t m be -48 + 22 + (-6080)/(-200). Factor 4*b**2 - m*b**3 + 8/5*b**4 - 6/5*b + 0.
2*b*(b - 1)**2*(4*b - 3)/5
Let v(a) = -12*a + 628. Let t be v(51). Let l be (t/(-80))/((-2)/10) + -1. Factor 0 - 10/11*i**2 + 2/11*i**3 + l*i.
2*i**2*(i - 5)/11
Let o be 34 - (33 + -2) - (-28)/6. Let -o*u**2 + 0 - u**3 - 14/3*u = 0. What is u?
-7, -2/3, 0
Let s(c) be the second derivative of -c**5/10 + 23*c**4/3 + 196*c**3/3 + 200*c**2 + 564*c. Factor s(f).
-2*(f - 50)*(f + 2)**2
Let m(a) be the second derivative of a**4/4 - 2*a**3 - 144*a**2 + 106*a. Factor m(t).
3*(t - 12)*(t + 8)
Let k(m) be the second derivative of -107*m**4/12 - m**3/2 - 124*m - 20. Factor k(s).
-s*(107*s + 3)
Suppose -39*l + 40*l = 3*r + 8, -3*r + 2 = 4*l. Let b(g) be the first derivative of 5/3*g**3 - 31 + 10*g**l + 0*g. Solve b(i) = 0 for i.
-4, 0
Let i(t) be the third derivative of -t**6/600 - 223*t**5/300 - 308*t**4/3 + 6272*t**3/15 + 2*t**2 - 271. Factor i(a).
-(a - 1)*(a + 112)**2/5
Let t = 879 + -7907/9. Let l(s) be the third derivative of -15*s**2 + 0 - 1/30*s**5 - t*s**3 - 1/360*s**6 + 0*s - 1/6*s**4. Factor l(k).
-(k + 2)**3/3
Let b be 11/(-2) - -4 - 45/2. Let d be 1/(5/(45/b) + 3). Factor -d*g**2 + 6*g**3 - g**4 - 2*g**4 + 285 - 285.
-3*g**2*(g - 1)**2
Let v(o) be the second derivative of -o**6/360 + o**5/6 - 19*o**4/24 + 21*o**3/2 - o + 71. Let p(l) be the second derivative of v(l). Let p(c) = 0. What is c?
1, 19
Find w such that 1077*w**2 - 2148*w**2 + 1070*w**2 - 1053 + 13*w - 79*w = 0.
-39, -27
Let u(p) be the second derivative of -p**6/240 - p**5/6 - 3*p**4/4 + 65*p**2/2 - 129*p. Let c(d) be the first derivative of u(d). Find z such that c(z) = 0.
-18, -2, 0
Find c, given that 2/5*c**3 + 64/5*c**2 - 1716/5 + 362/5*c = 0.
-22, -13, 3
Let p(r) = -10*r**3 - 2680*r**2 - 35170*r + 81070. Let g(i) = -i**3 - 298*i**2 - 3908*i + 9008. Let q(w) = 35*g(w) - 4*p(w). Factor q(o).
5*(o - 2)*(o + 30)**2
Let a(p) = -60*p + 4. Let j(i) be the second derivative of i**4/12 + 20*i**3 - 5*i**2 - 61*i. Let c(y) = -5*a(y) - 2*j(y). Solve c(m) = 0.
0, 30
Suppose 3*u = -d, 0 = -5*d + 35*u - 40*u + 10. Let z(x) be the second derivative of 0 + 11/24*x**4 + 5/3*x**d - x**2 + 15*x. Factor z(a).
(a + 2)*(11*a - 2)/2
Let b = 1871 + -16819/9. Let a = 886984 - 886981. Let 50/9*q**2 + 2/9*q**4 + 0*q + b*q**a + 0 = 0. Calculate q.
-5, 0
Suppose 8/3*r**3 + 0 + 13/3*r - 41/6*r**2 - 1/6*r**4 = 0. What is r?
0, 1, 2, 13
Let k(q) be the third derivative of -1/10*q**5 + 1/6*q**4 + 1/3*q**3 - 2*q + 0 + 24*q**2. Factor k(u).
-2*(u - 1)*(3*u + 1)
Let v be 0/(-18 - (7 + -26)). Let n(a) be the first derivative of 11 + 0*a + 0*a**2 + 6*a**5 + v*a**3 + 5/4*a**4. Factor n(c).
5*c**3*(6*c + 1)
Let 6/5 + 1/5*b**3 - 13/5*b + 7/5*b**2 - 1/5*b**4 = 0. Calculate b.
-3, 1, 2
Find g such that -200/11*g + 2/11*g**2 - 202/11 = 0.
