at is k?
-28, -6
Let f(p) be the third derivative of -3/8*p**3 + 0 + 167*p**2 + 1/240*p**5 + 0*p + 0*p**4. Find g such that f(g) = 0.
-3, 3
Let i(d) = -84*d**3 + 139*d**2 - 64*d + 12. Let t(k) = -84*k**3 + 136*k**2 - 60*k + 10. Let c(g) = 2*i(g) - 3*t(g). Factor c(r).
2*(r - 1)*(3*r - 1)*(14*r - 3)
Let t = 18/787283 + 61742637/124390714. Let q = t + 2/553. What is j in -q*j**3 - 5/4*j**2 + 1/2 - 1/4*j = 0?
-2, -1, 1/2
Factor -706/15*i + 4/15 - 142/3*i**2.
-2*(i + 1)*(355*i - 2)/15
Let g = -76 - -81. Suppose 3*m + g*y - 52 = 0, m + 58 = 4*m - y. Find w such that -34*w - m*w**2 - 5 + 9*w**2 - 7 = 0.
-3, -2/5
Let c(v) = -v + 1. Let f = -64 + 72. Let z(d) = -d + 3. Let q be z(f). Let l(u) = -3*u**2 - 9*u + 4. Let n(a) = q*c(a) + l(a). Let n(p) = 0. What is p?
-1, -1/3
Let k(t) be the first derivative of -14/3*t + 1/6*t**3 - 10/3*t**2 + 140. Factor k(o).
(o - 14)*(3*o + 2)/6
Let b(v) = -14*v**3 - 2*v**2 + 186*v - 274. Let x(c) = -5*c**3 - c**2 + 64*c - 92. Let w(a) = -4*b(a) + 11*x(a). Factor w(p).
(p - 7)*(p - 2)*(p + 6)
Solve 7/6*f**4 + 83/6*f**3 - 70/3 - 1/2*f**5 - 32/3*f + 39/2*f**2 = 0.
-2, -5/3, 1, 7
Let x be -1 + -1 + (-16)/(-18)*(-1647)/(-366). Suppose -16/5*k**x + 0*k + 0 + 4/5*k**4 - 16/5*k**3 + 4/5*k**5 = 0. Calculate k.
-2, -1, 0, 2
Let l be 353/(-5) - (2/5 + -1). Let g be ((-24)/l - (-19)/(-95))*10. Suppose -36/7*a**2 + g*a**3 + 2*a + 12/7 = 0. Calculate a.
-2/5, 1, 3
Let p(f) = -12*f**3 + 645*f**2 - 4608*f - 5175. Let i(g) = -9*g**3 + 486*g**2 - 3456*g - 3881. Let j(u) = 9*i(u) - 7*p(u). Let j(h) = 0. What is h?
-1, 12, 36
Suppose 102 + 18 = 2103*o - 2083*o. Suppose -37/5*q**2 + o*q**3 + 4*q - 4/5 - 9/5*q**4 = 0. What is q?
2/3, 1
Let l be (33 + 0)*38/(-3). Let n = 420 + l. Factor 5 - n*k + 1/5*k**2.
(k - 5)**2/5
Suppose 0 = 3*p - 4*p - 111. Let b be (p/4)/(30/(-40)). Suppose -4*v + b*v**2 - 66*v**2 + 33*v**2 = 0. What is v?
0, 1
Let v(m) = -m**3 - 2*m**2 - m + 2. Let z(x) = 18*x**3 + 34*x**2 + 17*x - 34. Let q(t) = 35*v(t) + 2*z(t). Factor q(n).
(n - 2)*(n - 1)*(n + 1)
Let t(u) be the third derivative of 0*u**3 + 0*u + 1/30*u**5 + 1/30*u**4 + 5 + 3*u**2. Suppose t(p) = 0. Calculate p.
-2/5, 0
Let z be (2*15/(-280))/((-91)/728). Factor 26/7*o + 20/7 - z*o**2 + 2/7*o**4 - 10/7*o**3.
2*(o - 5)*(o - 2)*(o + 1)**2/7
Let 144/5*b**2 + 3/5*b**3 + 0*b + 0 = 0. What is b?
-48, 0
Let o be 9 - 28/(84/9). Let y(v) be the third derivative of 1/72*v**5 + 0*v**o + 0*v**4 + 0 - 1/9*v**3 + 0*v - 1/1260*v**7 - 30*v**2. Solve y(u) = 0.
-2, -1, 1, 2
Let y = 13/34687 + 34661/69374. Solve 2809/2*h**2 - 2915/2*h**3 + 0*h + 0 + 107/2*h**4 - y*h**5 = 0.
