*v**3 - 1012*v**2 - 1744*v - 704. Let d(o) = -15*o**3 + 202*o**2 + 349*o + 141. Let a(g) = -16*d(g) - 3*x(g). Factor a(y).
4*(y - 18)*(y + 1)*(3*y + 2)
Let n(f) be the third derivative of f**7/10 + 181*f**6/8 - 1733*f**5/10 - 133*f**4 + 8380*f**2. Suppose n(k) = 0. What is k?
-133, -2/7, 0, 4
Suppose -5*c + 45*p + 153 = 44*p, -3*c = 5*p - 47. Let x(f) be the second derivative of 5/42*f**4 - c*f + 0*f**3 + 0 - 1/70*f**5 + 0*f**2. Factor x(v).
-2*v**2*(v - 5)/7
Let d be 57*(-480)/1824 + 218/14. Solve 36/7*f + 60/7*f**2 + 4*f**3 + 0 + d*f**4 = 0 for f.
-3, -1, 0
Let r(b) be the third derivative of -b**6/600 - 7*b**5/100 + 11*b**4/60 - 417*b**2. Let r(d) = 0. What is d?
-22, 0, 1
Let m(r) be the first derivative of r**5/100 - r**4/5 + 6*r**3/5 - 16*r**2/5 - 26*r + 230. Let a(h) be the first derivative of m(h). What is d in a(d) = 0?
2, 8
Suppose 36*v - 41*v + 3365 = 0. Let c = v - 12783/19. Solve 6/19*h - c - 2/19*h**2 = 0 for h.
1, 2
Let d(g) be the first derivative of 32 - 5/12*g**3 - 5/2*g - 15/8*g**2. Find h, given that d(h) = 0.
-2, -1
Factor 4*m**5 - 6*m**4 + 8716*m**3 - 4354*m**3 - 4347*m**3 - 8*m**2 - 5*m**5.
-m**2*(m - 1)**2*(m + 8)
Let w(f) = 1460*f + 420490. Let i be w(-288). Suppose -i*q**2 - 4000/3 + 200*q + 1/6*q**3 = 0. What is q?
20
Let d(x) = -12*x**2 - 140*x + 48. Let s(u) = -11*u**2. Let p(i) = d(i) - 4*s(i). Factor p(b).
4*(b - 4)*(8*b - 3)
Let q(n) be the second derivative of -7/12*n**4 + 0*n**2 + 0*n**3 - 101*n + 13/30*n**6 - 2/5*n**5 + 1/21*n**7 + 0. Factor q(i).
i**2*(i - 1)*(i + 7)*(2*i + 1)
Let n(m) = -27*m - 3. Let p be n(1). Let j = 30 + p. Let -25*f**4 - 68*f**3 + 15*f**5 - 5*f + 58*f**3 + j*f**5 + 30*f**2 - 2 - 3 = 0. Calculate f.
-1, -1/3, 1
Let k(j) be the first derivative of -j**3/9 - 43*j**2/2 - 126*j - 5616. Factor k(z).
-(z + 3)*(z + 126)/3
Suppose -48*u = -38*u - 5770. Let q = -8651/15 + u. Determine c so that q*c - 22/15*c**2 + 6/5*c**3 + 0 = 0.
0, 2/9, 1
Suppose -2*t + 2*n - 5*n = -5, 0 = -n + 5. Let i be (-11)/(-10) + 3/t*1. Find z, given that -z + i*z**2 + 1/2 = 0.
1
Let r(t) be the first derivative of 2*t**3/3 + 533*t**2 - 2140*t - 4635. Suppose r(s) = 0. What is s?
-535, 2
Let m = -4272 + 4272. Let w(v) be the third derivative of 1/735*v**7 + 0*v**6 - 1/210*v**5 + 0*v + 0*v**4 - 15*v**2 + m + 0*v**3. Suppose w(b) = 0. What is b?
-1, 0, 1
Let r(v) be the second derivative of v**4/16 - 23*v**3/8 + 63*v**2/4 - 136*v. Factor r(z).
3*(z - 21)*(z - 2)/4
Let l(y) be the first derivative of y**4/4 + 5*y**3/2 + 51*y - 81. Let d(b) be the first derivative of l(b). Find k, given that d(k) = 0.
-5, 0
Suppose -32*f = 9428 + 844. Let b = 1607/5 + f. What is c in -4/5 + 2/5*c**2 + b*c = 0?
-2, 1
Factor 450*h**3 + 38 - 13 - 30*h - 25 + 115*h**4 + 146*h**2 + 159*h**2.
