 + 9 + 63*r - 6 - 73*r - 12 + 0*r**2 = 0. What is r?
-9, -1
Let p = 3074/15395 + 1/3079. Factor 9/5*n - p*n**2 - 8/5.
-(n - 8)*(n - 1)/5
Suppose 378423*a + 699857*a + 495616 + 556736*a + 1876*a**4 - 4680*a**4 + 4*a**5 + 1478404*a**2 + 487180*a**3 - 150984*a = 0. Calculate a.
-1, 352
Let w be ((-3)/(-5))/(56214/104100). Determine x so that 0 - 6*x**3 + w*x**4 + 0*x + 20/9*x**2 = 0.
0, 2/5, 5
Let k be (-8)/1 + ((-44)/110 - 272/(-30)). Factor -2/3*f**2 - 5/3*f**3 - k*f**4 + 0*f + 0.
-f**2*(f + 2)*(2*f + 1)/3
Let h = 367564/77 + -33392/7. Factor -6/11*y**2 + 42/11*y - h.
-6*(y - 6)*(y - 1)/11
Let a(s) be the first derivative of -4*s**3/15 - 1142*s**2/5 + 2288*s/5 - 959. Suppose a(r) = 0. What is r?
-572, 1
Let w = -85 - 139. Let c be (w/(-40) + -6)*-5. Factor -8/13*d + 2/13*d**c + 6/13.
2*(d - 3)*(d - 1)/13
Let b(d) = 12*d**3 + 9060*d**2 + 18084*d + 9015. Let s(u) = 28*u**3 + 21140*u**2 + 42196*u + 21036. Let o(r) = -16*b(r) + 7*s(r). Factor o(v).
4*(v + 1)**2*(v + 753)
Let 1461/4*s**2 + 559/2*s**3 - 482*s - 161 - 7/4*s**4 = 0. What is s?
-2, -2/7, 1, 161
Let l(c) be the second derivative of 11/24*c**3 + 1/96*c**4 + 21/16*c**2 - 3*c - 12. Let l(n) = 0. What is n?
-21, -1
Let p(i) = -2*i + 76. Let w be p(40). Let o be ((-4)/(-6))/(-7*w/84). Factor -2/5*t + 1/5 + 1/5*t**o.
(t - 1)**2/5
Let i(n) be the first derivative of n**5/120 + 5*n**4/48 - 7*n**3/6 - 65*n**2/2 + 132. Let f(v) be the second derivative of i(v). Factor f(x).
(x - 2)*(x + 7)/2
Factor -390*h - 4068/7 - 464/7*h**2 - 2/7*h**3.
-2*(h + 3)**2*(h + 226)/7
Let t(a) be the second derivative of 9*a**4/10 + 1036*a**3/5 + 268324*a**2/15 + 11221*a. Factor t(m).
2*(9*m + 518)**2/15
Let b(y) be the first derivative of -y**3 + 117*y**2 - 4563*y - 1996. Factor b(t).
-3*(t - 39)**2
Let j be (-144)/(-27)*43/1548. Let m(k) be the second derivative of 1/90*k**5 - 2*k**2 + 35*k + 0 + 7/9*k**3 - j*k**4. What is p in m(p) = 0?
2, 3
Let y(b) = -30*b - 40. Let l be y(-23). Let m = -648 + l. Factor 5 + 5/2*o**m + 15/2*o.
5*(o + 1)*(o + 2)/2
Let s(r) = -2*r**4 - 7*r. Let v = 4 - 19. Let z be (0 + -1)*(-1 - v). Let b(u) = -u**4 - 3*u. Let g(m) = z*b(m) + 6*s(m). What is o in g(o) = 0?
0
Let t(f) be the second derivative of 5 + 11/3*f**4 + 14/3*f**3 - 294*f**2 - 3*f + 1/5*f**5. Factor t(o).
4*(o - 3)*(o + 7)**2
Let r(q) be the third derivative of q**5/420 - q**4/6 + 14*q**3/3 - 80*q**2 + 8. Find z, given that r(z) = 0.
14
Let h(m) be the second derivative of 0*m**2 + 0 + 45*m + 9/4*m**5 + 0*m**3 - 1/6*m**6 + 0*m**4. Factor h(i).
-5*i**3*(i - 9)
Let r(b) = 5*b**2 - 888*b - 205203. Let f(o) = 24*o**2 - 4443*o - 1026016. Let w(n) = 6*f(n) - 29*r(n). Suppose w(z) = 0. Calculate z.
-453
Let j = 94741/15 - 6323. Let i = 152/15 + j. Factor i + 2/5*l**2 - 12/5*l.