0, 1, 53
Suppose 0 = 14*j + 14 - 84. Let z(d) be the third derivative of 1/735*d**7 + 0*d + 0 + 0*d**4 + 15*d**2 + 1/210*d**6 + 1/210*d**j + 0*d**3. Factor z(o).
2*o**2*(o + 1)**2/7
Let g(t) = -t**3 + t**2. Let k(n) = 2*n**2 - 596*n**3 + 5*n**2 + n**4 + n + 590*n**3 - 3*n**2. Let o(h) = 5*g(h) - k(h). Factor o(y).
-y*(y - 1)**2*(y + 1)
Suppose 68 = -3*n + 4*q, n + 3*q + 27 + 0 = 0. Let s(y) = y**2 + 1. Let k(i) = -36*i**2 - 112*i + 56. Let b(d) = n*s(d) - k(d). Solve b(v) = 0 for v.
-10, 2/3
Let l = -13505 + 13511. Let t(p) be the second derivative of 0 - 11*p + 2/3*p**2 + 1/252*p**7 - 1/36*p**4 - 1/30*p**l - 1/3*p**3 + 11/120*p**5. Factor t(j).
(j - 2)**3*(j - 1)*(j + 1)/6
Let y(w) be the second derivative of w**7/315 - w**6/225 - 2*w**5/5 - 6*w**4/5 + 1313*w. Determine d, given that y(d) = 0.
-6, -2, 0, 9
Let q(s) be the second derivative of -s**6/45 - 262*s**5/15 + 1051*s**4/18 - 526*s**3/9 - 2*s - 1229. What is j in q(j) = 0?
-526, 0, 1
Let z be (-3 + 4 - 1)/(4/2). Let b(t) be the second derivative of -3/20*t**5 - 10/3*t**3 + 7/6*t**4 + 4*t**2 + 15*t + z. Factor b(p).
-(p - 2)**2*(3*p - 2)
Factor -12 + 2 + 129548*l**3 - 129601*l**3 + 316*l**2 - 253*l.
-(l - 5)*(l - 1)*(53*l + 2)
Let w(q) = 3*q**3 - 6*q**2 + 4*q - 3. Let c be w(2). Suppose -22*r + 5 = c. Factor 0 + 5/2*u - 5/2*u**3 + r*u**2.
-5*u*(u - 1)*(u + 1)/2
Let o(u) = 2*u + 4. Let g be (-14)/3*(-3)/2. Let f be o(g). Factor 22*q - 3*q**4 + 31 - 4*q - 4 - 8*q**2 - f*q**3 - 16*q**2.
-3*(q - 1)*(q + 1)*(q + 3)**2
Let u(i) be the third derivative of -i**5/140 + 27*i**4/56 + 29*i**3/7 + 152*i**2 - 2*i. Factor u(p).
-3*(p - 29)*(p + 2)/7
Let f(o) be the first derivative of -o**4/32 - 10*o**3/3 - 157*o**2/16 - 39*o/4 - 2272. Factor f(a).
-(a + 1)**2*(a + 78)/8
Let x(m) = 18*m**5 - m**2 + m**3 + 2*m - m - 17*m**5. Let v(l) = 3*l**5 + 14*l**4 - 5*l**3 - 19*l**2 + 17*l. Let g(w) = -v(w) + 5*x(w). Factor g(o).
2*o*(o - 6)*(o - 1)**2*(o + 1)
Let y be (217/(-35) + 7)/(66/1705). Find f, given that 17*f + 10/3 + y*f**2 + 7*f**3 = 0.
-5/3, -1, -2/7
Let t(w) be the first derivative of 9 + 0*w - 3*w**2 + 1/10*w**4 + 1/150*w**5 + 1/3*w**3. Let h(k) be the second derivative of t(k). Factor h(m).
2*(m + 1)*(m + 5)/5
Suppose 21*a - 40 - 2 = 0. Determine k so that 2*k**3 - 7*k**2 + k**4 + 9*k + 5*k**2 + k**a - 11*k = 0.
-2, -1, 0, 1
Let c(m) be the first derivative of -m**9/6048 - m**8/840 - m**7/420 - 10*m**3/3 - 7. Let v(b) be the third derivative of c(b). Factor v(l).
-l**3*(l + 2)**2/2
Suppose -5*m - 1 + 6 = 0. Let k be (-3 + -3 + 8)*m. Factor -4*z**4 + 3*z**3 + 17*z**3 + 12*z + 8*z**4 + 28*z**k.
4*z*(z + 1)**2*(z + 3)
Solve 8 - 46/3*q**3 - 136/3*q + 3/2*q**4 + 136/3*q**2 = 0 for q.
2/9, 2, 6
Let u be (4 - 5)/(4/(-8)). Let t be (-4*u/(-12))/(10/450). Let -39 + t - c**2 - 7*c + c = 0. What is c?
