+ 12. Factor b*h + 1 + 2*h**2 - 3*h**3 + 3*h - 3.
-(h - 1)*(h + 1)*(3*h - 2)
Find z, given that -250*z**3 + 792/5*z - 960*z**2 - 32/5 = 0.
-4, 2/25
Let k = -45 + 47. Find j such that 861*j**2 - 11*j - 853*j**2 + j + k*j**3 = 0.
-5, 0, 1
Factor -94*r**3 + 28*r - 29 - 11 + 16*r**2 + 90*r**3.
-4*(r - 5)*(r - 1)*(r + 2)
Let c = -47 - -50. Suppose -2*m - 4*t = c*m - 10, -5*m = 5*t - 10. Factor 1/4*y**m - 3/8 - 5/8*y.
(y - 3)*(2*y + 1)/8
Let v(i) be the first derivative of -1/18*i**4 + 6*i + 8 - 1/9*i**2 + 1/9*i**3 + 1/90*i**5. Let d(c) be the first derivative of v(c). Factor d(b).
2*(b - 1)**3/9
Let -42*p - 2110*p**4 - 25*p + 2094*p**4 + 4*p**5 + 64*p**2 + 3*p = 0. Calculate p.
-2, 0, 2
Let n(m) = m**3 - 6*m**2 + 11*m. Let r(w) be the third derivative of w**5/60 - w**4/24 + 5*w**2. Let v(c) = -4*n(c) - 36*r(c). Find k such that v(k) = 0.
-2, -1, 0
Let t(g) = g**2 - 23*g + 116. Let b be t(7). Let -2*u**2 + 9/2*u**b + 0 - 2*u + 9/2*u**3 = 0. What is u?
-1, -2/3, 0, 2/3
Let t = -33 - -35. Let c(a) = 2*a**4 - 6*a**3 + 14*a**2 - 10*a - 10. Let w(j) = j**2 - j - 1. Let v(g) = t*c(g) - 20*w(g). Factor v(l).
4*l**2*(l - 2)*(l - 1)
Let z(u) = 13*u**4 - 53*u**3 - 83*u**2 - 32*u - 5. Let s(h) = -7*h**4 + 26*h**3 + 42*h**2 + 16*h + 2. Let v(l) = 5*s(l) + 2*z(l). Let v(r) = 0. What is r?
-2/3, 0, 4
Determine s so that -82/7 - 80/7*s + 2/7*s**2 = 0.
-1, 41
Let h(q) be the third derivative of -28*q**2 - 8/21*q**3 + 1/21*q**5 + 1/21*q**4 - 1/420*q**6 + 0 - 1/1176*q**8 + 0*q - 4/735*q**7. Factor h(d).
-2*(d - 1)**2*(d + 2)**3/7
Suppose -14*t - 2*t + 256 = 0. Let x be (-12)/t - (-2 - 0). Let -x*w**2 - 1/4*w**4 + w**3 + 0 + 1/2*w = 0. What is w?
0, 1, 2
Suppose m = -2*k + 3*m + 4, 2 = k + m. Let i be ((-1)/(-3))/(4/72). Factor i*s + 6*s + 4*s**k - 4*s.
4*s*(s + 2)
Determine s so that 46/7*s**2 + 8*s + 16/7*s**3 + 2/7*s**4 + 24/7 = 0.
-3, -2, -1
Suppose -2*j + 86*x = 89*x - 5, x = -j + 3. Factor -12*p + 49/3*p**j + 4/3 + 109/3*p**2 - 42*p**3.
(p - 1)**2*(7*p - 2)**2/3
Let w(g) be the first derivative of -g**7/1365 - g**6/780 + 5*g**2/2 + 4. Let z(j) be the second derivative of w(j). Suppose z(n) = 0. What is n?
-1, 0
Suppose 0 = 2*i + 3*h - 7, 5*i + 2*h - 7 = 5*h. Suppose 12*c**3 - 6*c**4 - 4*c**i - 4*c**3 + c**2 + c**3 = 0. What is c?
0, 1/2, 1
Let c = -78 - -74. Let o be (-3 + -25)/c + -3. Factor 3/2*t**3 - 3/2*t + 3/2*t**2 + 0 - 3/2*t**o.
-3*t*(t - 1)**2*(t + 1)/2
Let d(z) be the first derivative of -1/33*z**6 + 0*z**2 + 0*z + 6/55*z**5 - 7 - 3/22*z**4 + 2/33*z**3. Find m, given that d(m) = 0.
0, 1
Let q be (6/5)/((-3)/(-5)). Factor f - 70 + 3*f**q - f + 67.
3*(f - 1)*(f + 1)
Suppose 4*d - 56 = -4*g, 0 = -4*d - 4*g - g + 60. Suppose 2*w - d = -3*w + s, -3*w + 6 = -4*s. Let -7*l + l + 2 + 2*l**w + 16 - 6*l = 0. Calculate l.