2*(l - 4)*(l - 2)/5
Solve -8295*d**2 - 4516 - 424 + 968*d + 16586*d**2 - 8287*d**2 = 0 for d.
-247, 5
Find f, given that 7*f**4 - 2*f**3 - f**2 + 24*f**4 + 500 - 30*f**4 - 74*f**2 - 100*f = 0.
-5, 2, 10
Let g(b) = -4*b**2 - 2008*b - 5986. Let t(i) = 60*i**2 + 30122*i + 89795. Let n(o) = 31*g(o) + 2*t(o). Factor n(l).
-4*(l + 3)*(l + 498)
Let u = -146 + 152. Let p be 4/20*-2*(-11 + u). Solve -4/3 - 1/3*f**p + 4/3*f = 0 for f.
2
Let b(s) be the third derivative of 1/16*s**6 + 0 - 142*s**2 - 17/120*s**5 - 7/12*s**4 + 0*s + 1/3*s**3. Factor b(p).
(p - 2)*(p + 1)*(15*p - 2)/2
Let c(d) be the second derivative of d**8/7560 + d**7/945 - d**6/1620 - d**5/135 + 19*d**3/6 - 2*d - 36. Let g(l) be the second derivative of c(l). Factor g(y).
2*y*(y - 1)*(y + 1)*(y + 4)/9
Let x(k) be the third derivative of k**5/510 - 959*k**4/102 + 919681*k**3/51 + 147*k**2 + 2*k. Factor x(m).
2*(m - 959)**2/17
Let n(l) be the first derivative of -l**8/2160 + l**7/3780 + 4*l**3/3 + 7*l**2/2 + 60. Let s(u) be the third derivative of n(u). Suppose s(i) = 0. Calculate i.
0, 2/7
Let d(h) = -6*h - 76. Let c be d(-13). Let i be (-5)/6 + (4 + -35 - -32). Factor -1/6 + 1/3*k - i*k**c.
-(k - 1)**2/6
Let p(a) be the first derivative of a**6/27 + 32*a**5/15 - 26*a**4/9 - 284*a**3/27 + 27*a**2 - 196*a/9 + 517. Suppose p(r) = 0. Calculate r.
-49, -2, 1
Factor -18/17*r**3 + 0 - 132/17*r - 598/17*r**2.
-2*r*(r + 33)*(9*r + 2)/17
Let n(p) = p**3 + p**2 + 2*p. Let d(l) = -l**3 + 23*l**2 - 30*l - 300. Let b(a) = d(a) + 5*n(a). Factor b(s).
4*(s - 3)*(s + 5)**2
Let s be 1/(-6)*(25 + 0 + -25). Let r(m) be the third derivative of s*m**3 - 5/24*m**4 - 1/12*m**5 + 0*m + 15*m**2 + 0. Determine g so that r(g) = 0.
-1, 0
Let g be 3/(90/32)*55/(-1980)*-81. Determine s so that -2/5*s + g - 2/15*s**2 = 0.
-6, 3
Let r(y) be the third derivative of y**7/42 + 262*y**6/3 + 137288*y**5 + 359694560*y**4/3 + 188479949440*y**3/3 - 5*y**2 + 108*y. What is d in r(d) = 0?
-524
Let g(x) be the third derivative of x**6/480 - x**5/20 + 15*x**4/32 - 9*x**3/4 + x**2 + 59*x. Factor g(h).
(h - 6)*(h - 3)**2/4
Let o(h) be the first derivative of -3*h**4/8 - 57*h**3/2 - 114*h**2 + 810*h + 7368. Determine d so that o(d) = 0.
-54, -5, 2
Let s(d) = d**2 + 37*d + 54. Let o(b) = -2*b. Let x(l) = 18*o(l) - 2*s(l). What is q in x(q) = 0?
-54, -1
Let s be (-66)/(-140) - (-8)/784*-7. Suppose -s*y**3 - 22/5*y**2 - 26/5 + 10*y = 0. Calculate y.
-13, 1
Let q(l) = 33*l**2 - 645*l - 217. Let k(c) = -21*c**2 + 323*c + 109. Let j(t) = 10*k(t) + 6*q(t). Solve j(g) = 0 for g.
-53, -1/3
Factor -33/4*k + 1/4*k**3 + 15/4*k**2 + 17/4.
(k - 1)**2*(k + 17)/4
Factor -u**3 + 82*u**2 + 213*u**2 + 4*u**3 + 23409 + 3621*u - 112*u**2.
3*(u + 17)**2*(u + 27)
Determine m so that 2/5*m**4 + 8208*m + 7884/5*m**2 + 58482/5 + 48*m**3 = 0.
-57, -3
Let w(p) be the first derivative of p**3/21 + 13*p**2/2 - 380*p/7 + 3987. Factor w(x).
