, 0, 4
Let f(t) be the third derivative of t**6/180 - 7*t**5/90 + 7*t**4/36 + 5*t**3/3 + 520*t**2. Suppose f(b) = 0. Calculate b.
-1, 3, 5
Suppose 2605*m**2 - 75*m**3 - 1088*m**2 + 126*m - 1232*m**2 = 0. What is m?
-2/5, 0, 21/5
Let c = -853 + 2162. Let p = c + -1307. Suppose -5/2*q**p + 0*q + 5/2 = 0. What is q?
-1, 1
Factor -212/3*v**2 + 874/3*v - 2/3*v**3 - 220.
-2*(v - 3)*(v - 1)*(v + 110)/3
Let i(o) be the second derivative of -1/11*o**2 - 17/44*o**4 + 0 + 47/220*o**5 + 7/22*o**3 - 27*o - 1/22*o**6. Factor i(c).
-(c - 1)**3*(15*c - 2)/11
Let m(f) = f - 1. Let p(x) = x**2 - 19*x + 31. Let u(i) = 6*m(i) + p(i). Let b be u(11). Suppose 4*n**b - 5*n**2 - 1 - 5*n**2 + 6*n + n**2 = 0. Calculate n.
1/4, 1
Let c(z) be the third derivative of 116*z**2 + 1/20*z**6 + 0*z**5 + 0*z**4 - 1/10*z**7 + 0 - 9/112*z**8 + 0*z + 0*z**3. Factor c(s).
-3*s**3*(s + 1)*(9*s - 2)
Let l(v) be the second derivative of -v**5/90 - 13*v**4/36 - 49*v**2 - 18*v. Let a(m) be the first derivative of l(m). Factor a(x).
-2*x*(x + 13)/3
Let z(j) be the third derivative of 1/3*j**4 - 7 + 0*j - j**2 + 0*j**3 + 1/3*j**5. Factor z(h).
4*h*(5*h + 2)
Let w(x) = 4*x**2 + 9*x**4 + 6*x**3 + 15*x + 5*x**2 - x - 4*x - 16 + 2*x. Let n(p) = -p**4 - p + 2. Let c(f) = -40*n(f) - 5*w(f). Factor c(j).
-5*j*(j + 1)**2*(j + 4)
Let t = -98/271 + 467/542. Let v be (16/(-4))/(-24)*9. Let -x + v*x**3 + 0 + t*x**2 = 0. What is x?
-1, 0, 2/3
Let x be (-15 + 15)*1/(-2). Let v(n) be the second derivative of 0 + 4*n + 1/12*n**4 + x*n**2 + 1/2*n**3. Suppose v(u) = 0. Calculate u.
-3, 0
Let x(r) be the second derivative of 39*r - 35/6*r**3 + 5/12*r**4 + 0 + 0*r**2. Factor x(a).
5*a*(a - 7)
Suppose 0 = 7*c - 2195 + 389. Factor -4*b**3 - b**4 - 258 + c + 0*b**4.
-b**3*(b + 4)
Let g(q) be the third derivative of q**7/294 + 17*q**6/140 + 5*q**5/4 + 73*q**4/21 + 26*q**3/7 + 1409*q**2. Find b such that g(b) = 0.
-13, -6, -1, -2/5
Let r(y) = y**3 + 21*y**2 + 124*y + 204. Let w be r(-6). What is d in w - 1/6*d**4 - 1/3*d - 2/3*d**3 - 5/6*d**2 = 0?
-2, -1, 0
Let f(r) be the second derivative of -1/15*r**5 + 0*r**2 + 4/9*r**4 - 2/3*r**3 - 4*r + 7. Find k such that f(k) = 0.
0, 1, 3
Let g be -74 + 77 + -3 + 4/3. Let o(j) be the third derivative of -1/15*j**5 + 0 - 1/6*j**4 + 5*j**2 + g*j**3 + 0*j. Factor o(w).
-4*(w - 1)*(w + 2)
Let s(l) be the first derivative of -l**6/255 + 2*l**5/85 + l**4/102 - 4*l**3/51 - 86*l - 29. Let c(g) be the first derivative of s(g). What is x in c(x) = 0?
-1, 0, 1, 4
Let v(k) be the second derivative of k**5/4 - 35*k**4/4 - 5*k**3/6 + 105*k**2/2 - 325*k - 1. Factor v(w).
5*(w - 21)*(w - 1)*(w + 1)
Factor -374/9*h**2 + 17296/9*h + 2/9*h**3 + 17672/9.
2*(h - 94)**2*(h + 1)/9
Let q(v) be the third derivative of v**6/210 + 622*v**5/105 - 6368*v**2. Factor q(g).
