**2 + 6. Find r, given that c(r) = 0.
-447, -1
Suppose 0 = 4*k - 6*w + 38, -2*k - k = 3*w + 21. Let b be (-32)/48 + k/(-6). Factor -2/3*y**2 - 2/3*y**3 + 2/3 + b*y.
-2*(y - 1)*(y + 1)**2/3
Let d(f) be the second derivative of 3*f**5/80 - 10317*f**4/16 + 35480163*f**3/8 - 122016280557*f**2/8 + f + 2569. Solve d(y) = 0.
3439
Let h(w) = w**4 + w**3 - 2*w + 3. Let n(x) = -3*x**5 - 27*x**4 - 33*x**3 + 3*x**2 + 48*x - 24. Let z(i) = 12*h(i) + n(i). Find m, given that z(m) = 0.
-2, -1, 1
Factor -285/7*m + 0 + 3/7*m**2.
3*m*(m - 95)/7
Let 69/2*v**3 + 17 - v**4 - 16*v**2 - 69/2*v = 0. What is v?
-1, 1/2, 1, 34
Let g(i) be the third derivative of i**5/60 - i**4 + 64*i**3/3 - 24*i**2 - 17*i. Factor g(x).
(x - 16)*(x - 8)
Find k such that -1630*k - 56*k**3 + 36*k**3 - 91*k**3 + 21870 + 189*k**4 - 7847*k + 1539*k**2 - 186*k**4 = 0.
9, 10
Let q = -4326 + 4328. Let x(j) be the second derivative of 0*j**q + 1/8*j**4 + 9*j + 0 + 0*j**5 - 1/60*j**6 + 1/6*j**3. Factor x(c).
-c*(c - 2)*(c + 1)**2/2
Suppose -5*h - 5*c = 5, h = 3*c + 17 - 14. Let f(x) be the third derivative of 0 + 0*x**5 - 1/600*x**6 + 0*x**3 + h*x + 1/120*x**4 + 6*x**2. Factor f(w).
-w*(w - 1)*(w + 1)/5
Let a(s) be the first derivative of -1815*s**4/34 + 4444*s**3/51 - 804*s**2/17 + 144*s/17 - 2872. Determine c so that a(c) = 0.
2/15, 6/11
Let p = -264/955 - -40756/955. Factor 5832/5 + 2/5*d**4 + 5402/5*d**2 - 11448/5*d + p*d**3.
2*(d - 1)**2*(d + 54)**2/5
Let k(r) = -r**2 - 16*r - 10. Let l be k(-15). Suppose -11*z = 2*z + l*z. Let -1/2*p + 1/2*p**2 + z = 0. What is p?
0, 1
Let n(y) be the third derivative of -y**8/12600 - y**7/2100 + y**5/225 + 16*y**3 + 59*y**2. Let h(x) be the first derivative of n(x). Factor h(r).
-2*r*(r - 1)*(r + 2)**2/15
Let s(a) be the second derivative of -a**6/135 - 17*a**5/45 + a**4/18 + 104*a**3/27 + 68*a**2/9 - 722*a. Suppose s(t) = 0. What is t?
-34, -1, 2
Let a = 247163/4 + -62923. Let m = 1136 + a. Factor -m*g + 3/2*g**2 + 0.
3*g*(2*g - 5)/4
Suppose 2*g + 7*d - 17 = 10*d, 0 = 2*g - 2*d - 14. Let a(q) be the third derivative of 0*q - 6*q**2 + 0 - 3/2*q**3 - 1/60*q**5 - 1/4*q**g. Factor a(h).
-(h + 3)**2
Suppose 0 = 4*f + 3*y - 1, -2*f + y + 6 = -7. Suppose 0 = -f*l + 11*l - 14. Factor -h**4 - h**5 + 3*h**3 + h**l - 2*h**3 + 0*h**5.
-h**2*(h - 1)*(h + 1)**2
Let u(j) be the first derivative of -5*j**6/6 - 273*j**5 - 91095*j**4/4 + 281525*j**3/3 - 142140*j**2 + 95220*j - 124. Determine t so that u(t) = 0.
-138, 1
Let f(w) be the first derivative of 1/34*w**4 + 6/17*w + 7/17*w**2 + 10/51*w**3 - 52. Determine x so that f(x) = 0.
-3, -1
Let x(a) = -a**2 - 36*a - 91. Let v be x(-33). Let u be (v/36)/(2/18). Factor 0 + 12*b - 3/2*b**u.
-3*b*(b - 8)/2
Suppose 0 = -3*u + 3*p + 2814, 23*p + 3728 = 4*u + 25*p. Let z = u - 930. Let -2/3*y**5 + 0*y**2 + 0*y - 4/3*y**3 + 0 + 2*y**z = 0. What is y?
