
Let v be ((-6)/9)/(3 + (-188)/60). Suppose 5*b - 20 = -v*b. Determine p, given that -15 + 3*p**b - 6*p + 39 + 3*p**3 - 24 = 0.
-2, 0, 1
What is y in 9458*y + 41 - 9629*y + 11 + 3*y**2 - 226 = 0?
-1, 58
Let r(l) be the first derivative of 121*l**3/9 - 4774*l**2/3 + 188356*l/3 + 1281. Factor r(o).
(11*o - 434)**2/3
Let h(v) be the third derivative of 0 - 2/21*v**7 + 0*v**4 + 130*v**2 + 5/336*v**8 + 0*v + 5/24*v**6 - 1/6*v**5 + 0*v**3. Factor h(c).
5*c**2*(c - 2)*(c - 1)**2
Let h(i) be the first derivative of 2*i**5/15 + 110*i**4 + 219116*i**3/9 + 72380*i**2 + 216482*i/3 - 5921. Factor h(a).
2*(a + 1)**2*(a + 329)**2/3
Let f(w) be the second derivative of -86*w**7/49 + 8*w**6/7 + 15*w**5/4 - 20*w**4/7 - 3*w**3/14 + 6746*w. Suppose f(i) = 0. Calculate i.
-1, -3/86, 0, 1/2, 1
Let v(j) be the third derivative of 0 + 1/21*j**8 - 58/15*j**5 - 8/3*j**3 + 25/6*j**4 + 0*j + 61/30*j**6 - 8/15*j**7 + 81*j**2. Suppose v(q) = 0. Calculate q.
1/2, 1, 4
Let n(g) be the second derivative of -g**6/90 - 3*g**5/10 + 1283*g**4/36 + 682*g**3 - 232562*g**2/3 - 10*g - 49. Factor n(o).
-(o - 22)**2*(o + 31)**2/3
Let o(x) be the first derivative of -x**6/6 + 13*x**5 - 1555*x**4/6 - 1170*x**3 - 3645*x**2/2 + 88*x + 2. Let l(v) be the first derivative of o(v). Factor l(q).
-5*(q - 27)**2*(q + 1)**2
Let g = 24 - -27. Let r = g - 45. Find f, given that f**5 + 0*f**5 - 4*f**5 + 6*f**2 - 3*f**3 - r*f**4 + 6*f**3 = 0.
-2, -1, 0, 1
Let s(n) = -n + 2. Let k be s(-3). Let u(j) = 4*j + 5. Let b be u(k). Factor 5 + 19*d - 13 + 87*d**2 - 3*d**2 + b*d.
4*(3*d + 2)*(7*d - 1)
Let p = 8 - 6. Let x be (4206/39256)/(2/84). Factor x*y - 3 - 3/2*y**p.
-3*(y - 2)*(y - 1)/2
Let x(r) be the third derivative of -r**6/60 - 163*r**5/30 + 124*r**4/3 - 332*r**3/3 + 6617*r**2. Find c such that x(c) = 0.
-166, 1, 2
Let w(y) be the first derivative of -y**4/6 - 20*y**3/3 + 44*y**2 - 48*y - 244. Let f(s) be the first derivative of w(s). Factor f(u).
-2*(u - 2)*(u + 22)
Let k(r) = r**3 + 11*r**2 + 6*r - 108. Let f be k(-9). Let c(o) be the second derivative of -35/6*o**3 + 5/4*o**4 + 5*o**2 + f - 5*o. Factor c(m).
5*(m - 2)*(3*m - 1)
Let t(i) be the second derivative of i - 1/3*i**3 + 32 + 5/24*i**4 + 1/10*i**5 - 9/8*i**2 - 1/120*i**6. Solve t(w) = 0.
-1, 1, 9
Let y(w) be the third derivative of 2/105*w**7 + 5 - 16*w**3 + 5*w**2 + 7/3*w**4 + 23/15*w**5 - 7/15*w**6 + 0*w. Solve y(t) = 0 for t.