3
Let p(k) be the first derivative of -k**6/780 + k**4/156 + 9*k**2/2 + 2*k - 8. Let l(u) be the second derivative of p(u). Factor l(m).
-2*m*(m - 1)*(m + 1)/13
Let i(m) be the third derivative of m**7/630 - m**6/360 - 2*m**5/15 + m**4/18 + 40*m**3/9 - 20*m**2 + 9. Find k such that i(k) = 0.
-4, -2, 2, 5
Let r(l) be the second derivative of -l**4/18 - 2*l**3 - 17*l**2/3 - l + 18. Solve r(b) = 0.
-17, -1
Let q(s) be the second derivative of s**6/10 + 9*s**5/10 + 7*s**4/4 - 3*s**3 - 12*s**2 + 33*s. What is t in q(t) = 0?
-4, -2, -1, 1
Suppose 3*h = 5*k - 4*k - 13, -2*k + h + 11 = 0. Suppose 10 = -i + s - k*s, -s = -4*i + 12. Factor -u + u**3 - 2/3 + 2/3*u**i.
(u - 1)*(u + 1)*(3*u + 2)/3
Suppose 21*o = -6*o + 100 - 19. Factor 0*t + 0*t**4 + 0 + 2/5*t**5 - 2/5*t**o + 0*t**2.
2*t**3*(t - 1)*(t + 1)/5
Suppose f = b + 80, -b = -4 + 2. Let v = f + -161/2. Let 0*j - v*j**4 - 3/2*j**2 - 3*j**3 + 0 = 0. What is j?
-1, 0
Suppose -k - 245 = -3*b, 3*b - 2*k + 148 = 395. Let v be 3/8*27/b. Determine h, given that -v*h**5 + 0 + 3/8*h**3 + 1/4*h**4 + 0*h + 0*h**2 = 0.
-1, 0, 3
Let k(t) = -10*t**2 + 20*t - 30. Let r(z) = 2*z + 10. Let g be r(-8). Let a(m) = 29*m**2 - 60*m + 89. Let v(i) = g*a(i) - 17*k(i). Factor v(w).
-4*(w - 3)*(w - 2)
Let m = -1142 + 2341/2. Let a = m + -163/6. Factor 0 + 2/3*d - a*d**2.
-2*d*(2*d - 1)/3
Let y(f) be the third derivative of -f**8/1680 - 2*f**7/525 - f**6/120 - f**5/150 + 11*f**2. Factor y(v).
-v**2*(v + 1)**2*(v + 2)/5
Suppose 147 = 13*j + 121. Factor -5/2 + 2*y + 1/2*y**j.
(y - 1)*(y + 5)/2
Suppose 4 = -3*n + 7*n. Suppose -10 = 2*p - 4*w, -w + 5 - n = 0. Suppose 0 + 2/11*a**4 - 2/11*a**2 - 2/11*a + 2/11*a**p = 0. Calculate a.
-1, 0, 1
Let t(h) = h**3 - h**2 - h - 1. Let l(b) = -8*b**3 + 41*b**2 + 5*b + 5. Let s(m) = l(m) + 5*t(m). Factor s(u).
-3*u**2*(u - 12)
What is k in -7*k**2 - k**5 + 5*k**4 + 8*k**2 - 6*k**2 - 6*k + 67*k**3 - 60*k**3 = 0?
-1, 0, 1, 6
Suppose 0 + 5/6*z**2 + 55/6*z = 0. Calculate z.
-11, 0
Let b(z) be the third derivative of -z**6/180 - z**5/36 + z**4/24 + 13*z**2 + 2. Find g such that b(g) = 0.
-3, 0, 1/2
Let d be (459/(-45) - -9)/(2/(-5)). Solve 0 + 2/3*q**2 + 0*q - 2/3*q**d = 0.
0, 1
Let h(f) = -10*f**2 - 37*f - 75. Let y be (-2)/(5*(-3)/(-15)). Let v(q) = 3*q**2 + 12*q + 25. Let x(p) = y*h(p) - 7*v(p). Determine l so that x(l) = 0.
-5
Let p(l) be the third derivative of l**5/60 - l**4/8 + l**3/3 - 11*l**2. Factor p(t).
(t - 2)*(t - 1)
Let i(x) = -33*x**3 - 17*x - 73*x + 23*x**3 + 55 + 100*x**2. Let l(y) = y**3 - 11*y**2 + 10*y - 6. Let t(u) = -6*i(u) - 55*l(u). Factor t(v).
5*v*(v - 1)*(v + 2)
Let k be -2 - 1/(3/(-51)). Suppose 0 = 3*h - u - 37 - 57, -3*h - 2*u + 100 = 0. Let 29 - 17 + 4*q**2 + 37 + h*q + k = 0. What is q?
