*2 + 24*o + 33. Let z(b) = -2*b**2 - 72*b - 98. Let q(y) = w*z(y) + 10*r(y). Factor q(t).
4*(t + 3)**2
Let l(r) be the second derivative of -r**5/80 - r**4/4 - 3*r**3/2 + 227*r. Factor l(f).
-f*(f + 6)**2/4
Let z(u) = -4*u - 27. Let v be z(-8). Suppose -4 = -5*g - r, v*g + 5 - 21 = -4*r. Solve 0 + 0*n + 1/5*n**5 + g*n**3 + 0*n**2 + 0*n**4 = 0.
0
Let v(g) = -3*g**2 - 21*g + 993. Let p be v(15). Determine j, given that 3*j + 1/3*j**p - 2*j**2 - 4/3 = 0.
1, 4
Factor 54*h**2 - 7*h - h + 7 + 61*h**2 - 114*h**2.
(h - 7)*(h - 1)
Let a(x) = -10*x**2 + 285*x + 5. Let j(f) = 9*f**2 - 286*f - 4. Let r(s) = 4*a(s) + 5*j(s). Factor r(z).
5*z*(z - 58)
Let -14/15*l + 0 + 2/15*l**3 - 4/5*l**2 = 0. What is l?
-1, 0, 7
Let f(q) be the third derivative of 13*q**7/1680 + 37*q**6/960 - 41*q**5/160 + 83*q**4/192 - 5*q**3/24 + 877*q**2. Let f(z) = 0. What is z?
-5, 2/13, 1
Let m(r) be the third derivative of r**6/780 - 4*r**5/195 - 11*r**4/52 + 8*r**2 + 13*r. Suppose m(t) = 0. Calculate t.
-3, 0, 11
Let w(n) = 34*n**2 + 5*n - 23. Let g(y) = 21*y**2 + 4*y - 15. Let c(i) = 8*g(i) - 5*w(i). Factor c(h).
-(h - 1)*(2*h - 5)
Let r(h) be the third derivative of -h**5/5 - 16*h**4/3 - 40*h**3/3 - h**2 - 8*h. Suppose r(p) = 0. Calculate p.
-10, -2/3
Suppose 2*i - n + 15 = 0, i = 3*i + 2*n + 6. Let s = 8 + i. Factor g**2 + 12*g - g**2 + 15*g**s - 8*g**3 - g**3 - 12.
-3*(g - 2)*(g + 1)*(3*g - 2)
Let j be (25 + 15080/(-609))/(10/4). Factor 4/21*z**4 - 4/21*z**2 + 0 + j*z**5 - 2/21*z + 0*z**3.
2*z*(z - 1)*(z + 1)**3/21
Let t(u) be the second derivative of 1/6*u**4 + 0 + 4/3*u**3 + 3*u**2 + 13*u. Suppose t(y) = 0. What is y?
-3, -1
Let a be (-21)/((-9)/3) - 5. Factor 3*s**4 + s**4 + 4 - 8*s**a + 0*s**2.
4*(s - 1)**2*(s + 1)**2
Factor -18*s**2 - 3*s**4 - 15*s**2 + 0*s**2 + 6*s**2 + 19*s + 47*s - 36*s**3.
-3*s*(s - 1)*(s + 2)*(s + 11)
Suppose -76 = 116*d - 135*d. Determine k so that -2/3*k**d + 0*k**3 + 0 + 0*k**2 + 0*k - 2/3*k**5 = 0.
-1, 0
Factor 516 + m**3 + 299 + 240*m**4 - 125*m**4 - 111 - 464*m - 116*m**4 + 84*m**2.
-(m - 4)**3*(m + 11)
Let o(r) be the third derivative of r**6/300 + 7*r**5/150 + r**4/10 + 10*r**2 + 2. Factor o(l).
2*l*(l + 1)*(l + 6)/5
Let p be ((-9)/(-24))/(((-1170)/(-40))/13). Let v(z) be the second derivative of 0 + p*z**4 + 1/5*z**5 + 1/15*z**6 - 6*z + 0*z**3 + 0*z**2. Factor v(s).
2*s**2*(s + 1)**2
Let a be 30/2 + 580/(-40). Determine k so that k**2 - k**4 - a*k + 1/2*k**5 + 0*k**3 + 0 = 0.
-1, 0, 1
Let z(f) = -3*f**4 - 13*f**3 + 80*f**2 - 62*f - 2. Let r(m) = m**4 + m**3 - m - 1. Let c(t) = -2*r(t) + z(t). Factor c(p).
-5*p*(p - 2)*(p - 1)*(p + 6)
Let l be 185/(-100) + 143/55. Factor -1/2*n - 1/4*n**2 + l.
-(n - 1)*(n + 3)/4
Let p(v) be the second derivative of v**6/45 - 7*v**5/15 + 25*v**4/18 - 4*v**3/3 - v - 11. Factor p(g).
