 - 2)/13
Let k = -394318 - -394321. Suppose -5/3*t**4 + 14/3*t**2 + 2/3*t**k - t - 3 + 1/3*t**5 = 0. Calculate t.
-1, 1, 3
Let y be (177/(-295))/((-18)/(-20))*(-65)/26. Factor y*g**2 + 0 - 25*g.
5*g*(g - 15)/3
Let w be (15 - 15 - (-2)/4)*-12. Let c be (13/104)/((-1)/w). Suppose -b - 1/4*b**2 - c = 0. What is b?
-3, -1
Factor 4/5*l + 1/5*l**2 - 1.
(l - 1)*(l + 5)/5
Suppose -2*a - 3*a = -5*n, -3*a - 12 = 3*n. Let l be (-126)/(-35) + (1 - a)*-1. Suppose 0 - l*r**2 - 3/5*r**3 + 3/5*r**5 + 0*r + 3/5*r**4 = 0. Calculate r.
-1, 0, 1
Suppose 216 = -8*h + 14*h. Factor 0*s**2 + 140 + h*s - 302 - 2*s**2.
-2*(s - 9)**2
Let t(o) = -o**3 - o**2 + 1. Let m(x) = -x**4 + 6*x**3 - 20*x**2 - 27*x + 5. Let y(v) = -m(v) + 5*t(v). Factor y(r).
r*(r - 9)*(r - 3)*(r + 1)
Let o = -52018 - -104037/2. Factor -5/4*h + 1/4*h**3 - o*h**2 + 3/2.
(h - 3)*(h - 1)*(h + 2)/4
Factor 776/7 + 2/7*k**3 + 384/7*k - 390/7*k**2.
2*(k - 194)*(k - 2)*(k + 1)/7
Let j be (38/(-4))/((-16)/24). Suppose -108*m = -182 - 142. Let 9/2 + j*v + 15/4*v**m + 27/2*v**2 = 0. Calculate v.
-2, -1, -3/5
Let p = 362123/4 + -90509. Let -273/2*q**3 - 3/2 - p*q**5 - 177/2*q**4 - 96*q**2 - 111/4*q = 0. Calculate q.
-1, -2/29
What is c in 459/2*c - 915/4 - 3/4*c**2 = 0?
1, 305
Let m(w) be the first derivative of -w**4 - 556*w**3/3 + 280*w**2 + 3086. Factor m(k).
-4*k*(k - 1)*(k + 140)
Let p = 553209 + -10510969/19. Solve 0 + 4/19*w - 2/19*w**2 - p*w**3 = 0.
-2, 0, 1
Let l be 280/(-6)*18/(-10). Let g be 735/l + 4 + -12. Factor 3/2*q**4 - g*q + 0*q**3 + 3/4*q**5 - 3/2*q**2 + 0.
3*q*(q - 1)*(q + 1)**3/4
Factor 735*t + 10302/7 - 3/7*t**2.
-3*(t - 1717)*(t + 2)/7
Let q(x) be the first derivative of -x**4/42 + x**3/7 - 2*x**2/7 + 226*x - 132. Let l(b) be the first derivative of q(b). Suppose l(z) = 0. Calculate z.
1, 2
Let x = 17 - 22. Let j be (-27)/x + 5 + (-154)/35. Determine l, given that 30*l**3 - 5*l**5 + j*l**4 + 20*l**2 + 2*l**4 - 40*l - 17*l**4 + 4*l**4 = 0.
-2, 0, 1, 2
Suppose 3*v + 3*w + 8 = 23, -39 = -3*v + 5*w. Suppose 0 = -2*u + v*u - 60. Factor 8*s**4 + 15*s**3 + 15*s**4 - 28*s**4 - u*s**2.
-5*s**2*(s - 2)*(s - 1)
Let b be (-2)/5 - (-44)/10. Factor -3*f**3 + 82*f**b + 90*f**4 - f**2 - 4*f**5 + 3*f**5 - 175*f**4.
-f**2*(f + 1)**3
Let b = -204 + 236. Find v such that -44*v**2 + 36*v + b*v**3 + 23*v**2 - 128*v**3 - 35*v**2 - 4 = 0.
-1, 1/6, 1/4
Let a(q) = 2*q**4 + 2*q**2 - 4*q. Let k(t) = 4*t**4 - t**3 + 6*t**2 - 9*t. Suppose 91*i + 260 = 65*i. Let b(n) = i*a(n) + 4*k(n). Factor b(s).
-4*s*(s - 1)*(s + 1)**2
Let f = 817 - 822. Let m be 0*-8*f/40. Determine g so that m + g + 1/3*g**4 + 7/3*g**2 + 5/3*g**3 = 0.
-3, -1, 0
Let t(z) be the third derivative of z**7/70 + 9*z**6/40 + 7*z**5/10 - 3*z**4 - 2846*z**2. What is n in t(n) = 0?