-4
Let k(m) be the second derivative of m**7/2205 - m**5/315 + m**3/63 - 13*m**2 - 20*m. Let b(f) be the first derivative of k(f). Let b(n) = 0. Calculate n.
-1, 1
Let s be (1 + (-1)/((-9)/(-6)))*753. Let f = -249 + s. Let 0 - 1/5*y - 1/5*y**3 + 2/5*y**f = 0. What is y?
0, 1
Let z be (21 - 3 - 22) + (-120)/(-26). Factor 12/13*w**4 + 2/13*w**5 + z*w + 24/13*w**2 + 2*w**3 + 0.
2*w*(w + 1)**2*(w + 2)**2/13
Let w be (8 - (-90)/(-11)) + (-15)/(-22). Determine u, given that 1/4*u**3 - 1/4*u + 1/2 - w*u**2 = 0.
-1, 1, 2
Let o be ((-80)/28)/(5 - 74/14). Let n be (-6)/o - 23580/(-3300). Solve 100/11*q**3 + n*q**2 + 10/11*q**5 + 0 + 16/11*q + 54/11*q**4 = 0 for q.
-2, -1, -2/5, 0
Determine o, given that -50/3 - 1/6*o**2 - 26/3*o = 0.
-50, -2
Let p(f) = f**3 + 8*f**2 + 12*f - 9. Let i be p(-7). Let w = -44 - i. Suppose 2/11*g**2 + w*g + 0 + 4/11*g**4 + 6/11*g**3 = 0. What is g?
-1, -1/2, 0
Let v be (-6*7/63)/((6/4)/(-3)). Solve -14/9*q**3 + v + 34/9*q**2 - 34/9*q + 2/9*q**4 = 0 for q.
1, 2, 3
Let v = -16430 - -115013/7. Factor -3/7*y**2 + 0*y + v*y**3 + 0.
3*y**2*(y - 1)/7
Let o(v) = 10*v**5 - 60*v**4 + 16*v**3 + 66*v**2 - 38*v - 12. Let t(g) = g**5 + g**2 + g. Let a(h) = -o(h) - 6*t(h). Determine n, given that a(n) = 0.
-1, -1/4, 1, 3
Let -3/4*v**3 + 3*v - 3/4*v**2 + 3 = 0. What is v?
-2, -1, 2
Let z(s) be the second derivative of s**8/1344 - s**7/252 - s**4/6 - 4*s. Let q(k) be the third derivative of z(k). Find d, given that q(d) = 0.
0, 2
Factor 17*h**3 - 49*h - h**4 - 48 - 331099*h**2 + 331102*h**2 + 14.
-(h - 17)*(h - 2)*(h + 1)**2
Let s(p) be the second derivative of -1/6*p**4 + 8/3*p**3 - 6*p + 0 - 16*p**2. Let s(u) = 0. Calculate u.
4
Suppose 0 = 5*a - 7 - 8. Suppose 0 = a*j - 8 - 4. Factor 4*z**2 + 3*z + 4*z + z + j.
4*(z + 1)**2
Suppose -8 = -3*q - 2. Let p(k) = 3*k + 1. Let t be p(q). Find h such that -3*h**2 + 2*h**2 - 7*h - t*h + 13*h = 0.
-1, 0
Let -52*d**4 - 24*d + 22*d**2 + 28*d**3 + 389*d**5 + 46*d**2 - 377*d**5 = 0. Calculate d.
-1, 0, 1/3, 2, 3
Let p(o) be the first derivative of -2*o**3/3 + 5*o**2/2 + 4*o - 1. Let s(x) = x**2 - x - 1. Let q(t) = 4*p(t) + 12*s(t). Factor q(h).
4*(h + 1)**2
Let l(d) be the third derivative of 0*d**4 + 1/750*d**6 + 0 + 0*d**3 + 9*d**2 + 1/250*d**5 + 0*d. Factor l(r).
2*r**2*(2*r + 3)/25
What is h in 9*h**3 + 4*h**5 - 11*h**3 - 2*h**5 + 34*h**4 - 37*h**4 = 0?
-1/2, 0, 2
Let l(u) be the second derivative of -22*u - 4/3*u**3 - 6*u**2 + 0 - 1/9*u**4. Factor l(b).
-4*(b + 3)**2/3
Suppose 3*f - 4*u = -3*u + 179, -3*f - 4*u + 154 = 0. Determine t so that -40*t + 4*t**4 - 24*t**3 + f + 36*t**2 - 46 + 12*t**2 = 0.
1, 3
Let c(l) be the first derivative of -l**6/180 - 2*l**5/15 + 3*l**4/4 - 8*l**3/3 - 14. Let d(z) be the third derivative of c(z). Fac