h - 4)*(h + 2)**2*(h + 5)
Let q(h) be the second derivative of 122*h**3 + 127*h + 0 - 4/3*h**4 + 92*h**2. Suppose q(z) = 0. Calculate z.
-1/4, 46
Let n be (-244)/(-8) + 4 - (-6)/(-4). Factor -57*s**3 + n*s**3 + 26*s**3 + 6*s - 2 - 6*s**2.
2*(s - 1)**3
Let p(i) = -i + 12 - i**3 + 10 - 23. Let u(d) = -2*d**5 + 4*d**4 + 5*d**3 - 4*d**2 + 3*d + 3. Let l(m) = -6*p(m) - 2*u(m). Factor l(f).
4*f**2*(f - 2)*(f - 1)*(f + 1)
Let l = -5059 - -5061. Let h(i) be the second derivative of 0 + i**l + 1/24*i**4 + 1/3*i**3 - 18*i. Solve h(y) = 0 for y.
-2
Let v be (21/(-14))/((-6)/80). Let n = 22 - v. Factor 5*w**n - 43*w**3 + 15*w**3 + 23*w**3.
-5*w**2*(w - 1)
Suppose -18557 = 39*u - 18635. Factor 1/2*a - 2 + 1/4*a**u.
(a - 2)*(a + 4)/4
Let m(q) = q**2 + q + 35. Let j(i) = 2*i**2 - 1446*i + 1555. Let c(u) = 2*j(u) - 6*m(u). Let c(r) = 0. What is r?
-1450, 1
Let a(s) = -2 + 5*s**2 - 8*s - 75*s**3 + 0 + 76*s**3. Let n(t) = -t**3 + t**2 + t + 1. Let i(d) = a(d) + 2*n(d). Find m, given that i(m) = 0.
0, 1, 6
Let x(z) be the first derivative of 73 + 14/33*z**3 + 16/11*z - 1/22*z**4 - 14/11*z**2. Factor x(w).
-2*(w - 4)*(w - 2)*(w - 1)/11
Let h(p) be the second derivative of 1/20*p**5 + 0 + 0*p**2 + 0*p**4 - 1/6*p**3 + 63*p. Factor h(z).
z*(z - 1)*(z + 1)
Let b = 22/859 - -4251/1718. Let o(f) be the second derivative of -3*f**2 - 3/4*f**4 - b*f**3 + 0 - 24*f. Factor o(q).
-3*(q + 1)*(3*q + 2)
Let 24*a - 3*a**3 - 47/2 + 281/2*a**2 = 0. What is a?
-1/2, 1/3, 47
Let t(i) be the second derivative of -205*i**4/12 - 3095*i**3/6 - 150*i**2 + 989*i. Factor t(h).
-5*(h + 15)*(41*h + 4)
Let x be 854/8 - 27/36. Factor x - 115*q + 19 + 5*q**2 - 15.
5*(q - 22)*(q - 1)
Let o = -499 - -497. Let z be 2*(5/o - -4). Factor -18/11*b + 0 - 24/11*b**z - 78/11*b**2.
-6*b*(b + 3)*(4*b + 1)/11
Let v(i) be the second derivative of -i**5/20 + i**4/2 - 2*i**3 + 59*i**2/2 - 23*i + 2. Let o(d) be the first derivative of v(d). Solve o(n) = 0 for n.
2
Let j(u) = 3*u**2 - 123*u + 122. Let o be j(40). Let n(s) be the first derivative of 5*s + 5/3*s**3 + 3 - 5*s**o. Factor n(g).
5*(g - 1)**2
Let c = -237781/3 + 79263. Determine q, given that c*q - 2/3*q**3 + 0 + 2*q**4 - 8*q**2 = 0.
-2, 0, 1/3, 2
Let c(v) be the second derivative of 4*v**5 + 5000/7*v**2 - 13/70*v**6 - 850/21*v**4 + 1/294*v**7 + 36*v + 0 + 1000/7*v**3. Factor c(g).
(g - 10)**4*(g + 1)/7
Suppose -1/2*o**3 - 1225/2*o + 0 - 35*o**2 = 0. What is o?
-35, 0
Let u(z) be the second derivative of -z**5/15 - 9*z**4 + 110*z**3/3 + 8*z**2 - 142*z. Let k(i) be the first derivative of u(i). Suppose k(f) = 0. What is f?
-55, 1
Let l(x) be the third derivative of -x**6/3600 + 7*x**5/1200 + x**4/30 - 229*x**3/6 - 183*x**2. Let t(d) be the first derivative of l(d). Factor t(z).