-6, -4, 0, 1
Suppose 0 = 7*r - 4*r - 6. Factor -12 + 6 - 6 - 3*o**2 - 18*o - o**r + 2*o.
-4*(o + 1)*(o + 3)
Let k be 14/(5/8 + (-3)/24). Factor 3*o**2 + 72*o + 17 - k + 11.
3*o*(o + 24)
Suppose -h + 16 = 17. Let d(g) = 7*g**2 + 4*g. Let n be d(h). Let n*c**4 - 12*c**3 - 3 - 12*c**2 - 12*c - 6*c**4 - 6*c**2 = 0. Calculate c.
-1
Let g(u) be the second derivative of 2*u**7/105 - 34*u**6/75 + 103*u**5/25 - 89*u**4/5 + 192*u**3/5 - 216*u**2/5 - 38*u. Determine a so that g(a) = 0.
1, 3, 6
Let c be (15/(-20))/((-99)/(198/18)). Let g(t) be the first derivative of 3/8*t**2 + 1/2*t + c*t**3 + 43. Factor g(a).
(a + 1)*(a + 2)/4
Let b(r) be the first derivative of -40/21*r**3 + 25/14*r**4 - 16 + 0*r + 3/7*r**2. Factor b(a).
2*a*(5*a - 3)*(5*a - 1)/7
Suppose -3*u + 19 = -2*p + 7*p, -11 = -4*p - u. Let m(b) be the second derivative of -7*b + 27/10*b**5 + 7*b**3 - 6*b**4 - 9/2*b**p + 0 - 1/2*b**6. Factor m(s).
-3*(s - 1)**3*(5*s - 3)
Determine p so that 6/7*p**5 - 284/7*p**3 + 278/7*p + 88/7 - 48/7*p**2 - 40/7*p**4 = 0.
-4, -1, -1/3, 1, 11
Let k be ((-4784)/(-176) + 2/(-11))/1. Factor -3*u**3 - k*u + 27327 - 27327 + 30*u**2.
-3*u*(u - 9)*(u - 1)
Let m = 2/47717 + 47713/95434. Factor -m*f - 2/3 - 1/6*f**4 + 5/6*f**2 + 1/2*f**3.
-(f - 4)*(f - 1)*(f + 1)**2/6
Factor 56*m**3 + 546*m**4 - 31*m**2 - 572*m**4 + 4*m**5 - 9*m**2.
2*m**2*(m - 2)**2*(2*m - 5)
Let z be 88/(7568/1634) - (-93)/(-5). Suppose -4*i - 15 = -9*i. Suppose -4/5 + 2/5*d**i + z*d**4 - 2*d - 6/5*d**2 = 0. What is d?
-1, 2
What is r in -10*r - 40*r**2 + 468*r**5 - 942*r**5 - 5*r**3 + 5 - 5*r**3 + 494*r**5 + 35*r**4 = 0?
-1, 1/4, 1
Let h be (-30*(-9)/63)/(2/28). Let 133*p**4 + 76*p**3 + 24*p**2 + 75*p**5 + 77*p**4 + h*p**3 - 4*p**3 = 0. What is p?
-2, -2/5, 0
Let l(q) = 102*q**2 + 5*q + 10. Let o be l(6). Let s(u) = 3712*u - u**2 - o*u. Let w(z) = -12*z**2 - 8*z + 4. Let c(t) = 16*s(t) - w(t). Factor c(n).
-4*(n - 1)**2
Let b be 5/((-15)/(-18)) - 3. Let a = 2 + b. Let -1854 - 30*d**3 - a*d + 20*d**2 + 1854 + 20*d**4 - 5*d**5 = 0. Calculate d.
0, 1
Suppose 14 - 170*w**3 - 2*w**4 + 146 + 37*w**4 - 945*w**2 + 348*w**3 + 250*w + 322*w**3 = 0. What is w?
-16, -2/7, 1
Suppose -19*r + 240 = -4*r. Factor 0*y**4 + 10*y**4 + 10*y**3 + r*y**4 + 2*y**3 + 6*y**4.
4*y**3*(8*y + 3)
Suppose -16*w - 106297*w**2 + 13*w**4 + w**5 + 53180*w**2 + 53164*w**2 - 45*w**3 = 0. Calculate w.
-16, 0, 1
Let y = 663601/12 - 55300. Determine n so that -1/6*n**2 + 0 + 1/12*n + y*n**3 = 0.
0, 1
Factor 15*n**3 - 1/2*n**4 + 66*n**2 + 0 + 68*n.
-n*(n - 34)*(n + 2)**2/2
Let h = 2/17485 + 3473/209820. Let o(s) be the second derivative of 11*s + 1/10*s**2 - h*s**4 + 0*s**3 + 0. Solve o(l) = 0.
