n**2 + 9*n + 7*n**2 + 6*n**2 + 5*n**2 = 0.
-3, 0
Suppose -5*v - k = -15, 3*v - 3*k + k + 4 = 0. Factor -4*s**v + s - s**4 - 6*s**3 + 5*s**2 + 5*s**3.
-s*(s - 1)*(s + 1)**2
Determine p, given that 4 - 4 + 7011*p**2 - 6*p - 6996*p**2 = 0.
0, 2/5
Let l(c) = -c + 24. Let j be l(21). Let d be j + (-5)/(-20)*0. Factor 1/5*r**2 - 1/5 - 1/5*r**d + 1/5*r.
-(r - 1)**2*(r + 1)/5
Find o, given that -3*o - 30/7 - 3/7*o**2 = 0.
-5, -2
Let w(j) = -2*j**2 - 8*j + 1. Let p(v) = 180*v - 91*v - 85*v + v**2. Suppose -3*x + 5*x = -14. Let y(g) = x*p(g) - 3*w(g). Solve y(l) = 0 for l.
-3, -1
Let -5*t**3 + t**3 - 20*t**2 + 464*t + 151*t**2 + 588 - 27*t**2 - 108 = 0. Calculate t.
-2, 30
Let f(j) be the first derivative of 1/6*j**3 + 5/2*j - 3/2*j**2 + 35. Factor f(b).
(b - 5)*(b - 1)/2
Suppose p - 22 = -10*p. Let u(g) be the first derivative of 2*g + 4 + 1/2*g**p - 1/3*g**3. Factor u(z).
-(z - 2)*(z + 1)
Determine x so that 20/3 + 2/3*x**2 + 22/3*x = 0.
-10, -1
Factor 0*m**2 + 0 + 0*m - 578/3*m**3 + 34/3*m**4 - 1/6*m**5.
-m**3*(m - 34)**2/6
Suppose 15 = -5*z - 3*w, -6*z = -z + 5*w + 25. Let q(a) be the third derivative of 1/30*a**5 - 5*a**2 - 1/3*a**3 + 0*a**4 + 0 + z*a. Let q(n) = 0. Calculate n.
-1, 1
Let k(n) be the second derivative of -5*n + 0*n**2 + 1/16*n**3 - 1/96*n**4 + 0. Let k(t) = 0. What is t?
0, 3
Suppose -33/2*v - 1/2*v**2 + 54 = 0. What is v?
-36, 3
Let o(f) be the first derivative of 0*f**4 + 0*f**3 + 0*f + 0*f**6 - 1/420*f**7 + 0*f**5 + 3 - 2*f**2. Let k(w) be the second derivative of o(w). Factor k(d).
-d**4/2
Factor 441/5 - 42/5*j + 1/5*j**2.
(j - 21)**2/5
Let u(j) be the second derivative of -1/30*j**4 + 4/5*j**2 + 0 - 5*j + 0*j**3. Let u(g) = 0. What is g?
-2, 2
Factor 10*o + 3*o**3 - 21*o**2 + 18*o**2 - 16*o.
3*o*(o - 2)*(o + 1)
Solve 0 - 1/2*a + a**3 + 1/2*a**2 = 0 for a.
-1, 0, 1/2
Let s = 14848/7 - 2120. Find l, given that -4/7 + s*l**3 + 4/7*l**4 + 0*l**2 - 8/7*l = 0.
-1, 1
Let r(x) be the first derivative of x**6/40 + 2*x**2 + 2*x - 4. Let u(i) be the first derivative of r(i). Let n(o) be the first derivative of u(o). Factor n(j).
3*j**3
Factor 6/5*d**3 + 0 - 2/5*d**4 + 0*d**2 + 0*d.
-2*d**3*(d - 3)/5
Let m(f) be the third derivative of -f**6/30 + 4*f**5/15 + 11*f**4/6 + 4*f**3 + 2*f**2 - 44. Find p, given that m(p) = 0.
-1, 6
Let h = -94 + 405/4. Let w = 31/4 - h. Factor -1/2*a + 1/2*a**2 - 1/2*a**4 + w*a**3 + 0.
-a*(a - 1)**2*(a + 1)/2
Let 8/5 + 1/5*p**4 + 4/5*p - 6/5*p**2 - 1/5*p**3 = 0. What is p?
-2, -1, 2
Suppose -8*j + 46 - 6 = 0. Let z be (-3)/(-9) + j/(-60). Factor -1/4*g + 0 - z*g**2.
-g*(g + 1)/4
Let t(k) be the first derivative of -12 + 5/7*k**2 + 2/21*k**3 + 8/7*k. Let t(x) = 0. What is x?
-4, -1
Solve 12*j**2 - 32*j - 3*j**3 + 30 + 12*j**2 + 7*j - 26*j + 0*j**3 = 0.
