et k(v) = -7*v**2 + 6*v - 15. Let d(h) = j*k(h) - 6*i(h). Factor d(z).
-2*(z - 6)*(z - 3)
Let l = -146263 - -146265. Let -2/7*t**l - 20*t - 350 = 0. What is t?
-35
Let o = -63896/3 + 21320. Let y(m) be the first derivative of -3*m**4 + o*m**3 - 44/5*m**5 + 3 + 0*m + 8/3*m**6 + 8*m**2. Let y(a) = 0. What is a?
-1, -1/4, 0, 2
Suppose 0 = 5*k + 4*b - 108, 4*k + 3*b - 34 = 53. Suppose 50*s - 42*s = k. Find z such that z**2 + 0 + z**5 + s*z**3 - 15/4*z**4 + 0*z = 0.
-1/4, 0, 2
Let f = 1256655/279254 + -6/139627. Let -5/2*v**2 + 0*v - f*v**3 + 0 + v**4 = 0. Calculate v.
-1/2, 0, 5
Let v(b) be the first derivative of b**4/16 + 17*b**3/36 + b**2/3 - 4*b + 1063. Suppose v(t) = 0. What is t?
-4, -3, 4/3
Let s(f) be the first derivative of 3/4*f + 1/8*f**6 - 3/8*f**4 + 6 + 3/20*f**5 + 3/8*f**2 - 1/2*f**3. Factor s(c).
3*(c - 1)**2*(c + 1)**3/4
Suppose 7*v - 96 - 2 = 0. Factor -v*k - 6*k**2 + 19*k**4 - 5*k**5 + 2*k**5 + 17*k - 13*k**4.
-3*k*(k - 1)**3*(k + 1)
Let b be (-12)/42 - (-172)/112. Let a(u) be the first derivative of 15/2*u**2 + 10*u - 37 + 0*u**3 - b*u**4. Determine r, given that a(r) = 0.
-1, 2
Let c(t) be the second derivative of -t**5/120 + 21*t**4/8 - 1323*t**3/4 + 28*t**2 - 70*t - 1. Let d(i) be the first derivative of c(i). What is j in d(j) = 0?
63
Let t(j) be the third derivative of 29*j**6/32 + 89*j**5/24 + 475*j**4/96 + 5*j**3/6 + 493*j**2. Suppose t(y) = 0. What is y?
-1, -4/87
Let f(n) be the third derivative of n**10/15120 - n**9/1890 + n**8/672 - n**7/630 - 9*n**4/4 - 40*n**2. Let c(x) be the second derivative of f(x). Factor c(g).
2*g**2*(g - 2)*(g - 1)**2
Let c(f) be the third derivative of 0 - 27/4*f**3 - 1/1680*f**7 + 33/16*f**4 - 37*f**2 + 11/480*f**6 + 0*f - 157/480*f**5. Factor c(i).
-(i - 9)**2*(i - 2)**2/8
Let p(t) be the first derivative of t**5/5 + 58*t**4 - 78*t**3 - 116*t**2 + 233*t - 1694. Determine v, given that p(v) = 0.
-233, -1, 1
Let d be ((-27)/(-72))/((-3)/5 - 4617/(-5670)). Let s(q) be the second derivative of 2*q + 0 - d*q**2 + 7/24*q**4 - 1/6*q**3 + 1/20*q**5. Factor s(o).
(o - 1)*(o + 1)*(2*o + 7)/2
Let m(f) be the first derivative of 144*f**3 - 3 + 6/5*f**5 + 1/30*f**6 + 13*f + 18*f**4 + 648*f**2. Let t(z) be the first derivative of m(z). Factor t(b).
(b + 6)**4
Let z(u) = -4*u**2 - 10*u. Let i be (16*(-2)/(-4))/2. Let g(k) = -8*k**2 + 4 - 8 + i - 19*k. Let l(f) = 6*g(f) - 11*z(f). Find r such that l(r) = 0.
-1, 0
Let s(p) be the third derivative of p**5/160 + 19*p**4/32 - 39*p**3/16 + 36*p**2 + 1. Factor s(k).
3*(k - 1)*(k + 39)/8
Solve 0*m + 59/2*m**3 + 1/2*m**4 + 0*m**2 + 0 = 0 for m.
-59, 0
Suppose 24 = 3*v + 6*f - 11*f, 4*v = -3*f + 3. Let g(m) be the second derivative of -1/3*m**v + 0*m**2 + 0*m**4 + 0 - 14*m + 1/10*m**5. Factor g(z).
2*z*(z - 1)*(z + 1)
Let p be 950/1140 + 4/(-24). Factor 12*g**2 - 2*g**3 + 0*g + 0 + p*g**5 - 8/3*g**4.
