9
Let k(a) be the third derivative of 1/24*a**4 + 1/120*a**6 - 1/15*a**5 + 0*a + 0 - 17*a**2 + a**3. Suppose k(c) = 0. Calculate c.
-1, 2, 3
Suppose -2*n = -g - 20, 2*g - 2*n + 9820 - 9800 = 0. Find y, given that -48/5*y - 12/5*y**3 - 4/5*y**4 + g + 64/5*y**2 = 0.
-6, 0, 1, 2
Let n be (0 + 1)/(35/21) + 42/30. Let b(l) be the second derivative of 2*l - 8/3*l**3 + 16*l**n + 0 + 1/6*l**4. Suppose b(q) = 0. What is q?
4
Suppose -17710 = 198*b - 221*b. Let w be (-2)/(-7) - (3930/b - 5). Let 0*m**2 + 0*m**3 - 2/11*m**5 + w*m**4 + 0*m + 0 = 0. Calculate m.
0, 1
Let i(z) be the first derivative of z**4/12 - z**3/2 - 67*z + 4. Let f(l) be the first derivative of i(l). Suppose f(a) = 0. What is a?
0, 3
Let v(g) be the second derivative of 2*g**7/21 + 32*g**6/15 + 18*g**5 + 200*g**4/3 + 250*g**3/3 - 1043*g - 1. Factor v(u).
4*u*(u + 1)*(u + 5)**3
Suppose -1296 = -473*d + 596. Let r(f) be the third derivative of 1/8*f**5 + 0 + 1/2*f**3 - 19/48*f**d + 22*f**2 + 0*f. Factor r(u).
(3*u - 2)*(5*u - 3)/2
Let i = -411 + 413. Let z be 2*(-11 + 15)/i. Find r such that 1/2 - 11/2*r**2 + 25/4*r**3 - 2*r**5 + 1/4*r + 1/2*r**z = 0.
-2, -1/4, 1/2, 1
Let w(i) be the third derivative of 0 + 4*i**2 - 11*i + 44/15*i**4 - 64/5*i**3 + 29/150*i**5 - 7/150*i**6 + 1/525*i**7. Factor w(v).
2*(v - 8)**2*(v - 1)*(v + 3)/5
Let t(b) be the third derivative of 0 + 2*b**2 - 50/3*b**3 + 2/105*b**7 + 8*b - 5/3*b**4 + 8/5*b**5 + 1/3*b**6. Factor t(l).
4*(l - 1)*(l + 1)*(l + 5)**2
Let q be 8*2/(-4) + 171. Suppose q - 67 = 5*t. Factor -5*f**4 + 9*f**4 + 0*f**4 + f**4 + t*f - 15*f**3.
5*f*(f - 2)**2*(f + 1)
Let o be 2/(-1) + 24/14 + 2624/1148. Let d(z) be the first derivative of 0*z - 1/6*z**3 + 1/16*z**4 + 0*z**o - 2. Determine w so that d(w) = 0.
0, 2
Let c(g) = -g**3 - 97*g**2 - 630*g - 1443. Let x(r) = 2*r**3 + 94*r**2 + 628*r + 1442. Let k(p) = -2*c(p) - 3*x(p). Solve k(b) = 0 for b.
-10, -6
Suppose 5*n - 8 = -2*x + 9, -2*x = -2*n + 18. Let p be (n*4/(-90))/(1/(-9)). Factor -7*c - 5*c**2 + c + 2*c**p + 2*c**3 - c**2.
2*c*(c - 3)*(c + 1)
Suppose 85 = 272*b - 277*b, 0 = 3*l + 3*b + 39. Find m, given that 38/3*m**3 + 112/3*m + 38*m**2 + 4/3*m**l + 32/3 = 0.
-4, -1, -1/2
Let b(z) be the first derivative of -z**6/60 - z**5/6 - z**2 - z + 117. Let h(d) be the second derivative of b(d). Factor h(j).
-2*j**2*(j + 5)
What is w in 376 + 10*w - 76*w + 5*w**2 - 19*w - 55*w + 524 = 0?
10, 18
Let z(n) = -20*n**3 + 10*n**2 + 255*n + 225. Let k(i) = -7*i**3 + 3*i**2 + 85*i + 75. Let b(f) = 17*k(f) - 6*z(f). Factor b(r).
(r - 15)*(r + 1)*(r + 5)
Let g(k) = 25*k**5 - 33*k**3 + 8*k - 17. Let n = -37 + 42. Let i(d) = -4*d**3 + 9*d**5 - 3 - 6*d**n + d + 1. Let f(r) = -6*g(r) + 51*i(r). Factor f(m).
