 1)
Let g(c) be the first derivative of 2*c**3/33 + 502*c**2/11 + 126002*c/11 - 428. Determine n, given that g(n) = 0.
-251
Let u = -65 - -62. Let m(t) = -6*t**2 + 26*t + 20. Let r(o) = 5*o**2 - 25*o - 21. Let x(f) = u*m(f) - 4*r(f). Factor x(h).
-2*(h - 12)*(h + 1)
Let m = 16147 - 16143. Factor -3/4 + 1/2*d**2 + 1/4*d**m - d + d**3.
(d - 1)*(d + 1)**2*(d + 3)/4
Let y(o) = o**2 - 64*o + 187. Let c be y(61). Factor -14/5*x**5 - 16/5*x**2 - 72/5*x**3 + 0*x + 0 - 12*x**c.
-2*x**2*(x + 2)**2*(7*x + 2)/5
Let z = -4416 - -48594/11. Factor z - 10/11*g**2 - 6/11*g - 2/11*g**3.
-2*(g - 1)*(g + 3)**2/11
Let c(r) be the first derivative of -r**4/2 + 176*r**3 - 17424*r**2 - 482. Find a such that c(a) = 0.
0, 132
Let o(c) be the first derivative of c**7/42 + c**6/24 - c**5/6 + 5*c**2/2 - c - 22. Let i(x) be the second derivative of o(x). Solve i(s) = 0.
-2, 0, 1
Factor -3388/17*g - 4*g**3 + 2/17*g**4 + 2662/17 + 792/17*g**2.
2*(g - 11)**3*(g - 1)/17
Let u be 351/108 - 3/(-4). Let t(d) be the first derivative of 4/15*d**3 - 2/15*d**6 - 2/5*d + u + 2/5*d**4 - 2/5*d**2 - 2/25*d**5. Let t(m) = 0. What is m?
-1, -1/2, 1
Factor 65*p**2 - 60*p**2 + 150*p**2 - 5*p**4 - 150*p**3.
-5*p**2*(p - 1)*(p + 31)
Let h be 6/((-39)/(-26)*(-30)/(-9)). Factor -4/5 - 2/5*t**2 - h*t.
-2*(t + 1)*(t + 2)/5
Let k = -30 - -34. Factor 1 - 15 - 48*o**2 - 24*o**3 - 40*o - k*o**4 + 2.
-4*(o + 1)**3*(o + 3)
Let g(z) be the first derivative of z**7/1960 - z**6/420 - z**5/280 + z**4/28 + z**3/3 + 15. Let s(v) be the third derivative of g(v). Let s(k) = 0. What is k?
-1, 1, 2
Let o be (-1253)/28 - (-1 - -1). Let j = o - -46. Determine l so that -5/4*l**3 + j*l - 1/2 + 1/2*l**2 = 0.
-1, 2/5, 1
Suppose 12 - 8 = w. Find y, given that -68*y**w - 38*y**2 - 6*y**2 + 84*y**3 - 19*y + 27*y + 20*y**5 = 0.
0, 2/5, 1
Let j = 4 - 1. Suppose -j*f - 3 = -9. Solve 5*s**f - 2*s + 4 - 2*s**3 + 3*s**3 + 10*s = 0 for s.
-2, -1
Let w(u) = 10*u**2 + 54*u - 61. Let g(z) = 34*z**2 + 160*z - 184. Let n(x) = 6*g(x) - 20*w(x). Find d such that n(d) = 0.
1, 29
Let b(o) be the first derivative of o**4/4 + 2*o**3 - o**2/2 - 4*o - 9. Let x be b(-6). Solve -70*a**2 + 6*a + 1 + x + 73*a**2 = 0.
-1
Let k(t) = -t**2 + 21*t + 4. Let v be k(21). Factor 0 + 0*g - 145/4*g**3 + 15/2*g**2 + 45/4*g**v.
5*g**2*(g - 3)*(9*g - 2)/4
Find d such that -14 + 12/7*d**2 + 3*d + 1/7*d**3 = 0.
-7, 2
Let m(y) = -7*y**2 + 9*y + 2. Let i be (-3)/(-6) - (0 - 1/2). Let c(x) = x**2 - x - 1. Let o(h) = i*m(h) + 4*c(h). Factor o(u).
-(u - 1)*(3*u - 2)
Let c be (5/6)/(0 - 15/(-9)). Let n(o) be the first derivative of 0*o + 1/12*o**3 + c*o**2 + 5. Let n(f) = 0. Calculate f.
-4, 0
Let f(c) = c - 3. Let o be f(9). Let m(l) = l**2 - 7*l + 9. Let w be m(o). Factor -2*b + 5*b - 5 + 21*b**2 + 14*b**4 + 3 + 25*b**w - 5*b**4.
