7. Determine t, given that 2*t**3 - 8 + 9*t**3 - 6*t - 12*t**3 - h*t**2 - 11*t = 0.
-8, -1
Let m(s) = s**2 + 1. Let o(w) = 15*w**2 + 36*w + 120. Let n = 40 + -19. Suppose 5*a - 59 = -x, -x + n - 82 = -5*a. Let c(k) = a*m(k) - o(k). Solve c(u) = 0.
-6
Solve 4/5*h**2 + 868/5 - 872/5*h = 0 for h.
1, 217
Suppose -2*n + 716 = -55*m + 50*m, 2*n = -4*m - 580. Let f be ((-108)/m)/(3/2) - 0. Factor 3/2 - f*k**2 - k.
-(k - 1)*(k + 3)/2
Let l(q) be the second derivative of 5*q**4/12 - 110*q**3/3 - 230*q**2 + 98*q. Suppose l(p) = 0. Calculate p.
-2, 46
Let -90 - 809/9*x + 1/9*x**2 = 0. What is x?
-1, 810
Suppose 29*k = 28*k + 5. Factor -432*u**2 + 23*u**5 + 360*u**3 + 24*u**5 + 69*u**4 - 61*u**5 + 17*u**k.
3*u**2*(u - 1)*(u + 12)**2
Let r(i) = -7*i + 15. Let t(q) = -65*q + 135. Let o(w) = -55*r(w) + 6*t(w). Let f be o(-8). Factor 0*p**2 + f*p**2 - 3*p**4 + 4*p**4 + 10*p**3.
p**2*(p + 5)**2
Let z(b) be the second derivative of -74*b + 0 + 1/18*b**4 + 784/3*b**2 - 56/9*b**3. Suppose z(g) = 0. What is g?
28
Let c(j) = -22*j**3 - 52*j**2 + 41*j + 84. Let n(k) = 3*k**3 + 7*k**2 - 6*k - 12. Let x(r) = 4*c(r) + 30*n(r). Factor x(a).
2*(a - 3)*(a + 2)**2
Let j(g) be the third derivative of -g**7/2940 + g**6/210 - g**5/84 - 22*g**3/3 + 27*g**2 - 1. Let q(a) be the first derivative of j(a). Factor q(s).
-2*s*(s - 5)*(s - 1)/7
Let k = -76 - -73. Let c be 6/6*(2 - (-9)/k). Let l(w) = -15*w**4 - 3*w**3 + w. Let z(h) = -h**4 + h**3 + h. Let m(x) = c*l(x) + z(x). Let m(s) = 0. What is s?
-2/7, 0
Let g(b) be the second derivative of -b**7/231 + 19*b**6/165 - 27*b**5/55 - 47*b**4/33 + 5*b**3/3 + 75*b**2/11 + 103*b + 5. Solve g(s) = 0.
-1, 1, 5, 15
Let a(z) be the second derivative of -z**5/10 - 5*z**4/3 + 141*z**3 - 2268*z**2 - 264*z. Factor a(d).
-2*(d - 9)**2*(d + 28)
Factor -1240*k - 154*k**2 + 68 + 321*k**2 + 208 + 256*k**2 + 4*k**3 + 120*k**2.
(k - 2)*(k + 138)*(4*k - 1)
Let m(i) be the first derivative of -25 - 1/10*i**6 + 0*i**2 - 1/2*i**3 - 9/20*i**5 - 8*i - 3/4*i**4. Let z(t) be the first derivative of m(t). Factor z(j).
-3*j*(j + 1)**3
Let x(a) = -a**3 - 36*a**2 - 288*a + 2. Let c be x(-24). Let r = -117 + 1757/15. Let r + 16/5*z**c + 32/15*z**3 + 6/5*z = 0. What is z?
-1, -1/4
Factor 19480*z**2 - 4 + 7242*z - 40711*z**2 + 28477*z**2.
2*(z + 1)*(3623*z - 2)
Let w(p) = 38*p**3 - 26*p**2 - 114*p + 54. Let c(v) = -2*v**3 + v - 3. Let a(k) = 36*c(k) + 2*w(k). Factor a(y).
4*y*(y - 16)*(y + 3)
Let l(r) be the second derivative of -2*r**4/3 - 454*r**3/3 - 226*r**2 - 1812*r. Factor l(o).
-4*(o + 113)*(2*o + 1)
Let k(r) = 2*r + 1. Let l(b) be the third derivative of b**5/12 - 9*b**4/8 - 13*b**3/3 + 10*b**2. Let f(i) = -6*k(i) - l(i). Solve f(h) = 0.
-1, 4
Let v(s) = -2*s**3 + 181*s**2 - 456*s - 259. Let i(q) = -q**3 + 5*q**2 - 5. Let m(z) = 4*i(z) + v(z). Find a such that m(a) = 0.