4*g**2*(g + 622)/7
Let v(b) = 4*b**3 - b + 4. Let k(s) = -22*s**3 + 68*s**2 - 103*s + 36. Let j(t) = -k(t) - 3*v(t). Solve j(f) = 0.
1, 24/5
Let c(s) be the second derivative of 0*s**3 + 13/35*s**5 - 37/105*s**6 - 1/49*s**7 + 0*s**2 - 4 - 4*s + 0*s**4. Factor c(x).
-2*x**3*(x + 13)*(3*x - 2)/7
Let k(t) be the first derivative of -2*t**6/3 - 256*t**5/5 - 1023*t**4 + 256*t**3/3 + 2048*t**2 + 1023. Solve k(j) = 0 for j.
-32, -1, 0, 1
Let l(h) be the third derivative of h**7/6720 - h**5/320 + h**4/96 - 25*h**3/6 + 125*h**2. Let v(n) be the first derivative of l(n). Solve v(i) = 0.
-2, 1
Let d be -7 - ((-765)/78 + (-6)/(-12)). Let s be (9/117)/((-1)/(-2))*4. Suppose -4/13 - d*x**3 + s*x**4 + 32/13*x**2 - 6/13*x = 0. What is x?
-1/4, 1, 2
Factor 0 - 11858/3*x - 52*x**3 - 1/3*x**4 - 2079*x**2.
-x*(x + 2)*(x + 77)**2/3
Let g = 2064 - 2061. Let p(s) = -3*s**2 + 3*s + 2. Let u(m) be the first derivative of -2*m**3/3 + m**2 + 3*m + 1. Let q(w) = g*p(w) - 2*u(w). Factor q(y).
-5*y*(y - 1)
Let s(t) be the third derivative of -8/15*t**5 + 0*t + 3 - 2/105*t**7 + 0*t**3 + 8/3*t**4 - 4*t**2 - 7/30*t**6. Let s(f) = 0. What is f?
-4, 0, 1
Let s(m) be the first derivative of -5*m**4/4 + 130*m**3/3 + 135*m**2/2 - 2257. Determine b so that s(b) = 0.
-1, 0, 27
Suppose -c = -2*c - 4*c - 0*c. Let y(j) be the third derivative of -1/60*j**6 - 1/15*j**5 + c*j + 11/48*j**4 - 1/4*j**3 - 10*j**2 + 0. Factor y(m).
-(m + 3)*(2*m - 1)**2/2
Let i(s) = 2*s**3 - 9*s**2 + 4*s + 3. Let t be i(4). Solve -2*f**4 + t*f**2 + 180*f - 7*f**4 + 149*f**3 - 191*f**3 + 108 = 0.
-3, -2/3, 2
Let a(t) be the third derivative of -t**6/40 - 21*t**5/20 - 21*t**4/2 - 32*t**3 + 3453*t**2. Factor a(d).
-3*(d + 1)*(d + 4)*(d + 16)
Let g(a) = 2*a**3 + 2. Let c(x) = -x**5 + 31*x**4 - 96*x**3 - 2114*x**2 - 3781*x - 1795. Let j(i) = -2*c(i) + 10*g(i). Find h such that j(h) = 0.
-5, -1, 19
Let k = 1304/35 + -916/7. Let p = -93 - k. Find y, given that -6/5*y - p*y**2 - 3/5 = 0.
-1
Let p = -11/282 + 29/141. Suppose 19*x - 26*x = -21. Factor -p - 11/6*z - 15*z**x - 27/2*z**4 - 23/3*z**2 - 9/2*z**5.
-(z + 1)**2*(3*z + 1)**3/6
Let m(w) be the first derivative of -w**4/28 + 5*w**3/7 + 9*w**2/14 - 135*w/7 - 926. Factor m(n).
-(n - 15)*(n - 3)*(n + 3)/7
Let n(k) = -14*k**4 + 25*k**3 + 2731*k**2 + 13375*k + 16272. Let j(c) = -3*c**4 + 5*c**3 + 547*c**2 + 2675*c + 3254. Let g(s) = 11*j(s) - 2*n(s). Factor g(h).
-5*(h - 13)*(h + 2)*(h + 5)**2
Factor 4/3 + 19/3*o + 11/3*o**2 - 4/3*o**3.
-(o - 4)*(o + 1)*(4*o + 1)/3
Suppose 263 - 291 = -14*g. Factor -11/5*z**g - 1/5*z**4 + 0 - 9/5*z**3 - 4/5*z + 1/5*z**5.
z*(z - 4)*(z + 1)**3/5
Suppose 6*m - 33 = -9. Factor -84*q**5 + 160*q**5 - 14*q**m + 20*q**3 - 74*q**5.