(b + 1)**3*(9*b - 2)
Let w be (1 - -8) + (5/(-5))/1. Let a be 650/280 + 2/w. Factor a*d - 4/7 - 8/7*d**2.
-2*(d - 2)*(4*d - 1)/7
Factor -4*a + 28*a**3 + 31*a**4 - 12*a**4 - 7*a**4 - 12*a.
4*a*(a + 1)*(a + 2)*(3*a - 2)
Let z be -4*(2 + (-9)/6). Let f be (-8)/z + (0 - 0). What is d in -8*d**3 - 4*d + f*d**3 + 4*d**2 + 12*d = 0?
-1, 0, 2
Let g(z) be the first derivative of -z**5/40 + 3*z**4/32 + z**3/24 - 3*z**2/16 - 35. What is l in g(l) = 0?
-1, 0, 1, 3
What is q in -147/4*q**4 - 570279*q**2 + 9135*q**3 - 46128 + 323640*q = 0?
2/7, 124
Let a = -918 - -19282/21. Solve a*y - 2/21*y**5 - 2/7*y**2 + 2/7*y**4 - 2/21*y**3 + 0 = 0 for y.
-1, 0, 1, 2
Suppose 2*h + 4*u = 34, -3*h - 2*u = -22 - 13. Let p = h + -7. Factor -11*k**2 + 7*k**2 + 7*k**p + 9*k**3.
3*k**2*(3*k + 1)
Factor 7/3*a**2 + 10/3*a - 1/3*a**3 - 16/3.
-(a - 8)*(a - 1)*(a + 2)/3
What is h in h**3 + 37*h**2 - 28 + 3*h**2 + 112*h + 3*h**3 + 124 = 0?
-6, -2
Suppose -2*w - 6 = -x, 7*x - 21 = 2*x + w. Let y(u) be the first derivative of 6 + 4*u**2 - 9/2*u**4 + 0*u - x*u**3 - u**5. Determine j, given that y(j) = 0.
-2, 0, 2/5
Let w(m) be the third derivative of 16*m**7/2415 + 13*m**6/1380 - m**5/230 - 59*m**2 - 2. Factor w(a).
2*a**2*(a + 1)*(16*a - 3)/23
Suppose 3*z = 15, -4*b = -21*z + 26*z - 37. Let p(a) be the first derivative of -8*a + 6*a**2 + 7 - 4/3*a**b. Determine y so that p(y) = 0.
1, 2
Factor -23*m**2 - 124*m + 3473 + 24*m**2 + 371.
(m - 62)**2
Solve -48 + 4/5*j**2 + 44/5*j = 0 for j.
-15, 4
Factor 0 + 3/2*g**4 + 15/2*g**3 + 9/2*g + 21/2*g**2.
3*g*(g + 1)**2*(g + 3)/2
Let n be ((-20)/8 + 0)*-2. Let v be n/5 + (-1 - -2). What is f in -2 - 3*f**v + 3*f**2 - 3*f - f**2 = 0?
-2, -1
Factor 38*q**2 - 61*q**2 - 147*q**2 + 4*q.
-2*q*(85*q - 2)
Suppose -k - 9 = -4*k - 3*h, -3*h - 3 = -3*k. Suppose 24*b + 20 - b**k - 10*b**2 + 15*b**2 = 0. What is b?
-5, -1
Let 116*g - 40/3*g**2 - 192 - 4/3*g**3 = 0. Calculate g.
-16, 3
Suppose -7/3*d**4 + 123*d + 54 - 655/3*d**2 + 131/3*d**3 = 0. What is d?
-2/7, 1, 9
Let q = 4447/7 - 635. Find t such that q*t**2 + 11/7*t - 11/7*t**3 - 2/7 = 0.
-1, 2/11, 1
Let q(n) be the first derivative of -n**6/39 + 2*n**5/65 - 31. Factor q(g).
-2*g**4*(g - 1)/13
Suppose -150*y**2 - 11520*y - 404*y**2 + 40*y**2 - 5*y**3 + 34*y**2 = 0. What is y?
-48, 0
Suppose -34*j + 12 = -15*j - 13*j. Determine c, given that -3 + 3/4*c**4 + 6*c - 3/4*c**j - 15/4*c**3 + 3/4*c**5 = 0.
-2, 1
Let d(g) be the first derivative of g**5 - 2*g**4 - 4*g**3/3 + 80. Factor d(s).
s**2*(s - 2)*(5*s + 2)
Let i(g) = -g**3 + g**2 - g. Let f(d) = 6*d**4 - 38*d**3 + d + 21*d + 6*d**2 + 8*d**2 + 27*d**2. Let v(k) = f(k) - 5*i(k). Factor v(q).
3*q*(q - 3)**2*(2*q + 1)
Suppose 1/3*i**3 + 88/3 - 175/3*i + 86/3*i**2 = 0. What is i?