-1, 1, 2, 12
Suppose 3*i + 55 = 4*g, -21 = -4*g - 5*i - 6. What is o in g*o**2 - 86 - 5*o - 92 + 178 = 0?
0, 1/2
Let c be 0/4 - 0 - 4/(-1). Suppose -1 = a - 5. Suppose 7*m - 55*m**a + 107*m**4 - 9*m**2 - 53*m**c - 2 + 5*m**3 = 0. What is m?
1, 2
Let z(x) = -15*x**3 - x**2. Let v be z(1). Let q = 51 + v. What is d in -q*d - 12*d**5 + 35*d**2 + 3*d**5 + 55*d**3 - 10 - 11*d**5 - 25*d**4 = 0?
-2, -1, -1/4, 1
Factor -810*k - 2257*k**4 + 1117*k**4 + 1135*k**4 + 765*k**2 + 50*k**3.
-5*k*(k - 18)*(k - 1)*(k + 9)
Let j(z) be the first derivative of -z**4/8 + 37*z**3/12 - 155*z**2/8 + 39*z + 2458. Find p such that j(p) = 0.
3/2, 4, 13
Let v = 149497/7 + -21299. Let h = v - 1992/35. Factor 0*p + 0 + 4/5*p**3 - 4/5*p**5 + h*p**2 - 4/5*p**4.
-4*p**2*(p - 1)*(p + 1)**2/5
Let t(b) be the second derivative of -b**7/105 + 2*b**6/75 + 13*b**5/25 - 18*b**4/5 + 9*b**3 - 54*b**2/5 - 1010*b. Determine p, given that t(p) = 0.
-6, 1, 3
Factor -262/9*t - 1/9 + 263/9*t**2.
(t - 1)*(263*t + 1)/9
Suppose 131*l - 132*l - 3 = 0. Let g(r) = r**4 + r**3 - r. Let z(p) = -p**5 - 6*p**4 - 8*p**3 - 2*p**2 + 9*p. Let n(d) = l*z(d) - 24*g(d). Solve n(j) = 0.
-1, 0, 1
Let x be (-96)/(-1848)*119 - 11/(121/2). Let 9/2*p**2 - x - 15/2*p**3 + 15/2*p + 3/2*p**4 = 0. Calculate p.
-1, 1, 4
Let b(n) be the third derivative of -n**5/12 + 85*n**4/24 + 95*n**3/3 + 27*n**2 + 6. Determine o so that b(o) = 0.
-2, 19
Factor 1/3*b**5 - 8 - 49/3*b + 26/3*b**4 + 16*b**3 - 2/3*b**2.
(b - 1)*(b + 1)**3*(b + 24)/3
Let s = 1145 + -1125. Let k(i) be the second derivative of 0 + 1/18*i**4 + s*i + 0*i**2 + 1/120*i**5 + 1/12*i**3. What is h in k(h) = 0?
-3, -1, 0
Let j be (-1)/((-154)/8 - -19). What is b in -2/11*b**5 + 24/11 - 14/11*b**j - 10/11*b**2 - 30/11*b**3 + 32/11*b = 0?
-3, -2, -1, 1
Let n(s) = -11*s**3 + 63*s**2 + 149*s - 51. Let c(i) = -64*i**2 - 34 - 148*i + 44 + 42 + 10*i**3. Let q(k) = 3*c(k) + 4*n(k). Find t, given that q(t) = 0.
-2, 2/7, 6
Let c(i) be the first derivative of 3*i**5/100 - i**4/20 + 68*i - 22. Let h(l) be the first derivative of c(l). Factor h(r).
3*r**2*(r - 1)/5
Let a(g) be the first derivative of g**4/12 + 22*g**3/9 + 7*g**2/2 + 924. What is u in a(u) = 0?
-21, -1, 0
Let r be ((-10)/4)/(-5 + 27/6). Suppose 0 = w + 3 - r. Factor 4*a + 0*a - 3 - 43*a**w + 41*a**2 + 1.
-2*(a - 1)**2
Factor -3/2*j**2 + 117/8*j + 15/4.
