. Determine g so that 2/5*g + 1/5*g**2 + 1/10*g**o - 2/5*g**3 - 3/10 = 0.
-1, 1, 3
Let o = -328497 + 328500. Suppose -6*f + 0 + 2/5*f**4 + 14/5*f**2 + 14/5*f**o = 0. What is f?
-5, -3, 0, 1
Let o(d) be the second derivative of 3*d**5/5 - 12*d**4 + 298*d**3/9 + 124*d**2/3 + 903*d. Solve o(f) = 0 for f.
-1/3, 2, 31/3
Let n = -111 - -111. Let m be (2/(-4) - n/(-16))*-4. Suppose -4 + 5*b**2 + m*b + 5*b**2 + 6*b**2 - 14*b**2 = 0. Calculate b.
-2, 1
Let b(p) be the third derivative of p**5/270 + 173*p**4/108 + 164*p**3/3 + 10*p**2 + 610*p. Suppose b(h) = 0. Calculate h.
-164, -9
Let v = 253425/13 + -19493. Let -4/13*g**2 + 0 - 2/13*g**3 + v*g = 0. Calculate g.
-4, 0, 2
Let a(d) be the second derivative of d**4/21 + 211*d**3/42 - 53*d**2/14 - 3535*d. Find o such that a(o) = 0.
-53, 1/4
Let q(g) be the second derivative of -g**5/110 + g**4/11 - 3*g**3/11 - 63*g**2/2 - g - 1. Let f(l) be the first derivative of q(l). Factor f(z).
-6*(z - 3)*(z - 1)/11
Suppose 19*f = 14*f + 40. Suppose -5*y + 3*c = -f, -c = y - 3*y + 4. Let 0 - 9/5*v**5 + 9/5*v**3 + 0*v - 3/5*v**2 + 3/5*v**y = 0. Calculate v.
-1, 0, 1/3, 1
Factor 10687 + 19940 - 3295*z + 26505 - 5813*z + 363*z**2.
3*(11*z - 138)**2
Let r(v) be the first derivative of -v**6/9 - 26*v**5/15 - 11*v**4/2 + 154*v**3/9 + 98*v**2/3 - 581. Find t, given that r(t) = 0.
-7, -1, 0, 2
Let z(l) be the first derivative of 2*l**6/3 - 332*l**5/5 + 311*l**4 + 1580*l**3/3 + 4499. Let z(x) = 0. What is x?
-1, 0, 5, 79
Let u(s) be the first derivative of s**6/6 + 199*s**5/5 - 253*s**4 + 1628*s**3/3 - 408*s**2 - 256. Factor u(n).
n*(n - 2)**2*(n - 1)*(n + 204)
Let y(z) = 5*z**4 + 3*z**2. Let q = -158 - -154. Let j(w) = 4*w**4 - w**3 + 3*w**2. Let o(g) = q*j(g) + 3*y(g). Factor o(a).
-a**2*(a - 3)*(a - 1)
Let a = 323 + -321. Determine y, given that 345*y - y**2 + 5*y**a + 363*y - 684*y + 20 = 0.
-5, -1
Let l(m) be the third derivative of -3*m**2 + 0*m**3 + 1/192*m**4 + 1/240*m**5 + 1/960*m**6 + 0 - 20*m. Factor l(j).
j*(j + 1)**2/8
Let f = -379352 - -5690318/15. Let -2/15*t**3 - f*t**2 - 32/3*t + 40/3 = 0. What is t?
-10, 1
Let r(j) = -j**4 + 103*j**3 + 399*j**2 + 497*j + 205. Let u(w) = -3*w**4 + 413*w**3 + 1597*w**2 + 1987*w + 817. Let o(p) = 22*r(p) - 6*u(p). Factor o(d).
-4*(d + 1)**2*(d + 2)*(d + 49)
Let o(y) be the second derivative of y**5/60 + 11*y**4/24 - 2*y**3 + 21*y**2/2 + 55*y. Let m(r) be the first derivative of o(r). Solve m(z) = 0 for z.
-12, 1
Suppose -251 = 97*t + 393 - 838. Let 0 - 2/11*n**t - 70/11*n = 0. What is n?
-35, 0
Let -3/5*c**2 + 1086 - 5427/5*c = 0. What is c?
-1810, 1
Let m be (3/(-15))/(2/(-50)). Factor 3*d**4 - 21*d**3 - 22*d - 5*d**2 - 46*d**2 - m*d.
3*d*(d - 9)*(d + 1)**2
Let r = -669419/9 + 74381. Factor 2/9*g**3 - 14/9 - r*g**2 - 26/9*g.