2*g**2*(g - 3)**2*(g + 2)/3
Let c(m) = 2*m**3 - m**2 - 1. Let p(j) = -4*j**4 - 64*j**3 - 326*j**2 + 84*j + 310. Let l(d) = -10*c(d) + p(d). What is u in l(u) = 0?
-16, -5, -1, 1
Let y(c) = -136*c + 1088. Let a be y(8). Factor a - 2*m - 1/6*m**2.
-m*(m + 12)/6
Let h = -101 + -3. Let z be h*((-68)/32*2 - -3). Find o, given that 87*o**4 + 15*o**3 - z*o**4 + o**2 - 64*o**5 + 91*o**4 = 0.
-1/8, 0, 1
Let a(j) be the second derivative of -j**6/110 + 43*j**5/220 - j**4/12 - 43*j**3/66 + 7*j**2/11 + 1524*j. Let a(k) = 0. What is k?
-1, 1/3, 1, 14
Factor 1053*w - 2176*w - w**3 + 16*w**4 - 300*w**2 + 1051*w - 43*w**3.
4*w*(w - 6)*(w + 3)*(4*w + 1)
Let w(c) be the first derivative of -c**5/140 + 3*c**4/7 + 25*c**3/14 - 65*c**2/2 + 204. Let n(k) be the second derivative of w(k). Factor n(i).
-3*(i - 25)*(i + 1)/7
Let n(g) be the first derivative of g**4/4 - 11*g**3/3 + 5*g**2 + 72*g + 447. Factor n(w).
(w - 9)*(w - 4)*(w + 2)
Let b(d) = 2*d**4 + 24*d**3 + 2*d**2 - 14*d. Let s(o) = -o**4 - 8*o**3 - o**2 + 5*o. Let y = -63 + 58. Let c(x) = y*b(x) - 14*s(x). Factor c(q).
4*q**2*(q - 1)**2
Suppose 4*u - 34*y + 29*y = 1469, -5*u + 1825 = 5*y. Let v = u + -365. Factor -11/6*t - v + 1/3*t**2.
(t - 6)*(2*t + 1)/6
Let w = 94/85 - 12/17. Let z = -3550976 - -17754884/5. Factor 0 + z*g + w*g**3 - 6/5*g**2.
2*g*(g - 2)*(g - 1)/5
Let f be (2/(-6))/(25/(-7475)). Let c = -99 + f. Find o such that 0 + 3*o**2 - c*o - 7/3*o**3 = 0.
0, 2/7, 1
Let x = 765 + -762. Suppose 28*p - 23*p + 3*t - 3 = 0, 2*p + x = 3*t. Factor 1/7*h + p + 1/7*h**2.
h*(h + 1)/7
Let g = -422 + 682. Let t be g/198 + 146/(-657). Solve 0 + 0*b + t*b**3 + 2/11*b**4 + 18/11*b**2 = 0.
-3, 0
Let i(b) be the third derivative of 0 + 1/22*b**4 + 7/33*b**3 - 1/330*b**5 - 68*b**2 + 0*b. Factor i(n).
-2*(n - 7)*(n + 1)/11
Factor 18*a**3 + 23*a**3 + 329*a**4 + 331*a**4 - 661*a**4.
-a**3*(a - 41)
Factor 8*x**3 - 5*x**3 - 1296*x + 4212 + 0*x**3 + 0*x**3 + 81*x**2.
3*(x - 6)**2*(x + 39)
Let o(j) be the third derivative of 9*j**6/160 + 111*j**5/10 + 589*j**4/32 + 49*j**3/4 - 1882*j**2. Find l such that o(l) = 0.
-98, -1/3
Let r(y) be the first derivative of 25/2*y**2 - 5/12*y**4 - 10/3*y**3 - 7*y + 2. Let h(n) be the first derivative of r(n). Suppose h(c) = 0. Calculate c.
-5, 1
Let m be ((-121500)/945)/(3/(-14)). Let p be (4/7 - 0)/(m/1680). Solve -1/5*o**3 + 0 - 2/5*o**2 + p*o = 0.
-4, 0, 2
Let t(k) be the second derivative of -5/42*k**7 + k**5 + 0*k**3 + 0 + 0*k**4 - 11*k + 0*k**2 - 1/2*k**6. Determine q so that t(q) = 0.
-4, 0, 1
Let s(x) be the second derivative of -x**5/20 - 2*x**4 + 27*x**3/2 - 2275*x. Let s(r) = 0. What is r?
-27, 0, 3
Let g(i) be the second derivative of 2 + 4/9*i**2 + 108*i + 8/27*i**3 + 1/18*i**4 - 1/45*i**5 - 1/135*i**6. Solve g(c) = 0 for c.
