r(v).
-(v - 40)*(v - 2)/5
What is h in 34*h - 12*h**2 + 2/3*h**3 + 140/3 = 0?
-1, 5, 14
Let j(w) be the first derivative of -w**5/10 - 15*w**4/8 - 7*w**3/3 - 647. Suppose j(y) = 0. Calculate y.
-14, -1, 0
Let w be -1*(1 - (-72)/(-40)). Let j(y) = 79*y**2 - 1816*y - 21. Let q be j(23). Factor w*k**q + 0 + 36/5*k.
4*k*(k + 9)/5
Let s(f) be the third derivative of f**8/336 + 2*f**7/15 - 193*f**6/120 + 92*f**5/15 - 17*f**4/2 + 1228*f**2. Suppose s(q) = 0. What is q?
-34, 0, 1, 2, 3
Let p(h) be the first derivative of h**6/1260 - 5*h**5/84 + 137*h**3/3 + 71. Let b(o) be the third derivative of p(o). Find z such that b(z) = 0.
0, 25
Let s(o) = -20*o**2 + 898*o - 3405. Let t(k) = 6*k**2 - 298*k + 1134. Let x(q) = -2*s(q) - 7*t(q). Let x(r) = 0. Calculate r.
4, 141
Let i(w) be the second derivative of w**7/168 + w**6/8 - w**5/80 - 5*w**4/16 + 7*w + 47. Determine p so that i(p) = 0.
-15, -1, 0, 1
Suppose 155*z = l + 157*z + 20, 10 = -z. Factor -2/5*o**3 - 14/5*o**2 + l*o + 0.
-2*o**2*(o + 7)/5
Let b(y) = -y**2 + 12*y - 8. Let x be b(11). Let z be (x + (-25)/10)/((-1)/(-614)). Factor 317*u + 2*u**2 - 25 - 3*u**2 - z*u.
-(u - 5)**2
Let h(s) be the first derivative of 6*s + 1/16*s**4 + 3/8*s**3 + 0*s**2 + 5. Let g(d) be the first derivative of h(d). Factor g(b).
3*b*(b + 3)/4
Factor -6508*k + 2*k**2 - 4702544 - 1949454 - 4*k**2 + 1357740 + 0*k**2.
-2*(k + 1627)**2
Let f(x) be the third derivative of x**6/24 - 219*x**5/4 + 22550*x**4 - 268960*x**3/3 - 2966*x**2. Solve f(c) = 0 for c.
1, 328
Let x = 519 - 359. Let f be (x/12)/4 - (-16)/(-12). Factor 6*v - 3*v**f - 232 - 3*v**3 + 232 + 0*v**3.
-3*v*(v - 1)*(v + 2)
Let g(z) = -5*z - 93. Let j be g(-19). Find f such that 58*f**j - 234*f**3 + 239*f**3 - 13*f**2 = 0.
-9, 0
Solve -4*c**3 - 5*c**4 + 2*c + 45248*c**5 - 6 - 45246*c**5 + 12*c**2 - c**4 = 0 for c.
-1, 1, 3
Let c(a) be the first derivative of a**4/4 - 11*a**3/3 - a**2/2 + 11*a + 3693. Suppose c(f) = 0. Calculate f.
-1, 1, 11
Let n(a) be the first derivative of 2*a**4/5 - 23*a**3/15 - 33*a**2/10 + 18*a - 3318. Factor n(x).
(x - 3)*(x + 2)*(8*x - 15)/5
Suppose 5*j = 50 + 50. Let u = j + -4. Factor 11*w**4 - 4*w**4 - u*w**3 - 4 - 8*w**2 + 23*w - 7*w + 5*w**4.
4*(w - 1)**2*(w + 1)*(3*w - 1)
Let h(f) = f**3 - 6*f**2 + 181*f - 512. Let d be h(3). Let x(b) be the first derivative of 3/2*b**d - 8 + b**3 + 2*b**6 + 0*b + 0*b**2 - 21/5*b**5. Factor x(i).
3*i**2*(i - 1)**2*(4*i + 1)
Let d(o) be the second derivative of o**7/28 + 13*o**6/40 + 9*o**5/80 - 19*o**4/16 - 5*o**3/8 + 9*o**2/4 + 20*o - 2. Let d(s) = 0. What is s?
-6, -1, 1/2, 1
Let r = 377 + -371. Let x(v) = v**2 - 15*v + 54. Let a be x(r). Factor 3/2 + a*b**4 + 3/4*b**5 - 3/2*b**2 + 9/4*b - 3*b**3.
3*(b - 2)*(b - 1)*(b + 1)**3/4
Let h be ((-12)/27)/(-2) - (-248)/18. Find v, given that -14*v - 115 + 78*v**2 - 66*v**3 + 231 - 128 + h*v**4 = 0.