2*(g - 7)*(g + 1)**2/9
Let d(m) be the third derivative of m**8/1680 + m**7/210 + m**6/90 + 47*m**4/24 - m**3/3 + 4*m**2 + 35. Let h(g) be the second derivative of d(g). Factor h(n).
4*n*(n + 1)*(n + 2)
Suppose 4*p - 48 - 124 = -4*o, p - 121 = -3*o. Suppose -3*f + 4*f - 100 + o*f + 7*f**2 - 2*f**2 = 0. What is f?
-10, 2
Let v = -1169 + 1172. Let j(f) be the third derivative of v*f**2 + 0 - 1/450*f**5 - 1/180*f**4 + 2/45*f**3 + 0*f. Factor j(x).
-2*(x - 1)*(x + 2)/15
Suppose t = 7*a - 2*a - 18, 5*t + 5*a - 30 = 0. Solve 6*m - 2936*m**3 + 2*m**t + 2*m + 2930*m**3 = 0.
-1, 0, 4/3
Let t = 168 - 98. Suppose k**3 + k**2 + t - 2*k**2 - 18 - 7 - 21*k = 0. Calculate k.
-5, 3
Let h(f) be the first derivative of -16/7*f + 259 + 1/7*f**4 + 4/21*f**3 - 8/7*f**2. Let h(d) = 0. What is d?
-2, -1, 2
Let z(k) be the second derivative of 3*k**5/25 - 39*k**4/20 - 53*k**3/5 - 36*k**2/5 - 32*k - 2. Factor z(c).
3*(c - 12)*(c + 2)*(4*c + 1)/5
Let h(c) be the first derivative of -c**4/2 - 34*c**3/3 - 52*c**2 + 2098. Suppose h(z) = 0. Calculate z.
-13, -4, 0
Let t(o) be the second derivative of 1 + 0*o**3 + 0*o**2 + 12*o + 3/4*o**5 + 5/12*o**4. Find n, given that t(n) = 0.
-1/3, 0
Let u(z) = -z**3 + 3*z**2 + 12*z - 27. Let f be u(4). Suppose f*n + 192 = 53*n. Factor n*k - 8/7 - 20/7*k**2.
-4*(k - 1)*(5*k - 2)/7
Factor 32 - 15*w - 1/2*w**2.
-(w - 2)*(w + 32)/2
Let o(q) = q**3 + 2*q**2 - 1. Let t(y) = -3*y**5 + 12*y**4 + 9*y**3 + 36*y**2 - 18. Suppose -2*z - 38 + 74 = 0. Let j(h) = z*o(h) - t(h). Factor j(i).
3*i**3*(i - 3)*(i - 1)
Let s(a) be the third derivative of a**7/3360 - a**6/720 + a**5/480 - 29*a**3/2 + 80*a**2. Let x(u) be the first derivative of s(u). Factor x(m).
m*(m - 1)**2/4
Let x = 65/1484 + 8579/7420. Factor x + 3/5*p**3 - 3/5*p**2 - 7/5*p + 1/5*p**4.
(p - 1)**2*(p + 2)*(p + 3)/5
Suppose -4*k + 25 = k. Suppose 2*l - k = -c - 4, -4*c - 3*l + 9 = 0. Factor 9*v + 9*v**2 - 34 + 67 - 30 + 3*v**c.
3*(v + 1)**3
Let z(f) = -21*f - 1572. Let y be z(-75). Let v(r) be the first derivative of 5/4*r - 3/4*r**2 + 15 + 1/12*r**y. Factor v(d).
(d - 5)*(d - 1)/4
What is c in 0*c - 2/3*c**5 - 16/3*c**4 + 0 - 8*c**2 - 38/3*c**3 = 0?
-4, -3, -1, 0
Let n(g) be the second derivative of 0*g**2 - 36 - 1/220*g**5 - 7/66*g**4 - 13/66*g**3 + g. Suppose n(j) = 0. Calculate j.
-13, -1, 0
Let m(o) be the second derivative of o**7/42 + 11*o**6/15 + 141*o**5/20 + 82*o**4/3 + 104*o**3/3 - 2388*o. Solve m(c) = 0.
-13, -4, -1, 0
Let p = -109 + 113. Factor -58*u**3 + 13*u**4 + 4*u**5 + 26*u**2 - 25*u**p + 30*u**3 + 72*u + 34*u**2.
4*u*(u - 3)**2*(u + 1)*(u + 2)
Let b = 4716669/4 + -1179167. Let i = 1/8 + 3/8. Factor 0*z + 0 - i*z**5 + 2*z**3 - 5/4*z**2 - b*z**4.
-z**2*(z - 1)**2*(2*z + 5)/4
Let u(l) be the second derivative of -33 + 40*l**2 - 10/3*l**4 + 0*l**3 + 1/6*l**6 + 0*l**5 + 2*l. Factor u(a).