3*m*(m - 1)**2*(m + 1)**2
Suppose 3*l - 6 = m, -5*l - m + 2*m + 12 = 0. Let i be (1 + (-1)/l)*75/200. Suppose 6*p - i*p**2 - 36 = 0. What is p?
12
Let a be (-6)/(-252)*12 + (-4526)/14. Let q be (-1 - (-2)/2) + (-38)/a. Factor q*o**2 + 10/17 + 12/17*o.
2*(o + 1)*(o + 5)/17
Let b be (-133)/(-49) - (-18)/63. Let u(v) be the second derivative of -2*v**b - 1/6*v**4 - 8*v**2 + 0 + 23*v. Factor u(h).
-2*(h + 2)*(h + 4)
Let j(g) be the third derivative of -g**5/60 - 13*g**4/12 - 24*g**3 + 98*g**2 + 4*g. Factor j(d).
-(d + 8)*(d + 18)
Let n(u) = -u + 20. Let i be n(6). Let x be 2*(20/4 - 4 - -1). Factor -x*l**4 + 21*l**3 + 16*l - 31*l**3 - 36*l**2 - i*l**3 + 48.
-4*(l - 1)*(l + 2)**2*(l + 3)
Let k = -646 - -647. Factor 18*z**2 - 81*z - 3*z**3 + 23 + 18 + 12 + k + 12*z**2.
-3*(z - 6)*(z - 3)*(z - 1)
Suppose 21*d - 54 = 12*d. Suppose 0 = -8*g + d - 6. Factor 3/4*j + g - 3/4*j**2.
-3*j*(j - 1)/4
Let y(f) be the second derivative of -3*f**4/8 - 53*f**3/24 + 3*f**2/8 + f + 88. Factor y(m).
-(m + 3)*(18*m - 1)/4
Let y(r) be the first derivative of -r**8/840 + r**7/210 + r**6/180 - r**5/30 + 10*r**3/3 + 2*r - 41. Let t(h) be the third derivative of y(h). Factor t(i).
-2*i*(i - 2)*(i - 1)*(i + 1)
Let g(i) = -43*i + 7*i + 1 + 1 + 2*i**2. Let b(m) = 3*m**2 - 74*m + 5. Let c(u) = 2*b(u) - 5*g(u). Factor c(a).
-4*a*(a - 8)
Let l(q) be the third derivative of 113*q**2 - 1/12*q**5 + 0*q - 1/48*q**6 + 5/6*q**3 + 0 + 5/48*q**4. Factor l(t).
-5*(t - 1)*(t + 1)*(t + 2)/2
Let o(l) = 2*l**3 - l**2 + 3*l - 2. Let j(t) = 4*t**3 - 163*t**2 - 327*t - 168. Let w(n) = 2*j(n) - 2*o(n). Determine p so that w(p) = 0.
-1, 83
Let y be (38/(43700/(-138)))/((-2)/50). Find p, given that 12/13*p**4 + 4/13*p**2 - 16/13 + 22/13*p**y - 24/13*p + 2/13*p**5 = 0.
-2, -1, 1
Let v = 66 - 66. Suppose 0 = -5*a + 25, v = -2*s + s - 4*a + 23. Factor 8*u**3 - 6*u + u**s - 5*u**3 - 2*u - 4*u**2.
4*u*(u - 2)*(u + 1)
Let t be (-190)/(-114)*(-6)/(-20). Let k(z) be the third derivative of -3*z**3 + t*z**4 - 1/10*z**6 - 20*z**2 + 4/15*z**5 + 0*z + 0 + 1/105*z**7. Factor k(p).
2*(p - 3)**2*(p - 1)*(p + 1)
Let l(n) be the second derivative of n**6/10 + 363*n**5/20 - 123*n**4/4 - 121*n**3/2 + 183*n**2 + 2*n - 155. Solve l(p) = 0.
-122, -1, 1
Let t(k) be the second derivative of k**7/14 + 511*k**6/30 + 14179*k**5/10 + 39469*k**4 - 1093300*k**3/3 - 390224*k**2 - 2440*k. Factor t(h).
(h - 4)*(h + 58)**3*(3*h + 1)
Let t(v) = -7996*v - 71962. Let r be t(-9). Factor -2/3*l**3 + 10/3*l + 2*l**r - 2/3*l**4 + 4/3.
-2*(l - 2)*(l + 1)**3/3
Suppose 0 - 69/2*l**3 + 27/4*l**2 + 15/4*l**4 + 0*l = 0. Calculate l.
0, 1/5, 9
Let d(m) be the first derivative of -48 + 1/5*m**5 - m**4 - 3*m + 2/3*m**3 + 2*m**2. Let d(u) = 0. Calculate u.