-2/7, 1, 3
Factor 64909010*f + 18720750*f + 20349049*f + 3*f**3 + 30591*f**2 + 117807990597.
3*(f + 3399)**3
Let a = -26761 - -26763. Let g(s) be the third derivative of -23/192*s**4 - 1/96*s**5 + 0*s + 5/24*s**3 + 0 + 4*s**a. Solve g(y) = 0 for y.
-5, 2/5
Let q(x) be the third derivative of 3*x**5/22 + 179*x**4/132 - 4*x**3/33 + 7484*x**2. Factor q(s).
2*(s + 4)*(45*s - 1)/11
Let c(o) = 20*o**3 + 415*o**2 - 1820*o + 1380. Let y(d) = -11*d**3 - 207*d**2 + 911*d - 690. Let n(i) = -3*c(i) - 5*y(i). Factor n(s).
-5*(s - 3)*(s - 1)*(s + 46)
Suppose 0 = 8*y + 22 - 302. Let q be 4/(-10) - (-189)/y. Determine p, given that -3/4*p**2 + 3/4*p**4 + 0 + 1/4*p**3 - 1/2*p + 1/4*p**q = 0.
-2, -1, 0, 1
Suppose -2/5*x**2 + 13228/5*x - 21872498/5 = 0. What is x?
3307
Let n(h) be the second derivative of h**5/14 + 677*h**4/42 + 750*h**3/7 + 792*h**2/7 - 808*h. Find w such that n(w) = 0.
-132, -3, -2/5
Let f = -11857 + 11884. Let k(j) be the second derivative of 0 + 1/12*j**5 + f*j + 0*j**3 + 0*j**2 - 1/126*j**7 + 0*j**4 + 2/45*j**6. Factor k(w).
-w**3*(w - 5)*(w + 1)/3
Let g be (4051/22692)/((-266)/294 + 1). Let j = g - -1/1891. Find x, given that 3/8*x**2 - 3/2*x - j = 0.
-1, 5
Let q(l) be the first derivative of -7 + 3*l + 25 + 3*l - 5*l. Let r(o) = -5*o**2 - 8*o - 8. Let w(k) = -5*q(k) - r(k). Suppose w(s) = 0. What is s?
-1, -3/5
Let r = -64507/2 - -129015/4. Find i, given that -2 + 3*i + r*i**3 - 3/2*i**2 = 0.
2
Let b(g) be the third derivative of -g**6/72 + 5*g**5/2 - 375*g**4/2 - 154*g**3/3 - 4*g**2. Let h(y) be the first derivative of b(y). Solve h(k) = 0.
30
Let p(f) be the first derivative of 4*f**4/9 + 4412*f**3/27 + 4388*f**2/9 + 1460*f/3 + 806. Suppose p(o) = 0. Calculate o.
-1095/4, -1
Let o = 113/40 - -51/8. Let d be (-5 - (-315)/25) + -6. Solve d - 6*v**3 + 32/5*v - o*v**2 = 0.
-2, -1/5, 2/3
Let a(l) be the third derivative of -2/7*l**4 - 26/21*l**3 + 1/105*l**5 + 6*l**2 + 1 + 0*l. Solve a(o) = 0.
-1, 13
Let c(n) = -n**4 - n**3 + 2*n**2 + n - 1. Let k(j) = 32 - 22*j**3 + 23*j - j**3 + 7*j**4 + 29*j**2 - 68*j**2. Let f(w) = 2*c(w) + k(w). Factor f(r).
5*(r - 6)*(r - 1)*(r + 1)**2
Let r = 8/25 - 28841/50. Let t = -574 - r. Determine y, given that -1/2*y**2 + 0 + t*y**3 + 0*y - 2*y**4 = 0.
0, 1/4, 1
Factor -3136 - 14*k**5 + 784*k**3 + 212*k**4 - 26*k**2 - 13*k**2 - 25*k**2 + 11*k**5 - 3200*k + 7*k**5.
4*(k - 2)*(k + 2)**3*(k + 49)
Suppose 200 + 7935*r**2 + 1511*r + 1489*r - 16*r**4 + 5272*r**3 + 298*r + 131 - 320*r = 0. Calculate r.
-1, -1/4, 331
Suppose 9*k - 108 = 6*k - 15*k. Let w(i) be the second derivative of 3/20*i**5 + 2/3*i**3 + 1/60*i**k + 1/2*i**4 + 0 + 0*i**2 + 17*i. Find x such that w(x) = 0.
-2, 0
Let n(f) be the third derivative of 0*f**3 + 1/70*f**7 + 0*f**4 + 0*f**6 + 0*f + 0 - 1/20*f**5 + 42*f**2. Factor n(z).
