n that 8*w + g*w**3 - 31 + 11 + 2*w**4 + 18*w**2 + 20 = 0.
-4, -1, 0
Factor 3*g**3 - 37*g**5 + 29*g**5 + g**3 + 4*g**4.
-4*g**3*(g - 1)*(2*g + 1)
Let u(n) be the first derivative of -2*n**5/65 + n**4/13 - 2*n**3/39 + 95. Factor u(k).
-2*k**2*(k - 1)**2/13
Let w(k) = -4*k**4 - 12*k**3 - 16*k**2 - 12*k - 16. Let p(n) = -n**2 - 2*n - 2. Let o(h) = 12*p(h) - w(h). Factor o(s).
4*(s - 1)*(s + 1)**2*(s + 2)
Find u, given that 4036*u**2 - 3791*u**2 - 185*u - 55*u - 5 = 0.
-1/49, 1
Let v(f) be the second derivative of f**5/20 + 2*f**4/3 - f**3/3 - 7*f**2/2 + 5*f. Let o be v(-8). Factor 0*b**2 + 2*b**2 + 12*b + o + b**2 + 0*b**2.
3*(b + 1)*(b + 3)
Factor -236/11*h - 6962/11 - 2/11*h**2.
-2*(h + 59)**2/11
Factor 36448/3*z**2 - 17956/3*z - 6344*z**3 + 0 - 4/3*z**5 + 544/3*z**4.
-4*z*(z - 67)**2*(z - 1)**2/3
Let o = 5746 + -40216/7. Find p such that -o - 2/7*p**2 - 8/7*p = 0.
-3, -1
Let r(s) = -2*s**3 - 14*s**2 - 3*s + 4. Let w(y) = 3*y**3 + 21*y**2 + 4*y - 7. Let i(d) = 7*r(d) + 5*w(d). Solve i(n) = 0 for n.
-7, -1, 1
Let o(i) = 1665*i**3 + 13365*i**2 - 11480*i + 2260. Let r(c) = -128*c**3 - 1028*c**2 + 883*c - 174. Let z(v) = 3*o(v) + 40*r(v). Find f such that z(f) = 0.
-9, 2/5
Let j(q) = 200*q + 4800. Let k(p) = p**2 - 402*p - 9599. Let u(t) = -5*j(t) - 2*k(t). Factor u(b).
-2*(b + 49)**2
Factor 3*k + 14/3*k**3 - 2/3 - 16/3*k**2 + 1/3*k**5 - 2*k**4.
(k - 2)*(k - 1)**4/3
Suppose -f = 5*r - 11, -2*r - 4*f = r + 7. Let k(q) = q - 1. Let s be k(r). Factor b**2 + 2*b**3 - b**5 - b + b**2 - s*b**2.
-b*(b - 1)**2*(b + 1)**2
Suppose 3*q + 5*d - 37 = 0, -2*d + 9 = q - 5. Let c be (-2 - -4)/(1/2). Factor 3*o**c - o**4 + 6*o**q - 4*o**4.
4*o**4
Let q be (-13*34/(-3315))/((-3)/(-15)). Let g = 2/43 + 80/129. What is p in -g*p - q - 1/6*p**2 = 0?
-2
Let f = 240 + -238. Let g(b) be the first derivative of 0*b**f + 0*b**3 - 2/3*b**6 + 0*b - 4/5*b**5 - 13 + 0*b**4. Factor g(p).
-4*p**4*(p + 1)
Let s(i) be the second derivative of i**6/135 + 2*i**5/45 - i**4/9 - 4*i**3/27 + 5*i**2/9 + 6*i - 2. Factor s(c).
2*(c - 1)**2*(c + 1)*(c + 5)/9
Let s(j) = -14*j**4 + 4*j**3 - 2*j**2 + 12*j + 6. Let u(m) = -12*m**4 + 2*m**3 - 3*m**2 + 10*m + 5. Let p(t) = -5*s(t) + 6*u(t). Determine a so that p(a) = 0.
-2, 0
Suppose -2*g + 23 = -57. Let i be (64/g)/((-7)/(-5)). Solve -16/7*t**2 + 10/7*t**3 - 2/7*t**4 + i*t + 0 = 0.
0, 1, 2
Suppose -5*a + 4*g = 2, g + 7 = -116*a + 121*a. Let -5/6*v**5 + 0*v + 1/3*v**a - 3/2*v**3 + 0 + 2*v**4 = 0. Calculate v.
0, 2/5, 1
Let m(u) = -4*u**2 - 2*u + 14. Suppose 3*h - 9 = 2*g - 4, h = -2*g - 9. Let y(d) = -d + 1. Let p(i) = h*m(i) + 6*y(i). Suppose p(o) = 0. Calculate o.
-1, 2
Let r(o) be the third derivative of o**7/945 + o**6/90 + 4*o**5/135 - o**4/18 - o**3/3 + 4*o**2 + 124*o. Factor r(d).