5*(a - 2)**2*(a + 2)**2
Suppose 87*j - 52*j = 6580. Let j - 528*h**2 - 179 + 20*h**3 - 1361 + 3588*h = 0. What is h?
2/5, 13
Determine g, given that -3/7*g**2 - 129*g + 0 = 0.
-301, 0
Factor -2/17*n**2 - 52/17 - 54/17*n.
-2*(n + 1)*(n + 26)/17
Let l(x) = 773*x + 1546. Let m be l(-2). Let q(g) be the second derivative of m + 2*g**2 - 1/3*g**4 - 32*g - g**3. Determine f so that q(f) = 0.
-2, 1/2
Let d(f) be the first derivative of 4*f**3/3 - 180*f**2 + 1044*f + 6514. What is r in d(r) = 0?
3, 87
Suppose 74*m + 1 = -2*d + 69*m, 5*m = 4*d - 13. Determine c so that -12/5*c + 8/5*c**3 + 4/5 + 4/5*c**5 - 12/5*c**4 + 8/5*c**d = 0.
-1, 1
Let r(m) be the third derivative of m**8/560 - m**7/280 - m**6/60 + 92*m**3/3 + 9*m**2. Let a(n) be the first derivative of r(n). Solve a(j) = 0.
-1, 0, 2
Let r = 321742 - 321739. Find p such that 1/8*p**r + 0*p + 0 - 3/8*p**2 = 0.
0, 3
Let j = -710447/9 + 78941. Factor -j*w + 2/9*w**3 - 4/3 - 8/9*w**2.
2*(w - 6)*(w + 1)**2/9
Let t(b) be the second derivative of -b**4/24 - 217*b**3/6 + 435*b**2/4 - 33*b - 3. Solve t(k) = 0.
-435, 1
Suppose -1495 = -24*d - 13*d - 1421. Find s, given that -2 - 165/2*s**d + 24*s + 121/2*s**3 = 0.
2/11, 1
Suppose 5*n - 98 = 4*x + 69, -2*x + 4*n - 76 = 0. Let u be 58/28 + x/84. Factor 9/2*r + 27/2 + u*r**3 - 15/2*r**2.
3*(r - 3)**2*(r + 1)/2
Factor -253/9*v - 50/3 + 95/9*v**2 + 2/9*v**3.
(v - 3)*(v + 50)*(2*v + 1)/9
Let a(r) be the first derivative of -91 + 0*r - 9/2*r**2 + 11/2*r**3. Factor a(y).
3*y*(11*y - 6)/2
Let 90*c - 361/4 + 1/4*c**2 = 0. Calculate c.
-361, 1
Let p(j) be the third derivative of j**5/120 - 81*j**4/16 - 61*j**3/3 - 2327*j**2. Let p(t) = 0. Calculate t.
-1, 244
Solve -8*z**5 - 518*z**2 - 3576*z**3 - 2930*z**2 - 322*z**4 - 3202*z**2 - 1444*z = 0.
-19, -2, -1/4, 0
Let w(n) be the first derivative of 5*n**6/2 - 4*n**5 - 10*n**4 + 10*n**3 + 25*n**2/2 - 10*n + 1113. Determine k, given that w(k) = 0.
-1, 1/3, 1, 2
Suppose 3*g + g - 694 + 794 = 27*l, 0 = 2*l - 5*g + 2. Let y be ((-3)/4)/(2/(-8)). Factor -4/3*j**y + 2/3*j**l + 0 + 0*j + 2/3*j**2.
2*j**2*(j - 1)**2/3
Let y(f) be the second derivative of f**7/35 + 4*f**6/15 + 17*f**5/50 - 28*f**4/15 + 16*f**3/15 - 133*f. Determine b, given that y(b) = 0.
-4, 0, 1/3, 1
Let m(w) = w**3 - 11*w**2 - 6*w - 42. Let a be m(12). Let l be ((-102)/(-153))/(4/a). Factor -3/2*u**3 - 1/2*u**2 - 3/2*u**4 + 0*u - 1/2*u**l + 0.
-u**2*(u + 1)**3/2
Suppose 0 = 136*k - 123*k - 52. Factor 30*o**3 + 459*o**k - 22*o**3 - 6*o - 456*o**4 - 5*o**2.
o*(o - 1)*(o + 3)*(3*o + 2)
Suppose 2*k - 34 = -x, 5*k + x = 5*x + 59. Let y = k + -12. Factor -4*g**3 + 8*g**y - 20*g**2 + 32*g - 8*g.
4*g*(g - 3)*(g - 2)
Determi