5*h*(h + 1)*(h + 3)*(23*h - 2)
Let v(g) = 7*g**2 - 40*g + 53. Let x(k) = -9*k**2 + 39*k - 55. Let b(c) = -5*v(c) - 4*x(c). Find r such that b(r) = 0.
-45, 1
Suppose 4*y - 4*w - 88 - 120 = 0, 0 = -2*y + 3*w + 99. Let d be ((-5)/6 - -1)*228/y. Find l such that -7/3*l**2 + 3*l**3 + d*l + 0 - 5/3*l**4 + 1/3*l**5 = 0.
0, 1, 2
Let w(c) be the second derivative of -c**4/60 - 176*c**3/5 - 139392*c**2/5 + 103*c. Suppose w(r) = 0. What is r?
-528
Let r(k) = -15*k**2 - 28*k + 43. Suppose 16 - 64 = 8*g. Let i(v) = 7*v**2 + 14*v - 21. Let q(u) = g*r(u) - 13*i(u). Solve q(p) = 0 for p.
-15, 1
Let f be 116 + 4*(-3)/(-2). What is a in 48*a**3 + 6*a**2 - 32*a + 104*a**4 + 22*a**2 + 6 - f*a**4 = 0?
-1, 1/3, 3
Determine h so that 3/4*h**4 - 141/2*h**2 + 0 - 279/4*h**3 + 0*h = 0.
-1, 0, 94
Let b(l) be the third derivative of l**8/2240 - l**7/280 + 10*l**4/3 + 67*l**2. Let u(y) be the second derivative of b(y). Factor u(t).
3*t**2*(t - 3)
Let t = -3078 - -34114/11. Let i = 258/11 - t. Factor -i*n**2 - 2/11*n + 0.
-2*n*(n + 1)/11
Let b(o) be the first derivative of 2/7*o**4 - o + 6/7*o**2 - 16/21*o**3 + 2 + 0*o**5 - 2/105*o**6. Let y(m) be the first derivative of b(m). Factor y(k).
-4*(k - 1)**3*(k + 3)/7
Let t(c) = -c**2 + 2. Let d(z) = -9*z - 119. Let l be d(-11). Let g(k) = 24*k**2 - 32*k + 8. Let o(y) = l*t(y) - g(y). Factor o(w).
-4*(w - 6)*(w - 2)
Let t(k) = 4*k**4 - k**2 + k. Let n(z) = 17*z**4 + 24*z**3 + 40*z**2 + 4*z. Let u(r) = n(r) - 4*t(r). Determine l so that u(l) = 0.
-22, -2, 0
Suppose -22*g + 25*g = 1587. Find k, given that -188*k - g*k**3 - 4 - 771*k**2 - 4 - 655*k**2 + 276*k**2 = 0.
-2, -2/23
Let s = 1353967 - 17601547/13. Solve 0 + 2/13*l**5 + 72/13*l - 22/13*l**3 + 4/13*l**4 - s*l**2 = 0.
-3, 0, 2
Let d(j) be the first derivative of 2*j**3/27 - 44*j**2/9 - 184*j/9 + 859. Find x, given that d(x) = 0.
-2, 46
Determine p, given that 1085*p**3 + 1088*p**3 - 37*p - 86*p**2 - 2172*p**3 - 50*p = 0.
-1, 0, 87
Suppose -5*p = 3*j - 41, 0 = j - p - 1409 + 1414. Factor 112*o + 4/5*o**4 + 72/5*o**j - 588/5 - 48/5*o**3.
4*(o - 7)**2*(o - 1)*(o + 3)/5
Let j(a) be the first derivative of -4*a**5/35 + 94*a**4/7 + 128*a**3/7 - 188*a**2/7 - 380*a/7 - 4427. Determine v so that j(v) = 0.
-1, 1, 95
Let m(g) be the second derivative of g**6/120 - g**5/40 - 3*g**4/16 + g**3/12 + g**2 + 2*g - 515. Determine t so that m(t) = 0.
-2, -1, 1, 4
Factor 11/4*h**2 + 87/4*h - 49/2.
(h - 1)*(11*h + 98)/4
Suppose 145 = -11*i + 222. Suppose 0*o = q + 2*o - 12, 0 = -q - o + i. Find y such that -1/2*y + y**3 - 3/4 + 5/4*y**q = 0.
-1, 3/4
Let a(x) be the first derivative of x**4/14 + 8*x**3/21 - 5*x**2/7 - 648. Factor a(d).
2*d*(d - 1)*(d + 5)/7
Let p(s) be the second derivative of -s**7/168 - 7*s**6/24 - 323*s**5/80 - 289*s**4/48 - 2*s + 1423. Determine j so that p(j) = 0.