2*g*(g - 12)*(g - 1)**2/3
Suppose 0 = 8*g + 9*g - 24 - 10. Solve 2/5 + 1/5*o**g + 3/5*o = 0 for o.
-2, -1
Suppose -y = 1, -k - 15 + 52 = -y. Factor -k*a**2 + 8 - 8*a - 20*a + 0*a.
-4*(a + 1)*(9*a - 2)
Suppose 5*t = -5*x - 30, -16 = 5*t - 4*t + 3*x. Let a be -4*(1 - 0)/t. Suppose 10*v**2 - 3*v - a*v**2 + v**3 - 4*v**3 = 0. Calculate v.
0, 1
Let g(i) be the second derivative of i**6/135 + 19*i**5/90 + 17*i**4/18 + 49*i**3/27 + 16*i**2/9 - 11*i + 2. Let g(n) = 0. What is n?
-16, -1
Let i(b) = 4 + 1 - b + 0 + 3. Let y be i(6). Factor 2*k**5 + 2*k**y - 5*k**3 - 3*k**3 + 2*k**3 + 2*k**2.
2*k**2*(k - 1)**2*(k + 2)
Factor -53*s**2 + 100*s + 52 + 17*s**2 + 28*s**2.
-4*(s - 13)*(2*s + 1)
Let m be (-12)/(((-66)/(-32))/(9/(-36))). Let h(y) = -y**3 - 4*y**2 + 2. Let n be h(-4). Let -32/11 + m*c - 2/11*c**n = 0. What is c?
4
Let r(i) = i**5 - i**4 - i**3 + i**2 + 2*i. Let c(a) = -a**4 + a**3 + a**2. Let l(y) = -2*c(y) + r(y). Let l(w) = 0. What is w?
-2, -1, 0, 1
Let 1/2*l**3 + 7/2*l + 5/2*l**2 + 3/2 = 0. Calculate l.
-3, -1
Let k(j) = 9*j**3 - 4*j**2 - 19*j - 6. Let l = 53 - 57. Let z(c) = -55*c**3 + 25*c**2 + 115*c + 35. Let d(w) = l*z(w) - 25*k(w). Factor d(u).
-5*(u - 2)*(u + 1)**2
Factor -72 - 764/3*t - 28/3*t**2.
-4*(t + 27)*(7*t + 2)/3
Factor -b**2 + 3*b**2 - 52 - 182 - 156 - 4*b**2 - 392*b.
-2*(b + 1)*(b + 195)
Let q(b) be the second derivative of -b**6/1260 - b**5/630 + b**4/252 + b**3/63 - 7*b**2/2 + 7*b. Let p(c) be the first derivative of q(c). Factor p(k).
-2*(k - 1)*(k + 1)**2/21
Factor 16/17 + 2/17*p**3 - 8/17*p - 4/17*p**2.
2*(p - 2)**2*(p + 2)/17
Let d be ((-45)/(-18))/((-7)/(-14)). Let n(w) be the first derivative of 0*w**2 + 0*w - 4/15*w**3 - 1 + 6/25*w**d - 1/10*w**4. What is k in n(k) = 0?
-2/3, 0, 1
Let i(b) = -b**2 - 2*b. Let s(a) = 8*a**2 + 14*a. Let q = -16 + 10. Let k(m) = q*s(m) - 44*i(m). Let k(c) = 0. What is c?
0, 1
Let d(m) be the first derivative of m**6/480 + m**5/80 + m**4/48 - 9*m**2/2 + 9. Let v(i) be the second derivative of d(i). What is n in v(n) = 0?
-2, -1, 0
Let w(j) = -4*j - 3. Let n(h) = 4*h**2 - 620*h - 619. Let p(o) = -n(o) + 5*w(o). Factor p(l).
-4*(l - 151)*(l + 1)
Let z(i) be the first derivative of i**4/10 - 8*i**3/3 - 21*i**2/5 - 90. Factor z(m).
2*m*(m - 21)*(m + 1)/5
Let q(w) be the first derivative of 3*w**4/28 + 4*w**3/7 + 15*w**2/14 + 6*w/7 + 68. Let q(j) = 0. Calculate j.
-2, -1
Determine y, given that -7/6*y**2 + 7/3*y + 1/6*y**3 - 4/3 = 0.
1, 2, 4
Let r = 5 + 1. Let k be (10/r)/5*33. Factor -3*f**2 + k*f**2 - 6*f - 11*f**2.
-3*f*(f + 2)
Let v = -127 - -132. Let i be v*11/(495/16). Determine w so that -4/9 - 2/9*w - 10/9*w**3 + i*w**2 = 0.
-2/5, 1
Let d be 3/(-1) - (-240)/70. Let i(u) be the first derivative of -12/7*u - d*u**3 - 1 + 12/7*u**2. What is x in i(x) = 0?
