r). Factor d(x).
-2*(x - 5)*(x - 1)/3
Let j = -89 - -62. Let k = j + 30. Suppose 9*c**k + 12*c**2 - 2*c**3 + 2*c**3 - 6 - 15*c = 0. What is c?
-2, -1/3, 1
Factor -3/8 - 3/8*v**3 + 3/8*v + 3/8*v**2.
-3*(v - 1)**2*(v + 1)/8
Let n(c) = -9 + 4*c**3 - 23*c**2 + 9*c - 22*c**4 + 6*c**3 + 25*c**4. Let d(v) = -v**4 + v**2 + v + 1. Let x(k) = 10*d(k) + 2*n(k). Factor x(r).
-4*(r - 2)*(r - 1)**3
Let s(t) = -t**2 + 21*t - 28. Let k = 8 + 11. Let a be s(k). Find z, given that -7*z**2 - 4*z**3 + 5*z**3 - 4*z**3 + 3*z - 3*z**4 + a*z**2 = 0.
-1, 0, 1
Let c be 3738/((-108)/(-72) + (-1)/(-2)). Let k = 1869 - c. Factor k*s**2 + 0*s - 2/3*s**4 + 0*s**3 + 0 - 2/3*s**5.
-2*s**4*(s + 1)/3
Let c(a) be the second derivative of -a**6/1260 + a**5/42 - a**4/4 + 32*a**3/3 - 115*a. Let i(b) be the second derivative of c(b). Find h such that i(h) = 0.
3, 7
Let o(l) be the first derivative of 30*l**2 - 160 - 1200*l - 1/4*l**3. Determine b so that o(b) = 0.
40
Suppose -122 + 272 = 10*v. Suppose 14 = n - z + v, -z = -4*n + 8. Factor 27 + 3/2*a**n + 12*a**2 + 63/2*a.
3*(a + 2)*(a + 3)**2/2
Let l(r) be the first derivative of -r**5/10 + 3*r**4/2 - 8*r**3 + 20*r**2 + 53*r - 21. Let s(t) be the first derivative of l(t). Factor s(u).
-2*(u - 5)*(u - 2)**2
Let r(u) be the third derivative of -3*u**5/5 + 131*u**4/3 - 58*u**3/3 + 2*u**2 + 3. Factor r(c).
-4*(c - 29)*(9*c - 1)
Let y be 0/(-3*(-7)/(-21)). Let m(q) be the third derivative of 4*q**2 - 1/60*q**5 - 1/8*q**4 + y*q**3 + 0 + 0*q. Find c such that m(c) = 0.
-3, 0
Let o be (-96 - -107 - (-86)/(-8))/(2 - (-3)/(-4)). Factor -o*r**2 + 7*r + 36/5.
-(r - 36)*(r + 1)/5
Let -431/10*i + 57/5 - 99/10*i**2 - 2/5*i**3 = 0. Calculate i.
-19, -6, 1/4
Suppose -r + 10*a + 12 = 9*a, -5*a = -3*r + 36. Find v such that -3*v**5 + 490*v - r*v**2 - 490*v - 15*v**4 - 24*v**3 = 0.
-2, -1, 0
Let m(n) be the second derivative of -38*n + 34/3*n**3 - 60*n**2 + 1/5*n**5 + 4*n**4 + 0. Factor m(x).
4*(x - 1)*(x + 3)*(x + 10)
Let i(j) be the third derivative of 0*j + 1/60*j**5 + 169/6*j**3 + 13/12*j**4 + 53*j**2 + 0. Find u such that i(u) = 0.
-13
Let g(x) = -x**2 - 5*x + 5. Let s(l) = 6*l**2 + 36*l - 127. Let w(n) = 5*g(n) + s(n). Solve w(r) = 0 for r.
-17, 6
Suppose 2/3*f**2 - 480 + 278/3*f = 0. What is f?
-144, 5
Let q(o) = o**3 + 90*o**2 + 485*o - 612. Let d(a) = 85*a**2 + 485*a - 615. Let k(g) = -4*d(g) + 5*q(g). Factor k(l).
5*(l - 1)*(l + 8)*(l + 15)
Let t(x) be the second derivative of x**5/40 + 11*x**4/24 - 67*x**3/3 - 143*x**2 + 2686*x + 1. Find p, given that t(p) = 0.
-22, -2, 13
Let n(c) be the first derivative of 7*c**3 + 66*c**2 + 36*c - 2156. Factor n(i).
3*(i + 6)*(7*i + 2)
Let c(a) = 3*a**2 - 34*a + 24. Let d = 28 - 42. Let l(t) = -602*t**2 + 8 - 4*t + 300*t**2 + 303*t**2 - 7*t. Let p(f) = d*l(f) + 4*c(f). Factor p(y).