-1, 1, 3
Let q(g) be the third derivative of g**5/630 + g**4/28 + 2*g**3/9 + 41*g**2. Factor q(r).
2*(r + 2)*(r + 7)/21
Find w such that -18*w**2 + 0 - 2/3*w**4 + 36*w - 18*w**3 + 2/3*w**5 = 0.
-3, 0, 1, 6
Let k(l) be the first derivative of -l**3/24 + 583*l**2/8 + 1167*l/8 - 6895. Factor k(h).
-(h - 1167)*(h + 1)/8
Find z such that -1/7*z**2 - 40 - 74/7*z = 0.
-70, -4
Find s, given that 72/17*s + 548/17*s**2 - 80/17 + 14/17*s**5 + 574/17*s**3 + 192/17*s**4 = 0.
-10, -2, -1, 2/7
Let j(i) be the third derivative of -i**8/141120 + i**7/7056 + 149*i**5/60 - i**2 - 16. Let r(d) be the third derivative of j(d). Suppose r(x) = 0. Calculate x.
0, 5
Let n be ((-6)/(-4))/(0 + 3)*4. Suppose -36*q**4 + 34*q**4 - 2*q**5 - 108*q**n + 86*q**2 + 8*q + 18*q**3 = 0. Calculate q.
-4, 0, 1
Let k(o) be the third derivative of -o**8/336 + 11*o**7/210 + 7*o**6/15 + o**5 - 17*o**2 + 12*o. Factor k(f).
-f**2*(f - 15)*(f + 2)**2
Let j(w) be the first derivative of 2*w**3/9 - 824*w**2/3 + 339488*w/3 + 1342. Factor j(l).
2*(l - 412)**2/3
Suppose 0 = -5877*c + 5824*c + 636. Factor -8*s**2 - 9/2 - c*s.
-(4*s + 3)**2/2
Let q = 1608739/4 + -11261053/28. Factor 2/7*j**2 - q + 4*j.
2*(j - 1)*(j + 15)/7
Let l(k) be the second derivative of 7/270*k**6 - 1/18*k**2 - 5/54*k**3 - 1/18*k**4 + 1/126*k**7 + 2*k - 17 + 1/90*k**5. Determine d, given that l(d) = 0.
-1, -1/3, 1
Let j(b) be the first derivative of -b**6/120 - 23*b**5/40 - 11*b**4/4 - 6*b**3 + 166. Let y(l) be the third derivative of j(l). Factor y(t).
-3*(t + 1)*(t + 22)
Let g(f) be the third derivative of 0*f + 0 - 250*f**2 + 41/20*f**5 + 1/40*f**6 + 79/8*f**4 + 39/2*f**3. Factor g(v).
3*(v + 1)**2*(v + 39)
Let x(s) = s**2 - 2*s + 1. Let a be x(1). Suppose k + 22 - 54 = a. What is f in -136*f**3 + k*f**2 - 8 - 28*f**5 + 82*f**4 + 22*f**4 + 4*f + 32*f**2 = 0?
-2/7, 1
Suppose 96*a = 65*a. Let v(y) be the third derivative of 0*y**7 + 1/140*y**6 - 1/105*y**5 + 13*y**2 + a*y**4 + 0*y + 0 + 0*y**3 - 1/1176*y**8. Factor v(t).
-2*t**2*(t - 1)**2*(t + 2)/7
Let x(f) be the first derivative of f**4/24 - 19*f**3/18 + 4*f**2 + 4168. Factor x(l).
l*(l - 16)*(l - 3)/6
Let 513*i**4 - 683*i**2 + 170*i**2 - 383843*i**3 + 39*i**5 + 383882*i**3 - 78*i = 0. Calculate i.
-13, -1, -2/13, 0, 1
Factor -14 + 16*z - 25*z + 4*z**2 - 5*z**2 + 0*z**2.
-(z + 2)*(z + 7)
Find d such that 112 - 230*d + 140*d + 139*d + 47*d - 4*d**3 + 12*d**2 = 0.
-2, 7
Let g = 148 - 133. Let f be (-6)/g + 493/145. Suppose -2/5*v**2 + 16/5*v - 2/5*v**f + 24/5 = 0. Calculate v.
-2, 3
Let x be 11*22682/22385 - (-8)/148. Factor 28/5*b + 8/5 + 4*b**3 - x*b**2.
4*(b - 2)*(b - 1)*(5*b + 1)/5
Let x(b) be the first derivative of -2*b**3/15 - 32*b**2/5 + 42*b - 1382. Factor x(v).
-2*(v - 3)*(v + 35)/5
Let z be -1*(-9)/21 + 26098/(-70). Let b = 373 + z. Determine l, given that 0 + 2/5*l - 1/5*l**