 13*v**7/210 - 13*v**6/150 + v**5/15 - 3772*v**2. What is s in p(s) = 0?
-1, 0, 2/7, 10
Let -1/2*q + 301 + 1/2*q**3 - 301*q**2 = 0. Calculate q.
-1, 1, 602
Let r(z) be the first derivative of -245 - 1/3*z**6 + 32*z - 14/5*z**5 + 38/3*z**3 - 38*z**2 + 11/2*z**4. Factor r(y).
-2*(y - 1)**3*(y + 2)*(y + 8)
Suppose -12*j + 5*j = -14. Factor d**2 + 6*d**2 - 9*d**2 + 240*d - 23*d**j - 576.
-(5*d - 24)**2
Suppose 6*d - 4*d - 9 = 3*i, 3*i + 9 = -5*d. Suppose 2*r + h = -0*r + 9, -3*r + 2*h + 3 = d. Factor 0*b + 3/7*b**r + 0 - 3/7*b**2.
3*b**2*(b - 1)/7
Let c(l) = -8*l**2 + 3103*l + 6383. Let d(q) = -9*q**2 + 3102*q + 6414. Let z(r) = 6*c(r) - 5*d(r). Factor z(n).
-3*(n - 1038)*(n + 2)
Let i(l) be the second derivative of -l**7/70 + 3*l**5/20 - l**4/4 - 4*l**2 - 18*l. Let u(d) be the first derivative of i(d). Factor u(o).
-3*o*(o - 1)**2*(o + 2)
Let j(n) be the second derivative of n**6/72 + 3*n**5/4 - n**3/6 + 22*n**2 - 88*n. Let a(i) be the second derivative of j(i). Factor a(w).
5*w*(w + 18)
Let c(k) = -k**3 + 53*k**2 + 15*k - 793. Let f be c(53). Factor -9/2*n**3 + 0 - 10*n + 12*n**f + 1/2*n**4.
n*(n - 5)*(n - 2)**2/2
Let g(l) = -l**3 + 9*l**2 - 18*l + 9. Let u be g(5). Suppose -11*a + u = -3. Let 36*s**a + 36*s**2 - 3*s**3 + 3*s - 3 - 69*s**2 = 0. Calculate s.
-1, 1
Let k be (-1)/((1 + -2)/(-1)) + (-29 - -38). Let y(a) be the first derivative of -4/3*a**3 + k + 16*a + 6*a**2. What is g in y(g) = 0?
-1, 4
Let x = 16 - 11. Let i be (3*(-4)/(-6))/(-4 + x). Factor 0 - 2/5*f + 2/5*f**3 - 3/5*f**i.
f*(f - 2)*(2*f + 1)/5
Factor 246/5*x - 10*x**2 - 342/5 + 2/5*x**3.
2*(x - 19)*(x - 3)**2/5
What is a in -9 + 13 + 11 + 5 - a**2 - 3 + 16*a = 0?
-1, 17
Let j(t) be the third derivative of -1/150*t**5 + t + 0 + 1/60*t**4 + 32*t**2 + 0*t**3. Factor j(n).
-2*n*(n - 1)/5
Let d(u) = -u**2 - 9*u - 10. Let n be d(-7). Suppose o + 0 = c - 4, -5*o = 0. Factor -c*z + 6*z**n - 5*z - 3*z**4 - 15*z**2 - 3*z**3.
3*z*(z - 3)*(z + 1)**2
Determine d, given that 1/5*d**3 + 0*d + 0 + 1074/5*d**2 = 0.
-1074, 0
Let b(n) be the first derivative of -n**5/25 - 17*n**4/20 + 118*n**2/5 - 64*n - 12364. Find s, given that b(s) = 0.
-16, -5, 2
Let j = 6599372735/791 - 8343077. Let v = -6/113 - j. Factor -2/7*h**2 - 16/7*h**3 - v*h**4 + 0 + 4/7*h.
-2*h*(h + 1)**2*(5*h - 2)/7
Let c be 6/(0 - 2 - (-7)/2). Suppose -204 = -c*f - 0*f. Factor 51 - 4*g + 4*g**3 - f.
4*g*(g - 1)*(g + 1)
Suppose -162/5 + 1/5*l**2 + 9/5*l = 0. Calculate l.
-18, 9
Let x(g) be the third derivative of 7/24*g**3 + 23/80*g**5 + 3/160*g**6 + 0*g + 3*g**2 + 5 + 43/96*g**4. Factor x(w).
(w + 7)*(3*w + 1)**2/4
Let h(r) be the first derivative of 1/3*r**3 + 0*r - 7*r**2 + 6. Determine k, given that h(k) = 0.