-3*(j - 10)*(4*j + 1)/8
Let t(c) be the second derivative of c**7/210 - c**6/90 - c**5/6 - c**4/2 - 2*c**3/3 + 5*c**2/2 - 178*c. Let i(b) be the second derivative of t(b). Factor i(f).
4*(f - 3)*(f + 1)**2
Let u(t) be the second derivative of 91*t**6/50 - 627*t**5/50 + 56*t**4/5 - 16*t**3/5 + 706*t - 1. Let u(h) = 0. Calculate h.
0, 2/7, 4/13, 4
Let o = -1021/14 + 514/7. Factor -1/2 - o*g**3 + 1/2*g**2 + 1/2*g.
-(g - 1)**2*(g + 1)/2
Let u = -2 - -5. Let w = -1707477/2 - -853739. Solve 20*y + 5*y**u - 33/2*y**2 - w*y**4 - 8 = 0.
1, 4
Let k(a) = -a**3 - 42*a**2 - 3*a - 122. Let b be k(-42). Factor -2*o**b + 92*o**3 - 28*o**2 - 138*o**3 - 2*o**4 + 78*o**3.
-4*o**2*(o - 7)*(o - 1)
Factor 12 - 354*n**3 - 28*n - 348*n**3 + 700*n**3 - n**4 + 19*n**2.
-(n - 2)*(n - 1)**2*(n + 6)
Let u(k) be the first derivative of -k**3/4 - 177*k**2/8 + 45*k + 570. Determine s, given that u(s) = 0.
-60, 1
Let r = 962869/3 + -320953. Determine j, given that -r*j + 0 + 5/3*j**3 - 5/3*j**2 = 0.
-1, 0, 2
Let c(x) be the second derivative of x**4/4 - 29*x**3 + 171*x**2/2 - 1175*x. Solve c(g) = 0 for g.
1, 57
Factor 8*d**2 + 46/5*d - 84/5 - 2/5*d**3.
-2*(d - 21)*(d - 1)*(d + 2)/5
Factor -452*p**4 + 217*p**4 - 51*p**2 + 5*p**5 - 194*p**2 - 485*p**3.
5*p**2*(p - 49)*(p + 1)**2
Suppose 4*w + 1564 = 4*a, 20*w + a + 1589 = 16*w. Let h = w + 396. Factor -2/3*u**4 + 0 + 0*u**2 - 2/9*u**5 + h*u - 4/9*u**3.
-2*u**3*(u + 1)*(u + 2)/9
Let v(u) be the first derivative of u**4/16 - 7*u**3/4 - 23*u**2/4 - 2554. Solve v(d) = 0 for d.
-2, 0, 23
Let t(h) be the third derivative of -1/1008*h**8 + 0*h**3 - 240*h**2 - 61/90*h**6 + 2/45*h**7 - 8*h**4 + 0*h + 0 + 56/15*h**5. Solve t(g) = 0.
0, 2, 12
Solve 294/19*x - 1372/19 + 0*x**2 - 2/19*x**3 = 0.
-14, 7
Let p(d) be the third derivative of d**6/120 + 11*d**5/60 + 5*d**4/12 + 4*d**2. Let q be p(-10). Determine s so that 2/13 - 2/13*s**2 + q*s = 0.
-1, 1
Let t be (-3)/(-12) + 15/4. Let g be ((-1944)/945)/(11/7 - 2). Factor 6/5 - 4*v - 12/5*v**3 + g*v**2 + 2/5*v**t.
2*(v - 3)*(v - 1)**3/5
Let p(g) be the first derivative of 7/4*g**2 + 1/12*g**3 - 15/4*g + 109. Factor p(c).
(c - 1)*(c + 15)/4
Let s be (9/15)/(3/20). Find l, given that -40*l + 40*l**3 + 42*l**s - 16*l**2 - 22*l**4 - 12 + 8*l**4 = 0.
-1, -3/7, 1
Factor -69*q + 420*q + 11509 + 3*q**2 - 10819.
3*(q +