-(z - 8)*(z + 1)/10
Let y(p) = p**2 - 1. Let c(b) be the first derivative of 3*b**4/4 + 12*b**3 - 15*b - 6. Let i(z) = c(z) - 15*y(z). Suppose i(v) = 0. What is v?
-7, 0
Let i(u) be the third derivative of 49*u**6/60 + 259*u**5/10 + 213*u**4/4 + 45*u**3 - 6*u**2 - 2*u + 1. Determine p, given that i(p) = 0.
-15, -3/7
Let t = -652423/5 + 130485. Factor -2*d - 6/5*d**3 + 14/5*d**2 + t.
-2*(d - 1)**2*(3*d - 1)/5
Suppose -2*v = 86352*l - 86354*l + 30, 3*v + 62 = 4*l. Factor 2/7*n**v + 20/7*n + 32/7.
2*(n + 2)*(n + 8)/7
Let t(w) = -14*w**2 - 13*w - 9. Let x(l) = 3*l**2 + l. Let z(u) = -4*t(u) - 20*x(u). Factor z(d).
-4*(d - 9)*(d + 1)
Let d(f) = 4*f**2 + 113*f - 117. Let s be (-6)/10*(-1 - (11 + -2)). Let o(c) = 2*c**2 + 57*c - 59. Let h(v) = s*d(v) - 14*o(v). Determine a so that h(a) = 0.
-31, 1
Let z(h) be the second derivative of -9/2*h**2 + 36 + 11/12*h**3 - 3*h - 1/24*h**4. Find p, given that z(p) = 0.
2, 9
Let t = 2 - 0. Let o(f) = -f**2 + 8*f + 13. Let k be o(9). Let -16 + 4*l + 12*l - k*l**2 + 2*l**t - 2*l**2 = 0. Calculate l.
2
Let c(y) = 119*y**2 + 747*y - 22. Let j(i) = -23*i**2 - 150*i + 5. Let w(g) = 3*c(g) + 14*j(g). Let w(q) = 0. What is q?
-4, -1/35
Suppose -64*d = -77*d - 433*d - 389*d + 1670. Factor 6/7*l**d + 26/7 - 80/7*l.
2*(l - 13)*(3*l - 1)/7
Let -98/5*h - 68/5 - 28/5*h**2 + 2/5*h**3 = 0. What is h?
-2, -1, 17
Let b(g) be the first derivative of -7*g**6/2 + 27*g**5/5 + 57*g**4/4 - 13*g**3 - 18*g**2 + 12*g - 7112. Determine f so that b(f) = 0.
-1, 2/7, 1, 2
Let w(p) be the third derivative of -p**6/200 + 47*p**5/50 - 115*p**4/2 + 2116*p**3/5 + 721*p**2. Let w(i) = 0. Calculate i.
2, 46
Let t be (612/272)/(4/22 - 501*1/(-1056)). Factor 8/7*y**2 - t*y**4 + 16/7 + 4/7*y**5 + 32/7*y**3 - 36/7*y.
4*(y - 4)*(y - 1)**3*(y + 1)/7
Let g = -317 + 289. Let l be 5/1 + (-7 - g/6). Suppose 4/3*c**2 + l*c + 4/3 = 0. What is c?
-1
Solve -116*d + 3*d**2 + 7*d - 47*d - 504 + d**2 = 0 for d.
-3, 42
Let w(i) be the third derivative of -7/4*i**4 + 13/2*i**3 + i**2 - 4*i + 0 + 1/20*i**5. Factor w(f).
3*(f - 13)*(f - 1)
Let m(s) be the third derivative of s**6/60 + 194*s**5/195 - 5*s**4/13 - 5254*s**2. Factor m(r).
2*r*(r + 30)*(13*r - 2)/13
Let o(x) be the first derivative of -x**5 - 45*x**4/4 + 20*x**3 + 50*x**2 + 627. Factor o(t).
-5*t*(t - 2)*(t + 1)*(t + 10)
Let l be (900/(-800))/(3/(-16))*15/12 - 6. Suppose l*c**2 + 5/4*c - 1/2 - c**4 + 3/4*c**5 - 2*c**3 = 0. What is c?
-1, 1/3, 1, 2
Let a(r) be the second derivative of 392*r**4/39 - 168*r**3/13 + 81*r**2/13 + 2*r - 154. What is k in a(k) = 0?
9/28
Suppose -25 + 153 = 2*y. Suppose 0 = 5*v, 24 = l - 2*v - 2*v. Let i**4 + 7*i**2 - 16*i**4 + y*i**2 + 25*i**5 + l*i**2 - 85*i**3 - 20 = 0. Calculate i.