-1, 101
Let x be (11 + -15)*(-1 - 1/(-2)). Let 136*c + 9*c - 18134*c**2 + 611*c - 12 + 6227*c**x = 0. Calculate c.
2/63
Let c be -5 + 12/90 + 85/(-10)*8/(-12). Determine n, given that c*n**2 + 36/5*n - 8 = 0.
-10, 1
Let p(h) be the third derivative of h**8/2184 + 5*h**7/91 + 1659*h**2. Suppose p(f) = 0. Calculate f.
-75, 0
Let -2/3*v**4 + 80*v - 158/3*v**2 + 0 + 32/3*v**3 = 0. Calculate v.
0, 3, 5, 8
Let v = 974 + -970. Let n(d) = 3*d**2 + 87*d + 88. Let m(q) = -4*q**2 - 89*q - 90. Let z(l) = v*m(l) + 5*n(l). Suppose z(k) = 0. Calculate k.
-1, 80
Let f(x) = -410*x**2 + 225*x - 560. Let g(o) = -49*o**2 + 28*o - 70. Let p(b) = -3*f(b) + 25*g(b). Factor p(q).
5*(q - 2)*(q + 7)
Let u(s) = s**3 + 12*s**2 + 4*s - 75. Let l be u(-11). Find p such that -54 - 2*p**2 + 215*p + p**2 - 164*p + 4*p**l = 0.
-18, 1
Let v(m) = -3*m**2 + 55*m + 40. Let i be v(19). Suppose 17*j = -i*j - 7*j. Let 1/3*a**2 - 1/6*a**3 + j - 1/6*a**4 + 0*a = 0. Calculate a.
-2, 0, 1
Factor t**3 - 2419*t - 3*t**2 + 8*t**2 + 2403*t - 80.
(t - 4)*(t + 4)*(t + 5)
Let n(k) = -39*k**2 - 33*k + 504. Let a(i) = -351*i**2 - 325*i + 4536. Let f(u) = -3*a(u) + 28*n(u). Solve f(b) = 0 for b.
-3, 56/13
Let y = -343/204 + 137/68. What is c in y*c**4 - 38/3*c + 4*c**3 - c**2 - 8 = 0?
-12, -1, 2
Let n(r) be the second derivative of -r**6/120 + 53*r**5/20 - 2809*r**4/8 - 49*r**3/2 - r + 1. Let a(g) be the second derivative of n(g). Factor a(s).
-3*(s - 53)**2
Suppose 4*j - 15 = r, -5*r - 3*j - 235 = -45. Let k = r - -248/7. Factor 0 + 0*s - 3/7*s**5 + k*s**4 + 3/7*s**3 - 3/7*s**2.
-3*s**2*(s - 1)**2*(s + 1)/7
Suppose 8197*v + 220 = 8208*v. Let w(b) be the first derivative of -1/2*b + 1/6*b**3 - 1/8*b**2 + v + 1/16*b**4. Suppose w(f) = 0. What is f?
-2, -1, 1
Let q(i) be the first derivative of -28*i**5/65 + 11*i**4/26 + 94*i**3/39 - 56*i**2/13 + 24*i/13 - 968. Suppose q(y) = 0. Calculate y.
-2, 2/7, 1, 3/2
Suppose -2/13*t**2 + 62/13*t + 0 = 0. Calculate t.
0, 31
Suppose -14*q = 9 + 5. Let c be (1*q)/((-81)/6 + 11). Determine o so that -12/5*o - 1/5*o**5 + 8/5 + 7/5*o**3 + 0*o**4 - c*o**2 = 0.
-2, 1, 2
Let w(l) be the third derivative of l**5/100 - 29*l**4/40 - 17*l**3 + 2254*l**2. Suppose w(x) = 0. What is x?
-5, 34
Let k(p) be the first derivative of p**5/80 - p**4/16 - 5*p**3/12 - 60*p + 79. Let n(d) be the first derivative of k(d). Factor n(b).
b*(b - 5)*(b + 2)/4
Let x(y) = -y**2 + 444*y. Let u(p) = -3*p**2 + 669*p. Let k(d) = 5*u(d) - 8*x(d). Suppose k(s) = 0. Calculate s.
-207/7, 0
Let k be (-8)/24*-21 + (602/28 - 15). Solve 0 - 3/2*h**4 + 21/2*h + k*h**3 - 45/2*h**2 = 0 for h.
0, 1, 7
Let z(n) be the first derivative of 0*n + 34 - 4/9*n**3 + 8*n**2. Factor z(f).
-4*f*(f - 12)/3
Let n be (2 + 23)/(-4 + (7 - 2)). Suppose -5*g = f - 17, 5*g - 3*f - n = g. Factor 324 + g*j**2 + 135*j - 212*j + 149*j.