0, 1, 2
Let m(t) be the second derivative of -1/24*t**4 - 1/10*t**5 + 0*t**3 + 0 - 17*t - 9/160*t**6 - 5*t**2. Let u(o) be the first derivative of m(o). Factor u(c).
-c*(3*c + 2)*(9*c + 2)/4
Solve -464*t + 20*t**4 - 534 + 360*t**2 - 138 + 199*t**3 - 99*t**3 - 68*t**4 + 4*t**5 = 0 for t.
-2, -1, 2, 6, 7
Let a = -6691 + 6694. Let g(l) be the second derivative of 15*l**2 + 5/6*l**a - 5/2*l**4 + 23*l + 0 - 1/4*l**5. Factor g(x).
-5*(x - 1)*(x + 1)*(x + 6)
Let o be ((-715)/39)/(13/((-364)/35)). Determine x so that o*x - 2/3*x**2 - 242/3 = 0.
11
Let p(y) = 3*y**3 + 2*y**2 - y + 6. Let n be p(-3). Let b = n + 56. Suppose f**2 + 2*f + 5*f + 3*f - 5 - 6*f**b = 0. What is f?
1
Let n(p) be the first derivative of 2*p**3/27 - 26*p**2 + 3042*p + 1314. Factor n(f).
2*(f - 117)**2/9
Let w = 32610 - 32610. Let f(s) be the third derivative of -1/720*s**5 - 1/144*s**4 + 0 + 19*s**2 + w*s**3 + 0*s. Factor f(o).
-o*(o + 2)/12
Let p(u) = 2*u - 28. Let z be p(0). Let i = -23 - z. Solve -5*x + 10*x + i*x**5 - 10*x**3 + 0*x**3 = 0.
-1, 0, 1
Let k(z) be the third derivative of -z**5/60 - 11*z**4/8 - 15*z**3 - 467*z**2. Factor k(o).
-(o + 3)*(o + 30)
Let f = 21421/12 + -1785. Let o(m) be the third derivative of 12*m**2 + 0 + 0*m - 5/3*m**3 - 5/24*m**4 + f*m**5. Let o(g) = 0. Calculate g.
-1, 2
Let a(k) = -k**4 - 9*k**3 - 3*k**2 + 19*k. Let t be 12/21 + ((-9)/(-21))/1. Let c(w) = w**4 + w**3 - w**2 + w. Let m(x) = t*a(x) - 3*c(x). Factor m(f).
-4*f*(f - 1)*(f + 2)**2
Let v(s) be the third derivative of -25*s**8/336 + 43*s**7/42 - 39*s**6/8 + 101*s**5/12 + 5*s**4/12 - 20*s**3 + 66*s**2 + 1. Solve v(k) = 0.
-2/5, 1, 3, 4
Let i = 85/151 - -1821/1057. Determine c so that -26/7*c - i - 11/7*c**2 - 1/7*c**3 = 0.
-8, -2, -1
Let d be 6 + -4*4/8. Suppose -14 = -f + d*y, -2*f + 13 = -5*y - 6. Determine o, given that o - o**3 - 1/3*o**4 - 1/3*o**f + 2/3 = 0.
-2, -1, 1
Let k(o) be the first derivative of -o**4/12 + 10*o**3/9 + 119*o**2/6 - 765. Find p such that k(p) = 0.
-7, 0, 17
Let t = -487 + 489. Let v be (-1*t/76)/(8/(-128)). Factor -v*k**2 + 6/19*k**3 - 8/19*k + 0.
2*k*(k - 2)*(3*k + 2)/19
Solve -7904*u - 1072*u - 14*u**2 - 4*u**2 + 2328 + 834*u - 3*u**2 = 0.
-388, 2/7
Let i be (-158*4/(-160) - 4)/(-7 + 2158/312). Factor -1/5*f - 2/5 + i*f**2.
(f - 1)*(3*f + 2)/5
Let i(c) be the first derivative of 1/30*c**6 - 1/25*c**5 + 13/15*c**3 + 4/5*c**2 - 12/5*c - 9/20*c**4 - 141. Let i(m) = 0. What is m?
-3, -1, 1, 2
Let p(u) = -15*u**2 - 68*u - 255. Let y(x) = -6*x**2 - x. Let v(f) = p(f) - 2*y(f). Solve v(i) = 0.
-17, -5
Let c = -57 - -60. Suppose -c*o = -5*o - 2, 3*t - 5*o - 23 = 0. Let 2*s**5 + t*s**4 - 12*s**2 + 6*s**4 - 3*s**4 + s**5 = 0. What is s?
