 = -101447/33 + 3073. Let x = w + 251/132. Factor -1/4*q**4 + x*q**2 + 1/4*q - 1/4*q**3 - 1/2.
-(q - 1)**2*(q + 1)*(q + 2)/4
Let h(f) = -172*f + 364. Let m(s) = -s**2 - 6. Let v(g) = h(g) + 2*m(g). Determine c so that v(c) = 0.
-88, 2
Suppose -5046 - 2/3*p**2 + 116*p = 0. What is p?
87
Let r(h) be the second derivative of h**8/10080 - h**7/1680 - 17*h**3/2 - 2*h - 7. Let g(n) be the second derivative of r(n). Let g(b) = 0. Calculate b.
0, 3
Suppose -b - 3*b = -8, -14 = -h - 5*b. Factor -7*c**5 + 24*c**2 + 19*c**5 - 8*c**4 - 10*c**5 - h*c**3 + 18*c.
2*c*(c - 3)**2*(c + 1)**2
Let r(s) be the third derivative of 40*s**2 + 0*s**3 + 1/78*s**4 + 0*s - 7/130*s**5 + 0. Factor r(i).
-2*i*(21*i - 2)/13
Let f(n) be the third derivative of -n**7/210 + 17*n**6/120 - 17*n**5/20 - 17*n**4/24 + 26*n**3/3 + 477*n**2 - 2. Let f(g) = 0. What is g?
-1, 1, 4, 13
Let -32/21*n + 2/21*n**3 - 2/21*n**2 - 40/21 = 0. What is n?
-2, 5
Solve -44*d**2 + 0 + 2/5*d = 0.
0, 1/110
Let i be 2 + 39/(-6) - 5/(-2). Let s be 6/i*(1 + 30/(-27)). Suppose 0 - s*l**2 + 0*l = 0. Calculate l.
0
Let m(x) be the second derivative of 5*x**4/12 + 4505*x**3/3 + 4059005*x**2/2 + 3096*x. What is o in m(o) = 0?
-901
Let l be 17/2992*-16 + -2*(69/(-66) + 1). Factor -2/7*i**2 + l*i + 0 - 3/7*i**3 + 1/7*i**5 + 0*i**4.
i**2*(i - 2)*(i + 1)**2/7
Let p = 26522 + -26518. Let o(x) be the second derivative of -1/36*x**p + 2/9*x**3 + 5/6*x**2 + 0 - 43*x. Factor o(u).
-(u - 5)*(u + 1)/3
Suppose 1120 = 21*a + 19*a. Suppose 0 = 154*f - 147*f - a. Find j such that -2/5*j**3 + 2/5*j**2 - 2/5*j**f + 0*j + 2/5*j**5 + 0 = 0.
-1, 0, 1
Let f = 2 - 0. Suppose -12 = -2*c + 2*w, f*c - 5*w - 22 = c. Factor -c*h**3 + 2*h**4 + 6*h + 7*h + h**2 - 11*h - 3*h**2.
2*h*(h - 1)**2*(h + 1)
Let j(d) be the second derivative of 2*d**6/15 - 43*d**5/5 + 26*d**4 + 344*d**3/3 - 656*d**2 + 40*d - 11. Factor j(u).
4*(u - 41)*(u - 2)**2*(u + 2)
Let y(o) be the third derivative of -o**8/16800 - o**7/3150 + o**6/600 - 25*o**4/8 + 107*o**2. Let v(n) be the second derivative of y(n). Factor v(g).
-2*g*(g - 1)*(g + 3)/5
Let t(n) be the second derivative of -n**4/18 - 98*n**3/9 - 2401*n**2/3 - 1771*n. Let t(h) = 0. Calculate h.
-49
Factor 1/4*j**5 - 247/4*j + 23/2*j**3 - 38*j**2 - 49/2 + 25/2*j**4.
(j - 2)*(j + 1)**3*(j + 49)/4
Let g be 15 + (-19 + 319)/(-20). Let f(m) be the first derivative of 14 + 0*m**2 - 2*m**3 + 9/4*m**4 + g*m - 3/5*m**5. Factor f(o).
-3*o**2*(o - 2)*(o - 1)
Let 264/7*p**4 - 72 - 1053/7*p**3 + 1236/7*p + 15/7*p**5 + 438/7*p**2 = 0. Calculate p.
-21, -1, 2/5, 2
Suppose 0 = -5*n, -235*y = -238*y + 2*n. Let o(g) be the third derivative of -121/3*g**3 + 0*g - 1/30*g**5 + y + 33*g**2 - 11/6*g**4. Let o(q) = 0. What is q?