4*(j + 9)**2
Let g(l) be the second derivative of -l**4/54 + 236*l**3/27 - 235*l**2/9 + 10*l - 3. Factor g(n).
-2*(n - 235)*(n - 1)/9
Solve 636/7 - 162/7*u**2 - 473/7*u - 1/7*u**3 = 0.
-159, -4, 1
Factor 143*u - 138 - 122 - 747*u - 11*u**2 + 308*u.
-(u + 26)*(11*u + 10)
Let n(f) = -7*f**2 + 70*f. Let p be n(10). Let k(r) be the first derivative of p*r - 3 + 0*r**2 - 3/10*r**4 + 6/25*r**5 + 0*r**3. Suppose k(h) = 0. What is h?
0, 1
Let f(o) be the first derivative of o**6/12 - 57*o**5/10 + 90*o**4 + 450*o**3 + 1056. Factor f(i).
i**2*(i - 30)**2*(i + 3)/2
Let s(j) = -16*j. Let u be s(-6). Suppose 87 = -258*n + 287*n. Suppose -u*l + n*l**4 + 116*l**2 - 25*l**3 + 0*l**4 - 44*l**2 + l**3 + 48 = 0. Calculate l.
2
Let a(l) be the first derivative of -14/9*l**3 + 225 + 2/15*l**5 + 0*l**4 + 0*l - 2*l**2. Factor a(d).
2*d*(d - 3)*(d + 1)*(d + 2)/3
Let q(h) be the second derivative of -1/17*h**5 + 2 + 9*h + 0*h**2 - 4/17*h**3 - 1/255*h**6 + 23/102*h**4. Solve q(c) = 0 for c.
-12, 0, 1
Let m be 4991/966 - 2/(-6). Let n(x) be the second derivative of -m*x**4 + 0 + 3*x**2 - 11*x - 5/2*x**3 - 9/4*x**5. Determine k, given that n(k) = 0.
-1, -2/3, 1/5
Let b be (-8)/((-32)/(-6))*(-4)/3. Suppose b = t - 0*t. Solve 4*r**4 + 0*r**2 + 4*r**3 - 5*r**t - 19*r**2 = 0 for r.
-3, 0, 2
Let 69/4*x**3 + 141/4*x**2 - 321/4*x - 3/2*x**4 + 117/4 = 0. Calculate x.
-3, 1/2, 1, 13
Let b(c) be the second derivative of 12*c**2 + 0 + 7/3*c**3 + 1/6*c**4 + 210*c. Factor b(n).
2*(n + 3)*(n + 4)
Factor -876*m + 331*m**2 - 567*m**3 + 569*m**3 - 197*m**2.
2*m*(m - 6)*(m + 73)
Let f = 970/27 - 61/27. Let d = f - 100/3. Factor -d*c**2 + 0 + 1/3*c.
-c*(c - 1)/3
Let p(q) be the third derivative of q**6/24 + 33*q**5/4 + 245*q**4/12 - 69*q**2 - 6*q. Factor p(n).
5*n*(n + 1)*(n + 98)
Let d be (-8)/(-5) + 3 + 52/(-20). Suppose d*s = -4*y, -2*y - 4 = 7*s - 5*s. Determine q so that -1/4*q**y - 1/2 + 3/4*q = 0.
1, 2
Let j be (20/50)/((-1)/(-10)). Suppose -62 = -j*f + 18. Let -11*p - f*p**3 + p + 20 - 20 - 25*p**2 - 5*p**4 = 0. What is p?
-2, -1, 0
Let p(s) be the first derivative of -s**3 - 11*s**2/4 + 17*s/2 + 3043. Factor p(y).
-(y - 1)*(6*y + 17)/2
Let d(k) = 9*k**2 - 810*k - 166466. Let j(g) = 32*g**2 - 2427*g - 499399. Let z(f) = -21*d(f) + 6*j(f). Let z(u) = 0. What is u?
-408
Suppose 31*s = 27*s + 276. Factor 3*z**5 - 8*z**4 - 71*z**2 + 143*z**2 - s*z**3 + 2*z**4 + 432*z.
3*z*(z - 4)**2*(z + 3)**2
Factor -2*x**3 + 0*x - 1/2*x**4 + 2*x**2 + 1/2*x**5 + 0.
x**2*(x - 2)*(x - 1)*(x + 2)/2
Let d be ((-9)/(-16))/(100/(-7280)*1). Let q = -201/5 - d. Find y such that 9/4*y**3 + 3*y**2 - 3*y**4 - 3*y + 0 + q*y**5 