(x - 4)*(x + 95)/7
Suppose -1129*j - 315 = -1234*j. Factor 14/9 + 10/9*o**j - 2/3*o**2 - 2*o.
2*(o - 1)**2*(5*o + 7)/9
Let r(d) = -5*d + 116. Let h be r(-9). Let x = h - 158. Solve 6*w + 3 + 3/4*w**x + 15/4*w**2 = 0 for w.
-2, -1
Suppose 0 = 2*n - 1127 + 1137, c + 22 = -5*n. Let -28/9*j**2 + 8/9*j - 4/3*j**5 + 0 + 28/9*j**4 + 4/9*j**c = 0. What is j?
-1, 0, 1/3, 1, 2
Let w(l) = -7*l**3 - 103*l**2 - 266*l - 179. Let a(z) = -13*z**3 - 205*z**2 - 534*z - 357. Let f(o) = -3*a(o) + 5*w(o). Solve f(c) = 0.
-22, -2, -1
Let x(l) = l**2 - 4*l - 5. Let p be x(5). Suppose -6*h = -53*h + 2*h. Factor 1/9*u**2 + 0*u**3 - 1/9*u**4 + p + h*u.
-u**2*(u - 1)*(u + 1)/9
Let -3025/6 + 52*l**3 - 3/2*l**4 - 1187/3*l**2 - 2860/3*l = 0. Calculate l.
-1, 55/3
Let t(g) be the second derivative of -1/15*g**6 - 1/21*g**7 + 1 + 0*g**2 + 32*g + 1/10*g**5 + 0*g**3 + 1/6*g**4. Suppose t(b) = 0. What is b?
-1, 0, 1
Factor -3070/3*l - 2356225/3 - 1/3*l**2.
-(l + 1535)**2/3
Let m be ((-4)/(-55))/((-252)/630)*11/(-3). Let m*h**5 + 28/3*h**3 + 6*h - 4/3 - 4*h**4 - 32/3*h**2 = 0. Calculate h.
1, 2
Let c be (3/(-2) + 2)*8. Suppose 94*f - 32*f - 543 = -109. Find z such that -f*z**5 + z**c - z**2 + z**3 - z**2 + 6*z**5 + z**2 = 0.
-1, 0, 1
Let h be (6/(-76))/(175/(-14420)) - (-21)/((-8778)/44). Factor 12/5*j**2 - h*j + 0 + 2/5*j**3.
2*j*(j - 2)*(j + 8)/5
Let z(u) be the first derivative of u**3/15 + 2194*u**2/5 + 4813636*u/5 - 4759. What is f in z(f) = 0?
-2194
Let g(n) be the second derivative of -n**5/4 - 230*n**4/3 + 5*n**3/6 + 460*n**2 - 2*n + 720. Find q such that g(q) = 0.
-184, -1, 1
What is l in 36/7*l**2 + 0 + 72/7*l + 4/7*l**3 = 0?
-6, -3, 0
Let h(c) be the first derivative of 2*c**6/3 - 22*c**5/5 - 11*c**4/2 + 154*c**3/3 + 33*c**2 - 180*c + 1651. Suppose h(a) = 0. What is a?
-2, -3/2, 1, 3, 5
Factor 326/11*t**3 - 1/11*t**4 + 355992/11*t - 1192464/11 - 28753/11*t**2.
-(t - 156)**2*(t - 7)**2/11
Suppose 4*p = -4*a + 24, 0*p + 5*a = 3*p + 14. Let k = -34851/11 + 69713/22. Let 0 + f - k*f**4 + 3/2*f**p + 0*f**3 = 0. What is f?
-1, 0, 2
Let a(n) = n**2 - n - 1. Suppose 1 = r + 2. Let u(m) = -2*m + 0*m - 6*m**2 - 3 + 6*m + 8*m. Let f(w) = r*u(w) - 3*a(w). Let f(v) = 0. What is v?
1, 2
Suppose 29*v + 44574 = -17*v. Let m = v - -971. Factor 24*f + 6*f**3 + 3/4*f**4 + 18*f**m + 12.
3*(f + 2)**4/4
Let r be 4 - 0 - 2 - (1 + 1). Suppose r*p = -p + 3. Suppose -3*f**3 - 2*f**5 - 4*f**3 + f**4 + 5*f**p + 3*f**4 = 0. Calculate f.
0, 1
Let f be 2424/49*(-217)/(-93806). Let h = f + 2/623. Factor -2/17*q**2 + 4/17 + h*q.
-2*(q - 2)*(q + 1)/17
Suppose 2031*h + 1437*h - 10176 = 76*h. Let 864