-11
Let a = -18565/76 + 4836/19. Let m be 4/14 - (-251)/28. Let -1/2 + g**5 + a*g**3 + 15/4*g - m*g**2 - 21/4*g**4 = 0. Calculate g.
1/4, 1, 2
Let v(g) be the second derivative of g**4/3 - 50*g**3/3 - 300*g**2 + 3*g + 129. Factor v(l).
4*(l - 30)*(l + 5)
Let k(d) be the second derivative of 1/10*d**5 - 18 + 16*d**2 + 6*d + 20/3*d**3 + 4/3*d**4. Factor k(m).
2*(m + 2)**2*(m + 4)
Let i(k) = k**5 - 5*k**4 + k**3 + 25*k**2 - 26*k. Let q(c) = -7*c**5 + 29*c**4 - 5*c**3 - 151*c**2 + 176*c. Let g(b) = -39*i(b) - 6*q(b). Factor g(h).
3*h*(h - 2)*(h + 1)**2*(h + 7)
Let f(a) = -2*a + 2. Let d be f(-5). Let y(t) = -t**2 + 12*t + 4. Let h be y(d). Factor o**2 + 4 + h - 3 - 11*o**2 + 5*o**4.
5*(o - 1)**2*(o + 1)**2
Let r(x) be the first derivative of -x**6/6 + 7*x**5/5 + 7*x**4/2 - 44*x**3/3 - 20*x**2 + 64*x - 2274. Determine k, given that r(k) = 0.
-2, 1, 2, 8
Let v(f) be the first derivative of -13*f**3 - 75*f**2 + 24*f - 54. Find q such that v(q) = 0.
-4, 2/13
Find o such that 11*o**4 - 93*o**4 - 23*o**4 - 5*o**5 + 2970 - 55*o**3 - 10080*o + 5345*o**2 + 1930 = 0.
-14, 1, 5
Suppose 20*w - 7 = 14*w + 11. Let x(q) be the second derivative of 5*q**2 + 0 - 5/6*q**4 - 9*q - 5/6*q**w + 1/4*q**5. Factor x(d).
5*(d - 2)*(d - 1)*(d + 1)
Suppose 4*h - w - 41 + 2 = 0, h + 5*w - 36 = 0. Suppose 2*m + k = 3*k - 4, -4*m - h = -5*k. Factor 4*c - m + 1 - 5*c + c**2.
c*(c - 1)
Let p be 6*(-245)/(-21) + 4. Let -65*m - p*m**2 - 30 + 96*m**2 + 5*m**4 - 57*m**2 + 5*m**3 = 0. Calculate m.
-2, -1, 3
Let s be 2*4 + -62 + 65. Let a be 689/39 - s - (0 - 4). What is l in -64/3*l + 2/3*l**4 + 16*l**2 - 16/3*l**3 + a = 0?
2
Let y(k) = -2*k**3 - 41*k**2 + 52*k. Let o(a) = -8*a**3 - 163*a**2 + 210*a. Let g(u) = 3*o(u) - 13*y(u). Factor g(s).
2*s*(s - 1)*(s + 23)
Suppose 8*l = 40*l + 11648. Let u = 366 + l. Factor -2*c + u*c**3 + 1/2*c**4 - 2 + 3/2*c**2.
(c - 1)*(c + 1)*(c + 2)**2/2
Let s(n) be the second derivative of -3*n**5/100 - 3*n**4/5 + 43*n**3/10 - 9*n**2 - n + 82. Factor s(l).
-3*(l - 2)*(l - 1)*(l + 15)/5
Let b = 97 + -81. Let c be (9/6)/(152/b - 7). Determine x so that 0*x - 3/5*x**2 + c = 0.
-1, 1
Factor -22*u**2 + 80*u**2 + 17*u**2 + 15*u**2 - 4*u**3 + 9*u**3.
5*u**2*(u + 18)
Suppose -3*u + 40 = 5*d, -5*u = -47*d + 50*d - 72. Let v be 3/u + 4847/740. Determine t, given that 9/2*t + 3/4*t**2 + v = 0.
-3
Let y(p) be the third derivative of p**8/392 + 5*p**7/147 - 11*p**6/84 - 3*p**5/14 + 13*p**4/21 + 20*p**3/21 - 64*p**2 - 5. Let y(t) = 0. Calculate t.
-10, -1, -1/3, 1, 2
Suppose -r = -t - 1, 0*r + 3 = 4*r - 3*t. Suppose -f = 5*k + 1933 - 1946, -2*k - 2 = -2*f. Suppose -4/11*v + r + 10/11*v**k = 0. What is v?
0, 2/5
Solve -7/8*b**3 + 1/8*b**4 - 4 + 4*b + 3/4*b**2 = 0.