0, 14
Let f be 7*6/(-21)*-8. Factor 16*q**3 - 3*q**2 + 35*q + f*q**3 + 36*q**2 + 5*q**4 + 12*q**2 - 7*q**3 + 10.
5*(q + 1)**3*(q + 2)
Let w(c) be the second derivative of c**6/660 + c**5/110 + c**4/66 - 46*c**2 - 2*c + 10. Let h(t) be the first derivative of w(t). Find q, given that h(q) = 0.
-2, -1, 0
Let i(j) be the first derivative of 4*j**5/15 - 5*j**4 - 152*j**3/3 - 488*j**2/3 - 224*j - 391. Suppose i(w) = 0. What is w?
-2, 21
Let y be (4/20)/((-4)/5)*(-1656)/207. Suppose 10/23*w**y - 48/23 - 116/23*w = 0. Calculate w.
-2/5, 12
Let t = -1/534523 + 28329721/1069046. Factor t - 3/2*k**2 + 79*k.
-(k - 53)*(3*k + 1)/2
Let g(q) be the first derivative of -q**4/20 + 523*q**3/15 + q**2/10 - 523*q/5 - 1723. Let g(b) = 0. Calculate b.
-1, 1, 523
Let j be ((-49455)/(-11018) + -3)*6/27. Let h = j + 2/787. Let 0 - h*u**3 + 2/3*u**2 - 1/3*u = 0. What is u?
0, 1
Let p(s) = 5*s**3 - 135*s - 270. Let u(v) = -5*v**3 + 135*v + 270. Let q(n) = -6*p(n) - 5*u(n). What is k in q(k) = 0?
-3, 6
Let s = -5448 + 5475. Let u(j) be the first derivative of s + 5*j**2 + 5/3*j**3 - 15*j. Factor u(r).
5*(r - 1)*(r + 3)
Let s = -574 - -594. What is j in -4 - s + 111*j + 21 - 28*j**2 + 2*j**3 - 25*j - 57 = 0?
1, 3, 10
Factor 11/5*i**2 + 48/5 + 136/5*i.
(i + 12)*(11*i + 4)/5
Let n(j) = j**3 - 10*j**2 + 14*j + 21. Let g be n(8). Suppose g*q**3 + 41*q**2 - 90 + 34*q**2 + 165*q + 20*q**3 + 65*q**2 = 0. Calculate q.
-3, 2/5
Suppose 69*j = 72*j - 6. Let 35*n + 23*n + 13*n**2 - 10*n + 32 + j*n**3 + 5*n**2 = 0. What is n?
-4, -1
Suppose 167*y + 253 - 253 = 3*y - 85*y. Let 40/3*r - 4/3*r**5 - 28/3*r**4 - 116/3*r**2 + y + 36*r**3 = 0. What is r?
-10, 0, 1
Suppose -3*o + 16 - 7 = 3*k, -5*o = -2*k - 15. Factor o*x**3 + 12*x + 52273*x**4 - 15*x**3 - 4*x**2 - 52269*x**4.
4*x*(x - 3)*(x - 1)*(x + 1)
Suppose -240*s + 477*s - 257*s + 300 = 0. Let g(v) be the first derivative of 5/3*v**3 - 9 - s*v**2 + 40*v. Factor g(m).
5*(m - 4)*(m - 2)
Let r(h) be the third derivative of 7*h**8/144 + 1993*h**7/45 + 3964069*h**6/360 - 37867*h**5/3 + 9025*h**4/2 + 85*h**2 - 9*h. Let r(y) = 0. Calculate y.
-285, 0, 2/7
Suppose 1 = 4*r - 11. Suppose -r*f - 4*j + 28 = 4, 3 = -3*f + 5*j. Find p, given that -1/5*p**2 + 1/5*p**5 + 1/5*p**f - 1/5*p**3 + 0*p + 0 = 0.
-1, 0, 1
Let w be 0/(-1*(42/6 + -4)). Let q(n) be the third derivative of 0 + 0*n**3 + w*n + 1/18*n**5 + 0*n**4 - 1/72*n**6 - 4*n**2. Solve q(r) = 0 for r.
0, 2
Let b be 4/6*(-6)/(-4). Let z(o) = 3*o**3 - o**2 - o + 1. Let y be z(b). Factor 18*d**3 - 2*d**2 - 10*d**4 - y*d**5 - 12*d**2 + 11*d - 7*d + 4*d**5.
2*d*(d - 2)*(d - 1)**3
Suppose 8*c - 6*c = r + 11, -r + 5*c = 26. Let i be r + 11 + (-390)/40. Determine s, given that -i*s**2 + 3/2*s - 9/4 = 0.
3
Suppose -3 - 5 = 581*y - 8. Factor -4/9*u**3 + y - 52/9*u**2 - 16/3*u.