-17, -1, 0
Suppose 11*a = 7*a + 4, 811 = -2*r - 5*a. Let w be 7/98 + r/(-560). Factor 4/5*s - w - 1/5*s**2.
-(s - 2)**2/5
Factor 0*q**2 + 5/7*q**4 - 4/7*q**5 - 1/7*q**3 + 0*q + 0.
-q**3*(q - 1)*(4*q - 1)/7
Let w = 6/2729 - -24519/19103. Let d(g) be the third derivative of -w*g**3 + 0*g + 0 - 1/280*g**6 - 13*g**2 + 3/56*g**4 + 1/35*g**5. Let d(s) = 0. Calculate s.
-2, 3
Suppose 84 - 148 = -4*b. Suppose n = 5*n - b. Solve 83*d**4 - 160*d**n + 2*d**2 - 4*d**3 + 79*d**4 = 0.
0, 1
Let i(f) be the first derivative of 3*f**5/5 - 543*f**4/2 + 32397*f**3 + 98826*f**2 + 99372*f - 1608. Suppose i(h) = 0. What is h?
-1, 182
Let r(q) be the third derivative of -q**7/42 - 5*q**6 - 235*q**5/12 + 25*q**4 + 590*q**3/3 + 8931*q**2. Suppose r(z) = 0. Calculate z.
-118, -2, -1, 1
Let w = -42 + 45. Let y be 0/((-2 - (-8)/w)*3). Factor 4 + y + 3*r + 1 - 9*r + r**2.
(r - 5)*(r - 1)
Let t(h) = 4*h - 25. Let j be t(5). Let b(o) = -3*o**4 + 4*o**3 - 5*o**2. Let a(q) = 2*q**4 - 4*q**3 + 4*q**2. Let p(s) = j*a(s) - 4*b(s). Solve p(x) = 0 for x.
-2, 0
Determine m, given that 74*m - 18*m**3 + 20 + 30*m + 56*m**2 - 257*m + 95*m = 0.
1, 10/9
Let u(r) be the third derivative of r**7/3780 - 31*r**6/540 + 961*r**5/180 + 5*r**4/4 - 93*r**2. Let y(m) be the second derivative of u(m). Factor y(i).
2*(i - 31)**2/3
Let q(g) be the second derivative of -1/4*g**4 + 214*g + 0*g**2 + 21*g**3 + 0. Factor q(m).
-3*m*(m - 42)
Let 312 - 1/2*m**2 + 23/2*m = 0. What is m?
-16, 39
Let b(m) = 8*m**2 - 122*m + 32. Let g(c) = 2*c**3 - 8*c**2 - c + 19. Let v be g(4). Let r be b(v). Determine d so that -2/9*d**r + 2/9*d + 4/3 = 0.
-2, 3
Let q(i) be the third derivative of 5/3*i**3 - 1/105*i**7 + 0*i + 2/5*i**5 - 1/30*i**6 - 7/6*i**4 + 0 + 15*i**2. What is s in q(s) = 0?
-5, 1
Let t(g) be the first derivative of -2*g**5/5 + 3*g**4/2 + 198*g**3 - 2299*g**2 + 3437. Factor t(s).
-2*s*(s - 11)**2*(s + 19)
Let o(r) = 42*r**4 - 84*r**3 + 16*r**2 - 62*r. Let k(i) = -2*i**4 + 4*i**3 + i**2 + i. Let f(x) = -44*k(x) - 2*o(x). Suppose f(w) = 0. What is w?
-4, 0, 1, 5
Factor -8/5*i**2 + 648/5 + 858/5*i.
-2*(i - 108)*(4*i + 3)/5
Let u(z) = -4*z**3 + 4*z**2 + 6*z + 2. Let m(b) = b**4 - 14*b**3 + 11*b**2 + 19*b + 7. Let i(k) = 2*m(k) - 7*u(k). Find n, given that i(n) = 0.
-1, 0, 2
Let k = 107218/348205 - 6/26785. Solve -8/13*g**3 - k*g + 10/13*g**2 + 2/13*g**4 + 0 = 0 for g.
0, 1, 2
Let k be -2 + 3 - -7 - ((-2520)/(-70))/6. Factor 4*r - 12 - 1/3*r**k.
-(r - 6)**2/3
Let s(c) be the second derivative of 7/10*c**2 + 1/60*c**4 + 2*c - 4/15*c**3 - 16. Factor s(w).
(w - 7)*(w - 1)/5
Let u(y) be the first derivative of 70*y**3/3 - y**2 - 2*y - 26. Let c be u(-1). Solve 5*a + 4*a**3 - c*a**5 - 4*a - 3*