-2, -1, 2
Let q(g) be the second derivative of -2*g - 24 - 1/30*g**6 + 0*g**3 + 3/10*g**5 - 3/4*g**4 + 0*g**2. Factor q(u).
-u**2*(u - 3)**2
Suppose 1750 = 6*d - 2*d + 5*f, -5*d + f = -2202. Let l be 8/(-18) - d/(-180). Suppose 2/9*j**3 + 4/9*j**l + 2/9*j + 0 = 0. Calculate j.
-1, 0
Suppose v + 4*q = -11, -4*q - 8 - 6 = -2*v. Let h be -1*(5 - v - 8). Find l, given that 19*l + 3*l**2 - 4 + 2*l - 24 + h = 0.
-8, 1
Let z(w) = -3*w**2 - 6*w - 36. Let a(q) = -q - 197 + 179 - 2*q - 2*q**2. Let v(n) = -5*a(n) + 3*z(n). Let v(x) = 0. What is x?
-3, 6
Find a such that -6/11*a**3 - 210/11*a - 100 + 166/11*a**2 - 2/11*a**4 = 0.
-11, -2, 5
Let i(d) = -d**3 - 3*d**2 - 6*d. Let r be i(-2). Factor 37*h**3 + 2*h**2 - r*h**2 - 36*h**3 - 2*h**2 - 20*h.
h*(h - 10)*(h + 2)
Let x(m) be the third derivative of 169*m**8/840 - 247*m**7/175 - 2111*m**6/150 - 2536*m**5/75 - 168*m**4/5 - 256*m**3/15 - 2323*m**2. Let x(w) = 0. What is w?
-2, -1, -4/13, 8
Suppose -4*i - 2*h + 58 = 0, -3*h - 2 = 1. Let j(x) = -714*x**2 + 411*x - 72. Let o(m) = 102*m**2 - 59*m + 10. Let l(f) = i*o(f) + 2*j(f). Factor l(q).
3*(2*q - 1)*(17*q - 2)
Let x(z) be the first derivative of -z**6/4 + 7*z**5/12 - 5*z**4/24 - 9*z**2/2 + 2*z + 14. Let n(h) be the second derivative of x(h). Find k such that n(k) = 0.
0, 1/6, 1
Let l be (-64)/(-24) + 10/(-15). Solve -58*c**2 - 52*c**l + 108*c + 162*c**2 - 56*c**2 = 0 for c.
0, 27
Let z = 165 + -160. Factor -2*f**5 - 8*f**z - 4*f**5 + 12*f**5 + 4*f**4.
-2*f**4*(f - 2)
Let x(f) = 19*f**3 - 1434*f**2 + 2837*f - 1448. Let p(a) = -3*a**3 + 239*a**2 - 473*a + 241. Let n(c) = 65*p(c) + 10*x(c). Factor n(z).
-5*(z - 237)*(z - 1)**2
Factor 3/7*o**3 + 24/7 + 6*o + 3*o**2.
3*(o + 1)*(o + 2)*(o + 4)/7
Solve 5*r**4 + r**5 + 11*r**3 - 2*r**3 - 4380*r**2 + 4387*r**2 + 2*r = 0.
-2, -1, 0
Suppose -3*b + 38 - 47 = 0. Let r be ((-7)/(-2) - 8)*10/b. Suppose 1394*j**3 - 492*j + 2197 - 1395*j**3 + 39*j**2 - r*j = 0. Calculate j.
13
Let 308*o**3 + 41*o**4 + 43*o**4 - 127*o**4 + 42*o**4 - 415*o**2 + 108*o**3 = 0. What is o?
0, 1, 415
Let m(p) be the second derivative of 0 - 3/80*p**5 + 3/2*p**3 + 60*p - 11/16*p**4 + 0*p**2. Factor m(o).
-3*o*(o - 1)*(o + 12)/4
Let a(l) be the third derivative of -l**6/180 + l**5/12 - 53*l**3/6 - 49*l**2. Let j(r) be the first derivative of a(r). Factor j(g).
-2*g*(g - 5)
Suppose 35*p - 132 = 13*p. Let j be 3 + 4/p + 3/(-3). What is s in -j*s + 2/3 + 25/6*s**2 - 1/6*s**5 - 19/6*s**3 + 7/6*s**4 = 0?
1, 2
Factor -24*h**4 + 75*h**2 - 307*h**3 + 267*h**3 + 29*h**4.
5*h**2*(h - 5)*(h - 3)
Let c be 8/56*1 - (-244)/7. Suppose 0 = -3*m - 2*g, -c*m + 4*g = -32*m - 18. Find h such that 