-3
Let a(s) be the third derivative of s**7/840 + s**6/120 - s**5/120 - s**4/8 + 3*s**3/8 - 168*s**2 + s. Factor a(l).
(l - 1)**2*(l + 3)**2/4
Let l = -511 - -596. Suppose -24*o + l = -11. Solve 4/5*b**2 + 0*b + 4/5*b**5 - 4/5*b**o + 0 - 4/5*b**3 = 0 for b.
-1, 0, 1
Let d(u) be the first derivative of -u**4/24 - u**3/12 + u**2/2 + 41*u + 44. Let n(s) be the first derivative of d(s). Determine g, given that n(g) = 0.
-2, 1
Let -10/3*n + 28/9 + 2/9*n**2 = 0. What is n?
1, 14
Let v be ((-20)/(-6))/2 + 51656/3522. What is s in 14/3*s + v + 1/3*s**2 = 0?
-7
Let a(i) = 11*i**2 + 188*i + 20. Suppose 116 = -9*n - 37. Let j be a(n). Find c such that 4/7*c + 4/7 - 4/7*c**2 - 4/7*c**j = 0.
-1, 1
Suppose -7*t = -5080 + 971. Factor -2*g**4 - 3 + 4*g + 3*g**5 + 3 - 596*g**3 + t*g**3.
g*(g - 2)*(g + 1)**2*(3*g - 2)
Let l(k) be the second derivative of -31*k**5/40 + 2*k**4/3 - 47*k + 8. Solve l(z) = 0 for z.
0, 16/31
Let h = -21297 - -21299. Let w(q) be the third derivative of -36*q**h + 0*q - 2/5*q**3 - 9/200*q**6 + 0 + 11/100*q**5 + 2/5*q**4. Factor w(c).
-3*(c - 2)*(c + 1)*(9*c - 2)/5
Let g(k) be the second derivative of 1/45*k**6 + 2/9*k**4 - 15*k - 5/3*k**2 + 1/5*k**5 - 2/3*k**3 + 2. Factor g(v).
2*(v - 1)*(v + 1)**2*(v + 5)/3
Let h = -228046 - -684146/3. Let 2/9*z**2 + h*z + 40/9 = 0. Calculate z.
-10, -2
Let b(z) be the first derivative of z**5/5 + 25*z**4/4 + 73*z**3 + 783*z**2/2 + 972*z + 2278. Find r such that b(r) = 0.
-9, -4, -3
Suppose -92 = -6*q - 40*q. Factor -4 - 30*g + 46*g - 4*g**2 + q + 2.
-4*g*(g - 4)
Let g = 207251/45 - 23024/5. Let r(d) be the first derivative of 5/12*d**4 - 5 + 1/2*d**2 - g*d**3 - 1/15*d**5 + 0*d. Factor r(l).
-l*(l - 3)*(l - 1)**2/3
Let x(b) = -2*b**3 - 38*b**2 - 35*b + 27. Let p be x(-18). Let a be 7 - (24/(-9))/((-6)/p). Suppose -2*f**a + 6/5*f**2 + 2/5*f**4 - 8/5 + 2*f = 0. What is f?
-1, 1, 4
Let c = -177592 - -710369/4. Factor c*h**2 + 1/2 + 3/4*h.
(h + 1)*(h + 2)/4
Let m be (-12)/(-15)*((-6)/(-18))/(30/225). Let n(s) be the first derivative of 1/5*s**5 + m*s**2 + 2*s**3 + s + 2 + s**4. Factor n(u).
(u + 1)**4
Let d(z) be the second derivative of z**6/40 + 63*z**5/40 - 33*z**4/4 + 67*z**3/4 - 135*z**2/8 - 2752*z. Factor d(r).
3*(r - 1)**3*(r + 45)/4
Let o(j) = -69*j**2 - 14017*j - 41. Let z(g) = -5*g**2 - 1001*g - 3. Let f(s) = 6*o(s) - 82*z(s). Factor f(p).
-4*p*(p + 505)
Factor 22/13*v**2 + 0*v - 20/13*v**3 + 0 - 2/13*v**4.
-2*v**2*(v - 1)*(v + 11)/13
Let s be (16/32)/((-2)/(-12)*120/504). What is w in s*w**2 + 18/5 + 27/5*w**3 + 3/5*w**4 + 57/5*w = 0?
-6, -1
Let h(g) be the third derivative of -g**6/24 - 371*g**5/60 - 6919*g**4/24 - 1369*g**3/6 + 7807*g**2. Let h(l) = 0. Calculate l.
-37, -1/5
Let y(v) = 41*v + 515. Let u be y(-13). Let b(i) = -i**3 - 21*i**2 - 53*i + 20. Let o be b(u). Factor 3/4*s - 1/4*s**o - 1/2.
-(s - 2)*(s - 1)/4
Let j(