3*z**2*(z - 1)*(z + 1)
Let 21638*m**2 - 21641*m**2 + 91*m - 16*m + 252 = 0. Calculate m.
-3, 28
Let p = 1552/13 + -12778/65. Let i = -1539/20 - p. Suppose 1/2 - 1/4*l - i*l**2 = 0. What is l?
-2, 1
Let u(t) be the second derivative of -25*t - 1/30*t**5 + 1/18*t**3 + 0*t**2 + 5/72*t**4 - 1/60*t**6 + 0. Suppose u(g) = 0. What is g?
-2, -1/3, 0, 1
Let q(t) = t**3 + 2*t**2 - 3*t + 3. Let i be q(-3). Let r = -321 + 326. Suppose 5*x + r*x**2 - 3*x - 2*x - 20*x**i = 0. Calculate x.
0, 1/4
Let l(c) = 15*c**2 + 31*c + 15. Let h(f) = 30*f**2 + 60*f + 25. Let o(g) = -3*h(g) + 5*l(g). Determine b so that o(b) = 0.
-5/3, 0
Let n(p) be the second derivative of 0 + 3*p + 0*p**4 - 1/10*p**6 - p**3 + 3/10*p**5 + 3/2*p**2. Let n(w) = 0. Calculate w.
-1, 1
Let g(z) = -2*z**3 - 127*z**2 - 55*z + 508. Let d be g(-63). Factor -3/2*k + 1/2*k**d - 1/2*k**2 + 0 + 3/2*k**3.
k*(k - 1)*(k + 1)*(k + 3)/2
Suppose 3 = 3*f - 3. Let l = -318/59 - -8644/531. Factor -8/9 + 80/9*i - 290/9*i**f + 470/9*i**3 - 350/9*i**4 + l*i**5.
2*(i - 1)**3*(7*i - 2)**2/9
Let j(y) = -3*y**5 - 51*y**3 + 111*y**2 - 63*y. Let o(v) = -v**5 - 51*v**3 + 110*v**2 - 62*v. Let p(c) = 2*j(c) - 3*o(c). Determine i so that p(i) = 0.
-5, 0, 1, 2
Let f(h) be the third derivative of -53*h**2 - 2/3*h**4 + 0*h - 2/105*h**7 - 1/6*h**6 - 8/15*h**5 + 0*h**3 + 0. Factor f(k).
-4*k*(k + 1)*(k + 2)**2
Factor -9557*q**2 + 4*q**3 + 9504 + 3392*q**2 + 3301*q**2 + 3176*q**2 + 3312*q.
4*(q + 6)**2*(q + 66)
Let r be (45306/(-216))/((-2)/(-6)). Let f = 630 + r. Factor 9/2 + f*o - 3/4*o**2.
-3*(o - 3)*(o + 2)/4
Let x(d) = -2*d**4 - 4*d**3 + d**2 + d - 1. Let r(c) = 8*c**4 - 52*c**3 + 126*c**2 + 190*c + 2. Let p(a) = r(a) + 2*x(a). Find n, given that p(n) = 0.
-1, 0, 4, 12
Let t(l) be the first derivative of -43 - 15*l**2 + 0*l + 5*l**4 + l**5 + 5/3*l**3. Let t(d) = 0. What is d?
-3, -2, 0, 1
Let g(s) = -63*s**4 - 357*s**3 + 4212*s**2 - 14697*s - 5376. Let p(d) = -8*d**4 - d**3 + d**2 - d. Let i(b) = -g(b) + 9*p(b). Let i(l) = 0. Calculate l.
-1/3, 7, 16
Let i(m) = -5*m**3 + 86*m**2 - 177*m + 82. Let r(w) = -12*w**3 + 171*w**2 - 356*w + 162. Let q(j) = 15*i(j) - 6*r(j). Factor q(l).
-3*(l - 86)*(l - 1)**2
Let q = 285 - -1359. Let y be q/340 + 57/(-95). Suppose 30/17*l - 4/17 - 38/17*l**2 - y*l**3 = 0. Calculate l.
-1, 2/9, 1/4
Let l = 6628/5 + -1316. Factor b**4 - 16*b - 12/5*b**3 + l - 96/5*b**2.
(b - 6)*(b + 2)**2*(5*b - 2)/5
Let v(n) = -285*n**2 + 3449*n + 2954950. Let y(r) = -26*r**2 + r - 1. Let m(u) = v(u) - 11*y(u). Factor m(i).
(i + 1719)**2
Let w(n) = -2*n**2 + 946*n - 80362. Let m be w(111). Factor -3/5*h**m + 27 - 