-1/2, 3, 31
Let p = 1363 + -12251/9. Let a(k) be the second derivative of -1/6*k**4 - 8/9*k**3 - p*k**2 + 0 - 5*k - 1/90*k**5. Factor a(z).
-2*(z + 1)*(z + 4)**2/9
Find s, given that 1/8*s**4 + 0*s - 69*s**2 + 137/4*s**3 + 0 = 0.
-276, 0, 2
Let v(m) = m**2 - 6*m + 10. Let i be v(4). Suppose 3*b = h + 15, 0 = -h + 5*h - i*b + 10. Factor h + 4 - c**2 - 3*c - 6.
-(c + 1)*(c + 2)
Let m(q) be the second derivative of q**7/357 - 49*q**6/255 + 141*q**5/170 - 139*q**4/102 + 46*q**3/51 + 1565*q. Factor m(s).
2*s*(s - 46)*(s - 1)**3/17
Let n(x) = x**2 + 7*x + 2. Let z be n(-7). Suppose -25 = -3*b - z*b. Let 2*j**3 + 0*j**3 + 0*j**2 - b*j**3 + 12 - 9*j**2 = 0. What is j?
-2, 1
Let z = 3881/21 - 1240/7. Factor -1/6*c**2 + z*c - 529/6.
-(c - 23)**2/6
Suppose -2*t - 2*t - h = 1, 0 = -2*t - 3*h - 3. Suppose -4*a + 8 = -t. Factor 6 + 4*s**3 + 20*s - 7 - 7 - 16*s**a.
4*(s - 2)*(s - 1)**2
Let v = 12634/35 - 1802/5. Let y be 7/(-35) - (-51)/105. Factor 2/7*w - y + v*w**2.
2*(w + 1)*(2*w - 1)/7
Let k(o) = -o**3 + 9*o**2 + 12*o - 18. Let c be (8/(-10))/(10/(-125)). Let q be k(c). Factor q*r**3 + 2*r**2 - 7*r**2 + 2*r + 2*r**2 - 3*r**3 - r**5 + 3*r**4.
-r*(r - 2)*(r - 1)**2*(r + 1)
Let t = 185/477 + 3/53. Let l(p) = 2*p**3 - 109*p**2 + 157*p + 108. Let k be l(53). What is a in 2/3 + t*a - 2/9*a**k = 0?
-1, 3
Let d(r) be the third derivative of r**8/420 - 43*r**7/350 + 34*r**6/75 - r**5/5 - 587*r**2. Let d(u) = 0. What is u?
0, 1/4, 2, 30
Let w(n) = 3*n**4 - 21*n**3 - 63*n**2 - 51*n - 18. Let d = -184 + 183. Let y(q) = q**4 - 2*q**2. Let h(z) = d*w(z) + 6*y(z). Suppose h(c) = 0. What is c?
-3, -2, -1
Let j(p) = p**2 - 4*p + 5. Let z(x) = -x**2 + 3. Let f be z(0). Let d be j(f). Factor -d - 16 + 3*b**2 - 6*b**2 + b**2 - 12*b.
-2*(b + 3)**2
Let s(z) be the third derivative of -z**8/132 - 10277*z**7/2310 - 10613*z**6/1320 + 92*z**5/165 + 61*z**4/22 + 107*z**2 - 2*z + 9. What is c in s(c) = 0?
-366, -1, -2/7, 0, 1/4
Let h(g) = g**2 - 1. Let o(s) = -3*s**2 - 2*s + 1. Let w = 10 + -16. Let k be ((-4)/w)/(14/(-21)). Let c(i) = k*o(i) - 2*h(i). Find d such that c(d) = 0.
-1
Let p(j) be the third derivative of j**7/504 + 73*j**6/72 + 5329*j**5/24 - 87*j**4/8 + 177*j**2. Let c(m) be the second derivative of p(m). Factor c(x).
5*(x + 73)**2
Let g(r) = -6*r. Let i be g(-4). Let x be 1*6/(-33) - i/(-11). Factor 0*t - 10*t**2 - 2*t + x*t**2 - 2*t - 4*t**3.
-4*t*(t + 1)**2
Suppose -387*t = -245*t - 568. Factor -8/7 - 232/7*v - 56*v**t - 1794/7*v**2 - 232*v**3.
-2*(v + 2)**2*(14*v + 1)**2/7
Suppose 0 = -2*r - 2*r. Let k = -230748 - -692246/3. Factor r + 0*o + 2/3*o**4 + 0*o**2 - 4/3*o**3 + k*o**5.
2*o**3*(o - 1)*(o + 2)/3
Let c be 266/(-95) - (-384)/60. Factor -4 + 1/10*h**3 - c*h - 3/5*h**2.