1, 2, 5
Let w = 134/3 + -2143/48. Let l(s) be the second derivative of -5*s + 2*s**2 + 0 - 1/3*s**3 + w*s**4. Let l(v) = 0. What is v?
4
Let r(f) = -f**3 + 7*f**2 - 5*f - 5. Let b(x) = x**3 + 5*x**2 + 3*x - 3. Let a be b(-3). Let q be r(a). Factor 1 - 2 - q - 6*k**2 - k + 7*k**2.
(k - 2)*(k + 1)
Let c(b) be the second derivative of b**9/3024 + b**8/672 + b**7/504 - 3*b**4/2 + 24*b. Let l(z) be the third derivative of c(z). Factor l(r).
5*r**2*(r + 1)**2
Let t(k) be the first derivative of 8*k + 14*k**2 + 3 - 16/3*k**3. Solve t(v) = 0 for v.
-1/4, 2
Let u(t) be the first derivative of -t**3/15 + t**2/5 - t/5 - 93. Factor u(h).
-(h - 1)**2/5
Let p(v) be the first derivative of 0*v**5 + 0*v**3 + 1/2*v**6 + 12 - 3/2*v**4 + 3/2*v**2 + 0*v. Factor p(g).
3*g*(g - 1)**2*(g + 1)**2
Find f, given that 0*f + 3 + 3/4*f**3 - 9/4*f**2 = 0.
-1, 2
Let l(t) be the third derivative of -t**10/12600 - t**9/7560 + 2*t**5/3 + 27*t**2. Let m(q) be the third derivative of l(q). What is r in m(r) = 0?
-2/3, 0
Let p be ((-88)/(-38) - 1)*-1. Let o = p + 296/95. Determine x so that 2/5 - 9/5*x + 2/5*x**4 + 14/5*x**2 - o*x**3 = 0.
1/2, 1, 2
Let x(y) be the first derivative of y**3/18 + 7*y**2/6 + 18. Let x(m) = 0. What is m?
-14, 0
Let x(f) = 8*f**4 - 4*f**3 - 16*f**2 - 12*f + 4. Let s(h) = 9*h**4 - 4*h**3 - 15*h**2 - 12*h + 5. Let n(i) = 4*s(i) - 5*x(i). Factor n(u).
-4*u*(u - 3)*(u + 1)**2
Let y = 398 - 2243. Let f = -5455/3 - y. Factor -35/3*g**3 + 20/3 + 25/3*g**2 + f*g.
-5*(g - 2)*(g + 1)*(7*g + 2)/3
Suppose 5*t + 3*g - 29 = 0, -5*t - g = -4*g - 11. Suppose j = t - 1. Factor -21/4*s**2 + 3/4*s - 9/4*s**4 + 1/2 + 25/4*s**j.
-(s - 1)**3*(9*s + 2)/4
Suppose -3*t - 2*l = -12 - 3, 4*t = -5*l + 27. Suppose -5*z + t*z = -5*b - 125, 4*z = b + 223. Factor -8*r**3 + 8*r + 4 - 4*r**4 - z*r**2 + 55*r**2.
-4*(r - 1)*(r + 1)**3
Let x be (-24)/3 + 580/72. Let y(a) be the second derivative of 2/9*a**3 + 9*a + 0 - 1/3*a**2 - x*a**4. Let y(h) = 0. Calculate h.
1
Let q(k) = -7*k**2 - 61*k + 20. Let r be q(-9). Let g(d) be the third derivative of r*d**3 + 0*d + 0 - 1/2*d**4 + 1/20*d**5 - d**2. Factor g(j).
3*(j - 2)**2
What is c in -19*c**4 - 4*c**5 + 112*c**3 + 12*c**2 - 140*c**3 + 39*c**4 = 0?
0, 1, 3
Suppose 6*g = 2*g + 176. Factor 25 + y**4 - 13*y**3 + 25*y**3 + g*y + 46*y**2 + 16*y.
(y + 1)**2*(y + 5)**2
Let b be (-1)/(-2) - 0/1. Let x = -6130 + 6132. Factor -b*g**x + 0 + g.
-g*(g - 2)/2
Let g be (63/15 - 3)*5/(-1). Let u(f) = f**3 - 85*f**2 - 406*f - 314. Let y(z) = -5*z**3 + 510*z**2 + 2435*z + 1885. Let w(r) = g*y(r) - 35*u(r). Factor w(q).
-5*(q + 1)*(q + 8)**2
Determine u so that 1210 - 35*u**3 + 784*u**2 - 111*u**2 + 107*u**2 - 4455*u = 0.
2/7, 11
Let r(t) be the second derivative of t**5/4 - 37*t**4/12 + 77*t**3/10 + 441*t**2/10 + 189*t. Factor r(w).