2*q**3*(q - 5)*(q - 2)
Find w such that 39/2*w**2 + 12*w**4 + 255/8*w**3 + 9/8*w**5 - 21/2*w + 0 = 0.
-7, -2, 0, 1/3
Factor 3/7*z**4 - 45/7*z**3 + 45/7*z + 183/7*z**2 - 150.
3*(z - 7)*(z - 5)**2*(z + 2)/7
Let z(y) = 10*y**2 + 26446*y + 7528. Let r(w) = 6*w**2 + 13218*w + 3764. Let c(h) = 9*r(h) - 4*z(h). Determine b, given that c(b) = 0.
-941, -2/7
Suppose 12*v + 6*v = 2628. Let m be v/70 + (-14)/49. Factor -12/5 + m*c**2 - 12/5*c + 3/5*c**4 + 12/5*c**3.
3*(c - 1)*(c + 1)*(c + 2)**2/5
Let p = -395 - -385. Let q be ((-18)/(-45))/(12/p)*-9. Solve 2/3*g**2 + 0 + 13/3*g**4 - 4/3*g**5 - 11/3*g**q + 0*g = 0 for g.
0, 1/4, 1, 2
Let g(j) = -136*j + 42. Let n be g(-6). Factor n - q**2 + q - 858.
-q*(q - 1)
Let d(k) be the first derivative of k**7/840 - k**6/160 - k**5/80 + 7*k**4/96 + k**3/4 - 73*k**2/2 + 61. Let h(m) be the second derivative of d(m). Factor h(w).
(w - 3)*(w - 2)*(w + 1)**2/4
Let k = 344 + -342. Let t be (-56)/(-21) - k/3. Determine l, given that 1 - 53/4*l**3 + 8*l - 9*l**4 + 53/4*l**t = 0.
-2, -1/4, -2/9, 1
Suppose 2/3*a**4 + 2392/3*a**2 - 1592/3*a - 802/3*a**3 + 0 = 0. What is a?
0, 1, 2, 398
Suppose -q - 7 = -4*n + 2*n, -17 = -n - 4*q. Let o(h) = -3*h**2 + 20*h - 25. Let c be o(n). Factor 0*t + c*t**4 + 3/4*t**3 + 0*t**2 + 0 - 3/4*t**5.
-3*t**3*(t - 1)*(t + 1)/4
Factor -1838/9*v + 2/9*v**2 - 1840/9.
2*(v - 920)*(v + 1)/9
Factor 121868*p + 52 + p**3 + 1074*p**2 + 29730*p - 52 + 136771*p.
p*(p + 537)**2
Let v = -8860 - -177203/20. Let d(n) be the first derivative of 11/12*n**3 + 27 - 1/24*n**6 + 1/16*n**4 + n - v*n**5 + 3/2*n**2. Factor d(t).
-(t - 2)*(t + 1)**3*(t + 2)/4
Let h(r) be the third derivative of -r**8/112 - 30*r**7/7 - 119*r**6/4 - 89*r**5 - 1185*r**4/8 - 148*r**3 - 28*r**2 + 44. What is j in h(j) = 0?
-296, -1
Solve -l**3 - 40*l**2 + 4*l**3 - 108*l - 8*l**3 + l**3 + 24*l = 0 for l.
-7, -3, 0
Let c(q) be the first derivative of 245*q**6/18 + 427*q**5/3 - 3565*q**4/12 - 4015*q**3/9 + 670*q**2/3 - 100*q/3 - 2209. What is v in c(v) = 0?
-10, -1, 1/7, 2
Let j(f) be the first derivative of 0*f - 19 - 1/28*f**4 + 0*f**2 + 0*f**3. Let j(m) = 0. What is m?
0
Let q(a) be the first derivative of -4*a**3/3 - 2464*a**2/3 - 1517824*a/9 + 2857. Factor q(y).
-4*(3*y + 616)**2/9
Let a(u) = -795*u**4 - 830*u**3 + 1545*u**2 + 45*u. Let o(i) = -397*i**4 - 413*i**3 + 774*i**2 + 22*i. Let d(r) = -2*a(r) + 5*o(r). Solve d(q) = 0 for q.
-2, -2/79, 0, 1
Let b(u) be the first derivative of -2/15*u**3 + 7/5*u**2 - 24/5*u + 135. Find r, given that b(r) = 0.
3, 4
Suppose 191*f = -5*v + 190*f - 12, -2*v - 3*f - 36 = 0. Find i, given that 1/6*i**5 + v - i**4 + 0*i**2 + 3/2*i**3 + 0*i = 0.
0, 3
Let v(q) be the second derivative of -q**6/10 + 57*q**5/10 - 33*q + 23. What is x in v(x) = 0?
0, 38
Let v(q) = q**2 