-2*(y - 8)*(y - 1)
Let c be ((-3)/6)/(-7 + 25/10). Let r(p) be the third derivative of -c*p**4 + 8/9*p**3 + 0*p + 1/180*p**5 + 9*p**2 + 0. Let r(g) = 0. Calculate g.
4
Find w, given that -905*w**2 + 533*w - 3185*w**3 - 3184*w**3 + 320*w + 51*w + 6370*w**3 = 0.
0, 1, 904
Suppose 3*a = -4*l - 0*l + 210, l = 3. Let q**4 + 17*q**3 + 3*q - a + q**2 + 64 - 20*q**3 = 0. Calculate q.
-1, 1, 2
Let s(j) be the second derivative of -1/135*j**6 - 52*j + 1/9*j**4 + 0 + 2/45*j**5 - 4/27*j**3 - 5/9*j**2. Determine r so that s(r) = 0.
-1, 1, 5
Suppose 624*i**3 - 69*i**4 - 3*i**5 + 177594*i**2 - 5184 + 6*i**5 + 6048*i - 180366*i**2 = 0. What is i?
3, 4, 6
Suppose 0 = -92*m + 96*m - 688. Let w = -858/5 + m. Factor -2/5 + 1/5*c**3 + w*c**2 - 1/5*c.
(c - 1)*(c + 1)*(c + 2)/5
Let c(o) = -5*o + 56. Let g be c(12). Let f(u) = -4*u - 12. Let k be f(g). Factor -d**2 + 16*d**3 + 3*d**4 - 15*d**2 - 7*d**k.
-4*d**2*(d - 2)**2
Suppose -42 = 13*a - 250. Suppose 3*i**5 + a*i**4 + 95*i**3 - 54*i**3 + i**5 - 61*i**3 = 0. Calculate i.
-5, 0, 1
Let -300 + 390*t**2 - 90*t**4 - 87*t - 118*t + 13*t**5 + 200*t**3 - 7*t**5 + t**5 - 2*t**5 = 0. What is t?
-1, 1, 4, 15
Let x(o) be the first derivative of -o**4/12 + 25*o**3/9 - 4*o**2 + 3228. Factor x(v).
-v*(v - 24)*(v - 1)/3
Let x = -13/1463 + 5917/7315. Factor 0 - 4/5*l**2 + x*l.
-4*l*(l - 1)/5
Let l(d) be the third derivative of 0 - 34*d**2 - 50/9*d**3 - 5/2*d**4 + 0*d - 9/20*d**5. Factor l(v).
-(9*v + 10)**2/3
Determine f so that -98272 - 81*f - 29*f - 161828 - f**2 + 1130*f = 0.
510
Let h(y) be the first derivative of y**4 + 0*y**2 + 2/3*y**3 - 291 + 0*y + 2/5*y**5. Factor h(t).
2*t**2*(t + 1)**2
Let u = 310 + -307. Factor 718*h**u - 25 - 59 + 129*h**2 - 703*h**3 + 156*h.
3*(h + 2)*(h + 7)*(5*h - 2)
Let f(y) be the second derivative of -y**6/10 - 33*y**5/10 - 4*y**4 + 51*y**3 - 189*y**2/2 - 3*y - 9. Factor f(p).
-3*(p - 1)**2*(p + 3)*(p + 21)
Let f(c) be the first derivative of -1/2*c**6 + 78 + 27/10*c**5 + 9/4*c**2 - 39/8*c**4 - 3*c + 5/2*c**3. What is b in f(b) = 0?
-1/2, 1, 2
Let r(t) = -9*t - 186. Let j be r(-21). Factor 30*w - 35*w**4 + 85*w**j + 0*w**5 + 15*w**2 - 100*w**2 + 7*w**5 - 2*w**5.
5*w*(w - 3)*(w - 2)*(w - 1)**2
Let c = 2394026 - 4175180473/1744. Let z = c + 1/1744. Factor 0*y + 2/3*y**5 + 0 + z*y**4 + 0*y**2 - 1/6*y**3.
y**3*(y + 1)*(4*y - 1)/6
Let g(p) be the third derivative of p**5/15 + 7*p**4/2 - 200*p**3/3 + 1017*p**2 - 2*p. Let g(z) = 0. Calculate z.
-25, 4
Let n = 7573/4 - 1893. Let p(m) be the first derivative of -n*m - 1/12*m**3 + 1/4*m**2 + 14. Factor p(v).
-(v - 1)**2/4
Suppose 4*n - 4*f + 34 = 1002, 234 = n + f. Suppose 0 = -241*i + n*i + 9. Determine t so that 0 - 1/4*t**4 + 1/4*t - 1/4*t**i + 1/4*t**2 = 0.