(h - 10)*(h + 2)**2/10
Let p(m) be the first derivative of 113 - 16/11*m + 6/11*m**2 - 2/33*m**3. Factor p(b).
-2*(b - 4)*(b - 2)/11
Let f be (-34)/85 - 62/(-30). Suppose f*i - 1/6*i**2 - 3/2 = 0. What is i?
1, 9
Suppose -63 = -13*u + 28. Let 192 - 23*t**2 + u*t**2 + 71*t**2 + 200*t + 48 + 5*t**3 = 0. Calculate t.
-4, -3
Let f(m) be the third derivative of 0*m**3 - 5/1848*m**8 + 16*m - 12/11*m**4 - 16/11*m**5 + 0 - 82/165*m**6 - 3*m**2 - 24/385*m**7. Solve f(i) = 0 for i.
-6, -2, -2/5, 0
Let a(g) be the third derivative of -2*g**2 + 0*g**3 + 0 + 7/15*g**5 + g**4 + 1/30*g**6 - 62*g. Factor a(b).
4*b*(b + 1)*(b + 6)
Let h(o) be the third derivative of -o**5/420 + 277*o**4/168 + 1461*o**2. What is n in h(n) = 0?
0, 277
Suppose -5*u + 43 = 3*z, 2*z = 1728*u - 1731*u + 27. Determine v so that 0 + 0*v + v**2 + 5/4*v**4 - 2*v**3 - 1/4*v**u = 0.
0, 1, 2
Suppose 2 = -20*z + 21*z, -5*f + 21 = -2*z. Suppose -11*g = -27*g + 64. Factor 4/7*m**2 + 2/7*m**f - 2/7*m**g + 2/7*m - 4/7*m**3 - 2/7.
2*(m - 1)**3*(m + 1)**2/7
Suppose 4*k - 7*z = -3*z + 36, 0 = k + z + 1. Factor 15*w**4 - 28*w**4 + 36*w**3 + 3*w**5 - 7*w**4 - 4*w**k.
3*w**3*(w - 6)*(w - 2)
Let j(t) be the third derivative of t**7/1120 - 3*t**5/160 + t**4/16 - 119*t**3/6 + 8*t**2 + 9. Let k(a) be the first derivative of j(a). Factor k(q).
3*(q - 1)**2*(q + 2)/4
Let s be ((-33)/429)/((-8)/26) - (-22)/8. Let n(p) be the second derivative of 0 - 5/42*p**4 + 0*p**2 + 1/21*p**s + 2/35*p**5 - 5*p. Solve n(t) = 0 for t.
0, 1/4, 1
Let z(w) = w**3 - w**2 + w. Let t(m) = 72*m + 76*m - 3*m**3 + 34*m**2 - 2*m**3 + 42*m. Let g(r) = 5*t(r) + 30*z(r). Factor g(v).
5*v*(v + 14)**2
Suppose 0 = 5*r + 4*c + 39, 5*r = 3*r - 5*c - 19. Let w(s) = s**3 + 7*s**2 - 3*s - 13. Let a be w(r). Factor -2*k**2 - 8*k - a*k**3 + 4*k**4 - 8*k - 26*k**2.
4*k*(k - 4)*(k + 1)**2
Let g be 27/13 - -1 - 281/3653. Let t(l) be the first derivative of 6*l - 18 - 3/5*l**5 + 9/2*l**2 - l**g - 9/4*l**4. Suppose t(p) = 0. Calculate p.
-2, -1, 1
Let l(f) be the second derivative of -2/15*f**6 + 0 - 1/21*f**7 + 3*f + 3/10*f**5 + 2/3*f**4 - 4/3*f**3 + 0*f**2. Find q such that l(q) = 0.
-2, 0, 1
Let a(b) = -120*b**3 - 1376*b**2 + 8136*b + 9532. Let r(q) = -13*q**3 - 153*q**2 + 904*q + 1059. Let l(s) = 3*a(s) - 28*r(s). Factor l(c).
4*(c - 6)*(c + 1)*(c + 44)
Let t(p) = -15*p**4 + 59*p**3 + 466*p**2 + 14*p. Let i(b) = -2*b**4 + b**3 - 2*b**2 + 2*b. Let v(a) = 35*i(a) - 5*t(a). Factor v(y).
5*y**2*(y - 60)*(y + 8)
Solve 2445*a**2 + 9802*a**3 - 540 + 9786*a**3 + 7200*a - 19383*a**3 = 0.
-6, 3/41
Suppose -35 = 14*g + 7. Let c be (105/56)/g - -1. Let c*f**2 - 3/4 + 3/8*f = 0. Calculate f.
-2, 1
Let y be (0 + -4)/(63/15 + -4). Let k be -5*y/125*5. Fi