-2, 0, 1
Suppose j - 2*j = -0*j - 3. Let a(i) be the first derivative of -1/12*i**j - 5/4*i + 3/4*i**2 - 17. Factor a(z).
-(z - 5)*(z - 1)/4
Factor -19*z**2 - 25*z**2 + 5*z**3 + 101*z**2 + 58*z**2.
5*z**2*(z + 23)
Let r(y) = y**3 + 21*y**2 - 4*y - 60. Let n(p) = -p**2 + p. Let o(a) = -60*n(a) - 5*r(a). Let o(x) = 0. Calculate x.
-6, -5, 2
Let f(r) be the first derivative of -1/24*r**4 + 111 - 31/12*r**2 - 5*r - 5/9*r**3. Suppose f(x) = 0. What is x?
-5, -3, -2
Factor -41/2*c - 21/2*c**2 - 61/6 - 1/6*c**3.
-(c + 1)**2*(c + 61)/6
Let i(c) be the third derivative of c**5/105 + 23*c**4/21 + 30*c**3/7 + 1693*c**2. Factor i(o).
4*(o + 1)*(o + 45)/7
Let b(t) = -2*t - 32. Let w be b(-19). Factor -7311*c**3 + 6*c**4 - 5*c - w*c**2 + 2*c**5 + 7313*c**3 + c.
2*c*(c - 1)*(c + 1)**2*(c + 2)
Let f(d) be the first derivative of d**6/4 - 26*d**5/15 - d**4/2 - 1391. Factor f(t).
t**3*(t - 6)*(9*t + 2)/6
Let m(k) be the first derivative of 168*k**6 - 3984*k**5/5 - 3089*k**4 - 104*k**3 + 424*k**2 + 96*k - 552. Solve m(a) = 0 for a.
-2, -1/6, 2/7, 6
Suppose 3*t - 43 = -4*r, 6*r = t + r - 8. Suppose t*j = -18*j + 5*j. Determine o, given that -1/4*o**4 + 0*o**2 + 0*o**3 + 0*o + j = 0.
0
Suppose 104*u - 271 + 63 = 0. Let a(r) be the first derivative of -45/4*r**u - 75/2*r - 10 - 3/8*r**4 + 9/2*r**3. Factor a(c).
-3*(c - 5)**2*(c + 1)/2
Factor 17/6*s - 1/6*s**3 - 7/3*s**2 + 5.
-(s - 2)*(s + 1)*(s + 15)/6
Suppose 8*r - 106 = 5*q, -2*r = -4*q + 105 - 115. Factor -31/5 - q*m + 1/5*m**2.
(m - 31)*(m + 1)/5
Factor -396/5 - 21/5*o**2 + 48*o.
-3*(o - 2)*(7*o - 66)/5
Let s(q) = -10*q**2 + 3337*q + 3305. Let d(x) = 28*x**2 - 10012*x - 9928. Let i(a) = 3*d(a) + 8*s(a). Factor i(p).
4*(p - 836)*(p + 1)
Suppose -197014975/2 - 594015/2*z - 1/10*z**3 - 597/2*z**2 = 0. Calculate z.
-995
Let -9116450 - 6007*q + 1117*q**2 + 1102*q**2 - 2221*q**2 - 2533*q = 0. Calculate q.
-2135
Suppose -218*k - 253*k + 654*k**3 - 659*k**3 - 115*k**2 - 159*k = 0. What is k?
-14, -9, 0
Let g(h) = -13404*h + 174254. Let a be g(13). Factor 18*k**2 + 33/2*k**3 + a*k**4 + 7/2*k + 0.
k*(k + 1)*(k + 7)*(4*k + 1)/2
Solve 2044416000*t - 674657280000 - 2323200*t**2 + 3520/3*t**3 - 2/9*t**4 = 0.
1320
Let k(y) = -y + 37. Let d be k(9). Suppose d = n + 22. Factor -21*u**2 - 12*u**2 + 48*u**3 + n*u - 49*u**4 + 28*u**4.
-3*u*(u - 1)**2*(7*u - 2)
Let s(i) be the second derivative of -2*i**6/105 + 2*i**5/35 + i**4 + 12*i**3/7 - 4*i + 421. Factor s(t).
-4*t*(t - 6)*(t + 1)*(t + 3)/7
Let t(z) be the third derivative of -z**6/60 - 11*z**5/30 + 65*z**4/12 + 25*z**3 - 32*z**2 - 37*z - 1. Let t(a) = 0. What is a?
-15, -1, 5
Let p(j) be the third derivative of j**5/20 - 189*j**4 + 285768*j**3 - 67*j**2 - 1. Suppose p(g) = 0. What is g?
756
Factor -35*v