-88, 1
Suppose 4 = 2*w + 3*v, -9*w + 6*v + 18 = 3*v. Let p(b) = b**3 + b**2 - b + 1. Let c be p(1). Solve c*i**2 - 4*i**2 + 4*i**w - 12*i + 8 + 2*i**2 = 0 for i.
1, 2
Factor 1899*s - 8*s**2 + 0*s**3 - s**3 - 1890*s.
-s*(s - 1)*(s + 9)
Let c be -4*(2 + -3) - 0. Find p such that p**4 - p**2 - 2*p**4 - 3*p**3 + 9*p**5 - 2*p**c - 10*p**5 = 0.
-1, 0
Let c(g) be the first derivative of 0*g + 4/57*g**3 + 1/19*g**2 - 28 + 1/38*g**4. Factor c(f).
2*f*(f + 1)**2/19
Let n be ((0/(-8))/7)/(-1). Let s(t) be the second derivative of 0 - 1/30*t**6 + 1/12*t**4 + n*t**2 + 7*t + 1/6*t**3 - 1/20*t**5. Solve s(g) = 0.
-1, 0, 1
Let l = 69 + -64. Suppose -4 = -l*y + 11. Suppose -3*t**2 - 6/7*t + 12/7*t**y + 0 = 0. What is t?
-1/4, 0, 2
Suppose 15*m**5 + 29897*m + 3034*m**2 - 22841*m - 1728 + 4379*m**2 + 327*m**4 + 2469*m**3 = 0. Calculate m.
-8, -3, 1/5
Suppose -7*z = -11*z + 20. Let c be 104/20 + (-1)/z. Solve 5*y - y + 2*y - 2*y - 6*y**4 + 6*y**2 + 10*y**c - 14*y**3 = 0.
-1, -2/5, 0, 1
Let k(z) be the first derivative of -27/4*z + 1 - 45/8*z**2 - 7/4*z**3 - 3/16*z**4. Factor k(c).
-3*(c + 1)*(c + 3)**2/4
Find c, given that -152/7 - 22*c - 2/7*c**2 = 0.
-76, -1
Find l, given that -18*l + 69*l**2 + 37*l**4 + 5*l**5 - 693*l**3 + 594*l**3 - 4*l**4 + 10*l**2 = 0.
-9, 0, 2/5, 1
Suppose -9 = -4*h + 3. Let s(c) = -2*c**2 + 67*c - 245. Let d(r) = -r**2 + r. Let v(w) = h*d(w) + s(w). Factor v(u).
-5*(u - 7)**2
Let k be (1 - 1)*(-5)/(-15). Let x(g) be the third derivative of -g**2 + k*g + 0*g**5 - 1/360*g**6 + 0 + 1/24*g**4 + 1/9*g**3. Factor x(n).
-(n - 2)*(n + 1)**2/3
Let v(f) be the first derivative of -7*f**3/9 + 41*f**2/3 + 8*f - 271. Determine x so that v(x) = 0.
-2/7, 12
Factor 42/13 + 40/13*x - 2/13*x**2.
-2*(x - 21)*(x + 1)/13
Factor 15/4*h - 33/4*h**2 - 1/2 - 9/4*h**4 + 29/4*h**3.
-(h - 1)**3*(9*h - 2)/4
Let u = 68/195 - 1/65. Let p(d) be the first derivative of 0*d**3 + u*d**2 + 0*d + 1/9*d**6 - 1/3*d**4 + 4 + 0*d**5. Find h such that p(h) = 0.
-1, 0, 1
Let r(x) be the first derivative of -x**4/6 + x**3/3 + 2*x + 23. Let w(t) be the first derivative of r(t). Factor w(m).
-2*m*(m - 1)
Determine y, given that -4556*y + 4613*y - 15*y**2 + 3*y**3 - 19 - 8 - 18*y**2 = 0.
1, 9
Suppose 13*j - 24 = 5*j. What is k in -12 - 34*k - 16*k**4 + 86*k**2 + 2*k**4 - 4*k**4 - 22*k**j = 0?
-3, -2/9, 1
Let k be (-1 + 40/32)/(11/8). Factor -2/11*r**2 + 12/11 + k*r.
-2*(r - 3)*(r + 2)/11
Let a(q) be the third derivative of -q**5/240 + 3*q**4/32 - q**2 + 71*q. Solve a(u) = 0 for u.
0, 9
Let c be -4 - 2/(-1) - (-4)/1. Suppose -i**5 + i + 2*i**5 + 10 + c*i**2 - 11 - 2*i**3 - i**4 = 0. Calculate i.
-1, 1
Let d(c) = c**2 - c - 4. Let t be d(3). What is n in 2*n**2 + 8*n**t - n**2 - n**2 + 4*n**3 = 0?
-2, 0
What is k in