-1, 0, 1
Let f = -17711 - -17727. Let q(a) be the second derivative of 0 + 13*a + 4/5*a**5 + 32/3*a**3 + f*a**2 + 4*a**4 + 1/15*a**6. Find n such that q(n) = 0.
-2
Determine t, given that 1541*t**2 - 3071*t**2 + 328*t + 1529*t**2 = 0.
0, 328
Let o be ((-16731)/(-2366))/((10/(-7))/5)*22/(-3). Solve o*k - 51 + 15/2*k**3 - 138*k**2 = 0.
2/5, 1, 17
Suppose -67 = -26*x + 33 + 4. Suppose 432/7*g - 54/7 - 342/7*g**x - 920/7*g**3 - 40/7*g**5 - 612/7*g**2 = 0. What is g?
-3, 1/5, 1/4
Let p(x) = -5*x**2 + 88*x - 403. Let g be (-8)/(-6) + 6/9. Let v(h) = 87*h + 20 + 3*h**2 - 5*h**2 - 3*h**2 - 422. Let t(b) = g*v(b) - 3*p(b). Factor t(k).
5*(k - 9)**2
Let s(c) be the second derivative of -2*c - 27/2*c**2 + 0 - 125/6*c**3 - 1/12*c**5 - 25/12*c**4. Let t(u) be the first derivative of s(u). Solve t(n) = 0.
-5
Let b = 7121/4356 + -1508/1089. Find w, given that -9/4*w**3 - 3 - 1/4*w**4 + 13/4*w**2 + 2*w + b*w**5 = 0.
-3, -1, 1, 2
Let h be 49665/350 - (-2)/(-4). Let r = h + -141. Determine c so that 8/5*c**3 - 32/5 + r*c**4 - 32/5*c + 0*c**2 = 0.
-2, 2
Let x(u) be the second derivative of u**6/50 - 9*u**5/100 - u**4/4 + 3*u**3/10 + 6*u**2/5 + 1447*u. Determine b, given that x(b) = 0.
-1, 1, 4
Let g be 554/1939*(-6)/(-4) - 2/(-224). Let a(f) be the first derivative of f**3 + 3/8*f**2 - 7 - 1/2*f + g*f**4. Determine y, given that a(y) = 0.
-1, 2/7
Suppose 3*x - 6*x = 3*x. Let 15*p**4 + 12 + 16*p + x*p - 4*p - 55*p**2 + 10*p**2 + 6*p**3 = 0. What is p?
-2, -2/5, 1
Let p(j) = 6*j**3 + 3*j + 3. Let k(w) = 54*w**3 + 125*w**2 + 3*w + 6. Let q(x) = -3*k(x) + 6*p(x). Find h such that q(h) = 0.
-3, 0, 1/42
Let r = 9090339/27484 - 3/13742. Factor -3/4*a**3 - 129/4*a**2 - 1449/4*a - r.
-3*(a + 1)*(a + 21)**2/4
Let x(g) be the first derivative of 5*g**6/18 - 15*g**5 - 45*g**4/2 + 1780*g**3/9 + 460*g**2 - 4511. Suppose x(s) = 0. What is s?
-2, 0, 3, 46
Let z(c) = c**2 + 4*c - 1. Let b = -270 - -271. Let y(n) = -3*n**2 - 26*n + 4. Let o(x) = b*y(x) + 4*z(x). Let o(r) = 0. What is r?
0, 10
Let h(p) be the second derivative of -p**4/72 - 341*p**3/36 + 343*p**2/6 - 3059*p. Solve h(d) = 0 for d.
-343, 2
Suppose -10 = -2*y + 7*p - 9*p, 0 = -y - 2*p + 7. Factor -y*t**2 + 2*t**2 - 470 + 3*t + 468.
-(t - 2)*(t - 1)
Let b(v) be the first derivative of v**3/9 - 37*v**2/2 - 460*v/3 + 9709. Solve b(y) = 0 for y.
-4, 115
Let w(k) be the first derivative of k**6/300 - k**5/25 + 3*k**4/20 - 4*k**3/15 + k**2 + 10*k + 114. Let n(x) be the second derivative of w(x). Factor n(u).
2*(u - 4)*(u - 1)**2/5
Let z(y) = -8*y**3 + 220*y**2 - 6273*y + 11670. Let n(b) = -2*b**3 - 3*b + 2. Let j(v) = 6*n(v) - 2*z(v). Determine o so that j(o) = 0.
2, 54
Factor 1/4*d**5 + 141/4*d**4 + 0 + 417/4*d**3 + 415/4*d**2 + 69/2*d.
d*(d + 1)**3*(d + 