2/3, 2
Let p be (18/24)/(9/48). Factor -p*l**3 - 9*l + 51*l**2 - 63*l**2 - 3*l - 4.
-4*(l + 1)**3
Let g(o) = 3*o**2 - 18*o + 19. Let v(m) be the second derivative of m**4/6 - 2*m**3 + 13*m**2/2 + 10*m. Let h(x) = -5*g(x) + 8*v(x). Factor h(j).
(j - 3)**2
Suppose 20*u - 23*u + 3 = 0. Suppose -d - 2*x + 8 - 4 = 0, u = 2*d - 3*x. Solve 4*s**d - s**2 - 3*s - 3*s = 0.
0, 2
Let b(o) be the second derivative of -o**4/2 + 37*o**3/3 - 12*o**2 + o - 97. Factor b(r).
-2*(r - 12)*(3*r - 1)
Let p(y) = -93*y - 182. Let d be p(-2). Factor 9/5*i**2 - 12/5*i**3 - 12/5 + 12/5*i + 3/5*i**d.
3*(i - 2)**2*(i - 1)*(i + 1)/5
Let n = -1866/7 - -22542/77. Let 864/11*z + 40/11*z**3 + n*z**2 + 864/11 + 2/11*z**4 = 0. Calculate z.
-6, -2
Let l(i) = 8*i**2 + 36*i + 58. Let q(w) = -7*w**2 - 34*w - 59. Let z(p) = -5*l(p) - 6*q(p). Suppose z(y) = 0. Calculate y.
-8, -4
Suppose 5 - 25 = -2*a - 4*y, -4*a + 24 = 4*y. Factor 83*r**2 + 78*r**2 - 162*r**a - 9 - 6*r.
-(r + 3)**2
Let k(l) = l**2 + 2*l. Let i be k(-2). Let f be -3 - (18 + i)/(-3). Find g such that -3*g - g + 2*g**2 + 2*g**f + 2*g - 3*g**2 + 1 = 0.
-1, 1/2, 1
Suppose 4*a + 0 - 20 = 0. Let k(g) = 2*g - 8. Let q be k(a). Factor 2/7*f**3 + 0 + 0*f**4 + 0*f**q - 2/7*f**5 + 0*f.
-2*f**3*(f - 1)*(f + 1)/7
Let p be ((-816)/952)/(30/(-28)). Let p*w**2 + 4/5*w - 8/5 = 0. Calculate w.
-2, 1
Suppose -3*g + 19 = -26. Suppose 0 = -4*d + 2*a + a + 9, -g = 5*d + 5*a. Suppose 0*u**2 + d - 2/9*u + 2/9*u**3 = 0. Calculate u.
-1, 0, 1
Let n(q) be the first derivative of q**4/2 - 2*q**3 + 2*q**2 - 14. Let x(h) = 6*h**3 - 18*h**2 + 11*h. Let d(t) = -11*n(t) + 4*x(t). Let d(m) = 0. What is m?
0, 3
Let z be (-4)/16 + (100/16 - 2). Suppose 16 - z = 4*r. Factor b**r - 1/2 - 1/2*b - 1/2*b**5 - 1/2*b**4 + b**2.
-(b - 1)**2*(b + 1)**3/2
Let z(s) be the first derivative of -4/5*s**5 - 8*s**4 + 0*s + s**6 - 3*s**2 - 28/3*s**3 - 28. Solve z(q) = 0 for q.
-1, -1/3, 0, 3
Let k(j) be the second derivative of j**4/6 + 79*j**3/3 + 78*j**2 - 855*j. Factor k(m).
2*(m + 1)*(m + 78)
Let t = -1 - -4. Suppose -2*j = -3*j + t. Factor -2*y**3 + 2 + 2*y**j - 6*y**2 - 4 + 2*y**3 + 6*y.
2*(y - 1)**3
Let w(r) = -6*r**2 + 205*r + 5. Let h(o) = -10*o**2 + 308*o + 8. Let d(u) = 5*h(u) - 8*w(u). Solve d(j) = 0 for j.
-50, 0
Let f(b) be the first derivative of 2*b**4 - 230*b**3 + 7482*b**2 - 3698*b - 60. What is l in f(l) = 0?
1/4, 43
Suppose -48 = -5*g + g. Suppose 6*o**2 + 4 + 10*o**2 + g*o - 11*o**2 = 0. What is o?
-2, -2/5
Let h(w) be the first derivative of 2*w**3/21 - 53*w**2/7 + 204*w/7 + 498. Factor h(o).
2*(o - 51)*(o - 2)/7
Factor -3*o**2 - 18 + 4*o**2 + 17 - 9*o + 11 + 8.
(o - 6)*(o - 3)
Let f(m) = -16*m - 4. Let j be f(-3). Factor 66*v