-4*u*(u + 1)*(u + 12)/9
Let i(b) = 32*b**2 + 84*b + 44. Let x(v) = -v**3 + 2*v - 1. Suppose 0 = -7*y, -3 = -5*k + 5*y - 23. Let u(o) = k*x(o) + i(o). Factor u(q).
4*(q + 1)*(q + 3)*(q + 4)
Suppose -55*l - 494 + 54 = 0. Let f be (-99)/66*l/6. Factor -6/7 + 6/7*i**f + 3/7*i - 3/7*i**3.
-3*(i - 2)*(i - 1)*(i + 1)/7
Suppose -1/9*t**2 - 16/3*t - 15 = 0. Calculate t.
-45, -3
Let m(f) be the third derivative of 0*f + 6*f**3 + 0 + 0*f**4 - 1/15*f**5 - 72*f**2. Suppose m(j) = 0. Calculate j.
-3, 3
Suppose -10*f**2 + 12*f**2 + 2*f - f**3 + 2*f - 2*f**2 = 0. What is f?
-2, 0, 2
Let y(n) be the second derivative of -5*n + 2 + 0*n**3 + 7/130*n**5 + 0*n**2 + 0*n**4 + 1/195*n**6. Suppose y(r) = 0. Calculate r.
-7, 0
Let f = 143699/5 - 28739. Find r such that f*r**4 + 1/5*r**3 + 1/5*r**5 - 8/5 - 14/5*r**2 - 4*r = 0.
-2, -1, 2
Let 18 - 171 + 5*n**3 - 87 + 327*n**2 - 307*n**2 - 100*n = 0. What is n?
-6, -2, 4
Let a = 3148 - 3145. Let i(t) be the first derivative of 5 - 5/4*t**4 - 5*t + 5/3*t**a + 5/2*t**2. Determine b, given that i(b) = 0.
-1, 1
Let w = 42 - 99. Let f = w - -75. Factor 1148*y - 1133*y + f + 4*y**2 - y**2.
3*(y + 2)*(y + 3)
Let o = 13 + -12. Let t be 14/8 - o - 5/(-60). Factor -25/3*m + t*m**2 + 125/6.
5*(m - 5)**2/6
Let m be (2/4)/(9/18). Let a be (1/1)/(m/3). Factor -12 + 12 + 6*w**2 - 3*w**a - 3*w.
-3*w*(w - 1)**2
Let k be -7 + 115/15 + 1038/(-9). Let d = k + 120. Determine s, given that 4/3 + 7/3*s**2 + d*s = 0.
-2, -2/7
Let y be -1*(3 - (-7 - -4)). Let p be 10/6 + (-2)/y. Solve p*r**4 - 2*r**2 - 14*r**2 - 9*r + 12 + 17*r - 8*r**3 + 2*r**4 = 0 for r.
-1, 1, 3
Let s be 3605/980 + 1/14. Let c(b) be the first derivative of 22 + 5/6*b**3 + 0*b + s*b**2. Suppose c(i) = 0. What is i?
-3, 0
Let l(c) be the first derivative of 33*c**5/10 - 25*c**4 + 46*c**3 - 4*c**2 - 1927. Find i such that l(i) = 0.
0, 2/33, 2, 4
Let w(t) be the first derivative of 3*t**4/4 - 72*t**3 + 1935*t**2/2 - 4650*t - 7385. Factor w(j).
3*(j - 62)*(j - 5)**2
Let u(v) = 98*v + 2 - 100*v - 44*v**3 - 4. Let y be u(-1). Factor 86*j**3 - 38*j**3 + 20*j + 8 - y*j**3 + 16*j**2.
4*(j + 1)**2*(j + 2)
Let r = -255 - -398. Let s = 147 - r. Solve 0 + 12/5*j**3 + 18/5*j**2 + 2/5*j**s + 0*j = 0.
-3, 0
Let i(n) be the first derivative of -2*n**5/5 + 8*n**4 - 148*n**3/3 + 104*n**2 - 90*n - 6768. Find t, given that i(t) = 0.
1, 5, 9
Let f(v) be the third derivative of 0*v - 841/27*v**3 - 58*v**2 - 29/54*v**4 + 0 - 1/270*v**5. Factor f(n).
-2*(n + 29)**2/9
Let q be ((4/(-18))/((-8)/(-3)))/((-7)/21). Find c, given that -c + 0 - q*c**3 - c**2 = 0.
-2, 0
Let u(i) be the second derivative of -i**4/36 + 23*i**3/9 + 47*i**2/6 + 5811*i. Solve u(m) = 0 for m.
-1, 47
Let a = 543 + -542. Let q be (7 + -15)/((-3 - 3)/a). Factor -2/3*f**4 + 0*f**2 + q*f**5 + 0*f - 2/