-2, 1, 4
Let w(n) be the first derivative of n**6/480 + 7*n**5/60 - 225*n**2/2 - 120. Let l(v) be the second derivative of w(v). Find h, given that l(h) = 0.
-28, 0
Let g = 74 - -676. Let n = g + -2997/4. Factor -n + 0*l + 3/4*l**2.
3*(l - 1)*(l + 1)/4
Let i(l) be the second derivative of -l**5/40 + 5*l**4/4 + 24*l**3 + 152*l**2 + 4800*l - 2. Factor i(c).
-(c - 38)*(c + 4)**2/2
Let j(u) be the first derivative of u**6/150 - 2*u**5/25 + 11*u**4/30 - 4*u**3/5 - 53*u**2/2 + 13. Let x(v) be the second derivative of j(v). Factor x(a).
4*(a - 3)*(a - 2)*(a - 1)/5
Let u be (246/140 - 66/77) + 3/(-5). Let b(v) be the third derivative of 0*v - 5/6*v**4 + 0 - u*v**6 - 7*v**2 + 4/3*v**3 - 16/15*v**5. Factor b(f).
-4*(f + 1)**2*(9*f - 2)
Let j(z) be the first derivative of -z**4/8 + 13*z**3/6 - 3*z**2 - 9171. Factor j(c).
-c*(c - 12)*(c - 1)/2
Factor -145800 - 360*h - 2/9*h**2.
-2*(h + 810)**2/9
Factor 330750*j**3 - 7717500*j**2 + 243/4*j**5 + 90037500*j - 420175000 - 14175/2*j**4.
(3*j - 70)**5/4
Suppose -5*x - 25*l - 55 = -30*l, 0 = -5*x - 10*l + 140. Determine k, given that -3/7 - 8/7*k**x - 11/7*k = 0.
-1, -3/8
Let l(x) = x**3 + 2*x**2 - x - 2. Let f(d) = 238 - 12*d**3 - 208 + 63*d - 36*d**2 - 18*d**2. Let z(a) = -f(a) - 15*l(a). Factor z(q).
-3*q*(q - 4)**2
Suppose 102*n**4 + 5*n**5 + 115*n**4 + 243*n + 340*n**3 - 91*n**4 + 500*n**2 - 41*n**4 - 3*n = 0. Calculate n.
-12, -2, -1, 0
Let p(z) be the third derivative of -z**6/360 + 19*z**5/360 - 25*z**4/144 + 2*z**3/9 + 192*z**2 - 1. Suppose p(a) = 0. What is a?
1/2, 1, 8
Let g(n) be the first derivative of n**4/6 + 46*n**3/3 + 529*n**2 + 85*n - 152. Let f(m) be the first derivative of g(m). Determine v so that f(v) = 0.
-23
Let w(u) be the third derivative of -u**8/840 + u**6/60 - u**4/15 + 2*u**2 - 65*u. Determine i, given that w(i) = 0.
-2, -1, 0, 1, 2
Let a(f) be the third derivative of -31/72*f**4 + 0 - 5/18*f**3 - 17/60*f**5 - 1/40*f**6 + 0*f - 38*f**2. Factor a(r).
-(r + 5)*(3*r + 1)**2/3
Let -2680*x**2 - 432*x + 5420*x**2 - 2730*x**2 - 352 = 0. Calculate x.
-4/5, 44
Suppose 2*c - 4 = -0*c. Suppose 68*d - 207 = 269. Factor -d + 7 - 4*u**4 + 4*u**3 + 0 + 4*u**c - 4*u**5.
-4*u**2*(u - 1)*(u + 1)**2
Let -27 - 1/3*a**3 + 1/3*a**2 + 27*a = 0. Calculate a.
-9, 1, 9
Let q = -354 + 358. Factor -3 - 6*c**3 + 4*c**q - 6*c**2 + 89*c - 3*c**5 - 80*c + 5*c**4.
-3*(c - 1)**4*(c + 1)
Factor 2/13*j**3 + 172/13*j**2 - 358/13*j - 528/13.
2*(j - 3)*(j + 1)*(j + 88)/13
Let k = 1 - -1. Suppose -k = -y + 1. Factor -t**3 + 3*t**2 + 2*t**3 + 0*t**y + 2*t**3 - 6*t.
3*t*(t - 1)*(t + 2)
Factor 768 - 32*u + 1/3*u**2.
(u - 48)**2/3
Let w(r) be the first derivative of -r**4/5 + 92*r**3/15 - 236*r**2/5 + 384*r/5 + 218. Factor w(u).
-4*(u - 16)*(u - 6)*(u - 1)/5
Let v be ((-3)/(-2))/(3/(-6)) + 19877/6116. Solve -v*u**3 - 27/4 + 9/4*u + 3/4*u**2 = 0.
-3, 3