(w + 1)*(5*w - 21)**2/5
Suppose -209*g + 104 = -314. What is u in -32/9*u - 128/9 - 2/9*u**g = 0?
-8
Let p(v) be the third derivative of -1/4*v**5 - 1/8*v**6 - 1/4*v**3 + 0*v - 1/224*v**8 + 0 - 5/16*v**4 + 5*v**2 - 1/28*v**7. Let p(w) = 0. Calculate w.
-1
Let a(u) = -2*u**2 + 7*u + 6. Let l be a(6). Let j = l + 33. Let 5*v**3 - 1 + 4 - j*v**2 - 11*v**3 = 0. Calculate v.
-1, 1/2
Let -2/5*q**3 + 1/5*q**5 + 1/5*q + 0*q**4 + 0 + 0*q**2 = 0. What is q?
-1, 0, 1
Let z = -1 - -7. Suppose r + a - 3 = 0, z = 2*r + 4*a - 0*a. What is c in -2*c**2 + 13*c**3 - 14*c**r + 4*c**2 = 0?
0, 2
Suppose 0 = 3*d - d. Suppose d = g - 3*z - 8, 2 = -g - 4*z + 2*z. Factor 2*l**2 - l**2 - 3*l**3 + g*l**3 + 0*l**3.
-l**2*(l - 1)
Let m(c) = -c + 4. Let d be m(3). Let h be (-6)/(-2) + 5 + -5. Solve d - 3*n**2 + n**2 + 4*n**4 - h*n**4 = 0.
-1, 1
Let s(j) = 2*j - 5. Suppose -t - 15 = -5*i + 6, 0 = -4*i - 3*t + 13. Let m be s(i). Factor -2*n - 4*n**2 + n**3 + 0*n**2 - 3*n**m + 0*n**3.
-2*n*(n + 1)**2
Let n(j) be the first derivative of -25*j + 45/2*j**2 - 24 - 5/4*j**4 - 5*j**3. Factor n(c).
-5*(c - 1)**2*(c + 5)
Let f(g) be the first derivative of 1/24*g**6 + 0*g - 3/20*g**5 + 1/4*g**3 - 1/4*g**2 + 15 + 1/16*g**4. Solve f(q) = 0.
-1, 0, 1, 2
Let p = -2197/7 + 314. Suppose 4/7*a - 4/7 - p*a**2 = 0. What is a?
2
Suppose 0 = -92*j - 62*j + 32*j. Solve j*a + 0 + 0*a**3 + 2/9*a**4 - 2/9*a**2 = 0 for a.
-1, 0, 1
Let t(o) be the first derivative of 3*o**4/4 - 372*o**3 + 69192*o**2 - 5719872*o + 407. Suppose t(c) = 0. Calculate c.
124
Let n(k) be the first derivative of k**6/2 + 6*k**5/5 - 3*k**4/4 - 2*k**3 + 300. Factor n(h).
3*h**2*(h - 1)*(h + 1)*(h + 2)
Suppose 2 = -197*t + 1 + 1. Determine m, given that -3/2*m + 1/2*m**2 + t = 0.
0, 3
Suppose 149*k - 143*k - 12 = 0. Suppose 8/7 - 24/7*x + 18/7*x**k = 0. Calculate x.
2/3
Factor -89*p + 4*p**4 - 16*p**3 - 24*p**2 + 20 + 59*p + 46*p.
4*(p - 5)*(p - 1)*(p + 1)**2
Let p = 882 - 4374/5. Solve -p*h**3 - 9/5*h**2 + 0 + 6/5*h - 21/5*h**4 = 0.
-1, 0, 2/7
Let b be (-84)/49*14/(-4). Let f(o) be the second derivative of 1/60*o**5 + 0*o**3 + 0 + 0*o**4 + 0*o**2 - 5*o - 1/90*o**b. Find u, given that f(u) = 0.
0, 1
Let x(g) be the second derivative of g**7/28 - 7*g**6/30 + 17*g**5/40 + g**4/4 - 5*g**3/3 + 2*g**2 + g - 2. Let x(l) = 0. Calculate l.
-1, 2/3, 1, 2
Let r(b) = 13*b**2 + 17*b. Let q(m) = 7*m**2 + 9*m. Suppose 16 = -2*n - 6. Let o(s) = n*q(s) + 6*r(s). Factor o(l).
l*(l + 3)
Let i = -2/50333 - -100684/452997. Suppose 4/3*w - i*w**3 + 2/9*w**2 + 0 = 0. Calculate w.
-2, 0, 3
Let z(w) = -w**4 + w**3 + 3*w**2 - 2*w. Let p(h) = -5*h**5 + 265*h**4 - 4525*h**3 + 40965*h**2 - 181390*h + 311040. Let d(y) = p(y) + 25*z(y). Factor d(u).
-5*(u - 