-1, 1
Let o(h) be the second derivative of h**7/231 + h**6/165 - 3*h**5/110 - h**4/66 + 2*h**3/33 - 829*h - 1. Suppose o(x) = 0. Calculate x.
-2, -1, 0, 1
Let n(h) = -5*h**4 + 10*h**3 - 10*h**2 + 5. Let a = 299 - 304. Let s(g) = 5*g**4 - 11*g**3 + 8*g**2 - 4. Let x(p) = a*s(p) - 4*n(p). Factor x(t).
-5*t**3*(t - 3)
Let r = -289 - -292. Find m, given that 3*m + 5*m**2 - 6*m**2 - 8*m**2 + 6 + r*m**2 - 3*m**3 = 0.
-2, -1, 1
Let v(x) = -8*x**2 + 109*x + 3030. Let l(d) = -25*d**2 + 320*d + 9075. Let m(c) = 3*l(c) - 10*v(c). Find w such that m(w) = 0.
-15, 41
Let w = 8331/740 - 1607/148. Factor -1152/5 + 1056/5*m + w*m**3 + 94/5*m**2.
2*(m - 1)*(m + 24)**2/5
Let k be (42/2576*23)/((-18)/(-8)). Let y(q) be the second derivative of -k*q**3 - q**2 - 37*q + 1/12*q**4 + 0. Determine l so that y(l) = 0.
-1, 2
Let d(s) be the first derivative of 1/30*s**5 + 7/18*s**3 + 1/2*s**2 - 1/4*s**4 - 100 - 4/3*s. Solve d(v) = 0 for v.
-1, 1, 2, 4
Let x(a) = -172*a**3 + 67*a**3 - 50 + 50*a**3 - 5*a**2 + 90*a. Let f(u) = 18*u**3 + 2*u**2 - 31*u + 17. Let h(l) = -10*f(l) - 3*x(l). Factor h(k).
-5*(k - 1)*(k + 2)*(3*k - 2)
Let r be (-10)/3*48/(-40). Factor -4*v**3 - 30*v**4 - 38*v**r + 13*v**2 + 35*v**5 - 31*v + 57*v**2 - 2.
(v - 1)**3*(v + 1)*(35*v + 2)
Let f(b) be the first derivative of -b**5/5 + b**4 + 23*b**3 - 108*b**2 + 11593. Factor f(j).
-j*(j - 9)*(j - 3)*(j + 8)
Let s(k) be the first derivative of 2*k**3/63 - 73*k**2/21 - 316*k/7 - 5908. Factor s(v).
2*(v - 79)*(v + 6)/21
Let l(h) = 14*h**3 - 2*h**2 - 8*h - 16*h**3 - h. Let v(q) = q**3 + q**2 + 4*q. Let f = 33 - 20. Let r(k) = f*v(k) + 6*l(k). Factor r(a).
a*(a - 1)*(a + 2)
Let v(c) be the third derivative of c**7/672 - c**6/144 + 131*c**3/6 + 140*c**2. Let m(q) be the first derivative of v(q). Solve m(w) = 0.
0, 2
Suppose 66*y - y - 9880 = 0. Let s = -455/3 + y. Factor -s*r**2 + 2 - 1/3*r.
-(r - 2)*(r + 3)/3
Let x(u) be the first derivative of -u**6/50 + u**4/20 - 124*u - 102. Let r(y) be the first derivative of x(y). Factor r(o).
-3*o**2*(o - 1)*(o + 1)/5
Let t(f) = -4*f**2 - 7*f - 5. Let v be t(-1). Let d be (v/40)/(5/(-40)). Factor -6/5*z + d*z**2 + 0.
2*z*(z - 3)/5
Suppose -3*b - 4 = 5*i, -2*i + 3*b + 18 = -14. Determine k, given that -9/4*k**3 + 3/4*k**i + 0 + 3/4*k**5 - 3/2*k - 15/4*k**2 = 0.
-1, 0, 2
Let j(y) be the second derivative of 2/21*y**5 + 0*y**3 - 5*y**2 + 1/21*y**4 - 15*y + 0 + 5/84*y**6. Let s(r) be the first derivative of j(r). Factor s(f).
2*f*(5*f + 2)**2/7
Let r = -16 + -9. Let n = r - -27. Factor 3 - n + y**2 + 2*y + 0.
(y + 1)**2
Let f = -29320 - -29324. Let y(t) be the first derivative of -8*t + 2/3*t**3 - 1/2*t**f + 20 + 4*t**2. What is x in y(x) = 0?
-2, 1, 2
Let k = -1997/210 - -1051/105. Solve 1/2 + 0*q - k*q**2 = 0.
-1, 1
Let s(a) be the third derivative of -6*a**5/35 - 79*a**4/7 - 6241*a**3/21 - a**2 + 12*a + 42.