-2, -2/5, 1
Suppose -r = 3, -5*r - 52 - 7 = -4*y. Let g(t) be the first derivative of -12 + 40*t**2 - 33*t**2 - t**3 - 108*t + y*t**2. Factor g(x).
-3*(x - 6)**2
Suppose -35 = 37*y - 44*y. Suppose -2*k = 5*q + 1, -5*q - 10 + 15 = y*k. Factor 4/9 - 2/9*s**k - 2/9*s.
-2*(s - 1)*(s + 2)/9
Let h(b) = -25*b + 252. Let u be h(10). Find m, given that 15*m**u - 102*m**3 - 28*m - 12*m**2 - 57*m**2 + 8*m**4 + 4*m**2 - 88*m**2 = 0.
-1, -1/4, 0, 14
Let u(a) = 18160*a**2 + 21997830*a + 8879784655. Let d(l) = -l**3 - l**2 + 3*l. Let q(o) = 5*d(o) - u(o). Find b such that q(b) = 0.
-1211
Let z(g) be the third derivative of -6 + 1/140*g**7 + 0*g + 1/40*g**5 + 13/360*g**6 + g**2 - 1/36*g**4 - 1/504*g**8 + 0*g**3. Solve z(x) = 0 for x.
-1, 0, 1/4, 4
Let p be -6 + -2 + 3 - (-45790)/8070. Let t = -2/269 + p. Factor t*q**3 + 4/3*q**2 - 8/3*q - 16/3.
2*(q - 2)*(q + 2)**2/3
Suppose -1952*x = -1451*x - 1002. Determine d, given that 0 - 4/9*d**4 - 2/3*d + 8/9*d**3 + 4/9*d**x - 2/9*d**5 = 0.
-3, -1, 0, 1
Let w = 5071/6042 - 6/1007. Let o(x) be the first derivative of 1/8*x**4 + 7/4*x**2 - 24 + 3/2*x + w*x**3. Suppose o(a) = 0. What is a?
-3, -1
Let p = -227 - -245. Determine n so that 7*n + p*n - 8*n**2 + 3*n**2 = 0.
0, 5
Let z be ((-40)/(-25))/(24/20). Let j = -1/16 - -35/48. Factor 2/3*p**2 + z*p + j.
2*(p + 1)**2/3
Let c(k) be the first derivative of k**5/15 - 2*k**4 + 24*k**3 - 22*k**2 + 74. Let p(u) be the second derivative of c(u). Factor p(h).
4*(h - 6)**2
Suppose -7*i = 5*i - 36. Suppose -2*x = -0*x - 6, 11 = y + i*x. Factor 2*c**3 + 2*c**y + 4*c**3 + 0*c**3 - 4*c**3.
2*c**2*(c + 1)
Let b be (5/15)/(((-104)/(-468))/((-8)/(-6))). Let r(h) be the first derivative of 2/3*h**3 + 16 - h**b + 0*h. Factor r(t).
2*t*(t - 1)
Let k(v) be the first derivative of v**5/5 + 35*v**4/3 + 646*v**3/3 + 578*v**2 + 94*v - 87. Let d(y) be the first derivative of k(y). Factor d(r).
4*(r + 1)*(r + 17)**2
Suppose -10 = -4*z - 2. Suppose 0 = 3*v - z*b - 22, -3*v + b = 5*b - 28. Factor 3 - 5 - 5*a**2 - 15*a - v.
-5*(a + 1)*(a + 2)
Factor 60 - 15/4*p**3 + 1/4*p**4 - 3*p**2 + 41*p.
(p - 15)*(p - 4)*(p + 2)**2/4
Let h(r) = 5*r**2 - 116*r - 246. Let y(t) = -4*t**2 + 118*t + 248. Let z(u) = -2*h(u) - 3*y(u). Let z(m) = 0. What is m?
-2, 63
Let l(y) be the third derivative of 142*y**2 - 1/210*y**5 + 0*y**3 + 0*y + 1/2*y**4 + 2. Factor l(h).
-2*h*(h - 42)/7
Let z = 219531/7 - 31298. Let k = -3998/63 + z. Determine n so that 1/9*n**4 + 0 + 0*n**2 + 0*n + k*n**3 = 0.
-1, 0
Let b be 6 + 9/(225/(-134)). Let v(q) be the first derivative of 0*q + 0*q**3 - 1/5*q**4 - b*q**5 + 0*q**2 - 7/30*q**6 + 17. Solve v(r) = 0 for r.
-2, -2/7, 0
Let l(f) be the first derivative of 1/34*f**4 + 0*f - 87 + 28/51*f**3 + 49/17*f**2. Factor l(d).
2*d*(d + 7)**2/17
Let b = 2844 + -2842. Let w = -200 + 200. 