2*(d - 1)*(d + 1)*(d + 3)**2/9
Let s(b) = b**2 + 2*b + 7. Let w be s(0). Solve -16*d**2 + 4*d**5 + 19*d**4 + d**3 - 5*d**3 - w*d**4 + 4*d**2 = 0 for d.
-3, -1, 0, 1
Let g(m) = m**3 - 17*m**2 - 18*m + 2. Let x be g(18). Suppose 0*a = a + x*l - 3, -5*l + 9 = 3*a. Factor 0 - 1/5*k**5 + 0*k**2 - 2/5*k**a + 0*k + 3/5*k**4.
-k**3*(k - 2)*(k - 1)/5
Factor 4/21*s + 0 + 166/21*s**2.
2*s*(83*s + 2)/21
Suppose -3 = 3*r + 9. Let a be 1/((-2)/r)*1. Factor -l**2 + 6*l**4 - 8*l**3 - 10*l**4 - 3*l**a.
-4*l**2*(l + 1)**2
Suppose 0 = -h + 3*u + 35, 0*u - 207 = -5*h - u. What is w in -w - 6 + 14 + h*w**2 - 31*w**2 - 15*w - 2*w**3 = 0?
1, 2
Let g(s) = 2*s + 29. Let u be g(-13). Factor -u - 8*h**3 + 19*h**2 - 4*h**2 - 3*h - h**3.
-3*(h - 1)**2*(3*h + 1)
Let n be 15/18 - (-266)/(-684). Factor -n*a + 2/9*a**2 + 0.
2*a*(a - 2)/9
Let z(q) be the first derivative of -4*q**5/5 + 9*q**4 - 20*q**3 - 50*q**2 + 128. Factor z(r).
-4*r*(r - 5)**2*(r + 1)
Let r(z) be the first derivative of -z**4/16 + 5*z**3/6 - 7*z**2/2 + 6*z + 41. Solve r(d) = 0 for d.
2, 6
Let x(b) be the third derivative of -b**8/6720 + b**6/1440 - 4*b**3/3 + b**2. Let k(g) be the first derivative of x(g). What is j in k(j) = 0?
-1, 0, 1
Let b(c) = 21*c**3 + 48*c**2 + 135*c + 27. Let j(h) = h**3 - 3*h**2 + h. Let d(s) = -b(s) + 9*j(s). Factor d(r).
-3*(r + 3)**2*(4*r + 1)
Suppose 0 + 16/7*l**2 + 2/21*l**3 + 46/21*l = 0. What is l?
-23, -1, 0
Let k = -68/333 - -24/37. Let m = -178 - -180. Determine u, given that -2/9*u + 2/9*u**m - k = 0.
-1, 2
Suppose 4*l = 5*q + 2, 0 = 5*q + l - 3*l - 4. Solve -2 + 20*m + 6 + 0*m**2 - 5*m**q - 6*m**2 = 0 for m.
-2/11, 2
Let o(d) be the second derivative of d**6/6 + d**5 + 5*d**4/4 - 10*d**3/3 - 10*d**2 - 326*d. Factor o(g).
5*(g - 1)*(g + 1)*(g + 2)**2
Determine o, given that 8/3*o**2 - 8/3*o**3 + 0 + 2/3*o**4 + 0*o = 0.
0, 2
Solve -36*v - 3*v**2 + 2 - 88 - 3*v - 22 = 0 for v.
-9, -4
Let o be (-4)/(-34) - 12/102. Let z = -65/6 + 23/2. Determine v, given that o + 0*v - 2/3*v**2 + z*v**4 + 0*v**3 = 0.
-1, 0, 1
Let k(l) be the first derivative of l**4/12 - 14*l**3/3 + 147*l**2/2 + 19. Factor k(m).
m*(m - 21)**2/3
Let p = 490/11 - 7339/165. Let u(x) be the first derivative of 1/5*x**2 + 8 + 3/5*x**4 - 8/25*x**5 + 0*x - 8/15*x**3 + p*x**6. Factor u(z).
2*z*(z - 1)**4/5
Let i = 3033 + -3031. Let o(t) be the first derivative of t**4 - 4*t + 4/3*t**3 - i*t**2 - 13. Factor o(h).
4*(h - 1)*(h + 1)**2
Let h be 19/((-532)/8)*350/(-15). Solve h*x + 50/3 + 2/3*x**2 = 0.
-5
Let m(p) be the third derivative of p**6/180 - p**5/30 + 4*p**3/9 - 6*p**2 - 2. What is n in m(n) = 0?
-1, 2
Suppose 27*y - 12*y**4 - 24*y**3 + 6 - 11*y**3 + 8*y**3 + 6*y**2 = 0. What is y?
-2, -1, -1/4, 1
Suppose -34 = -5*g - 3*x, 4*x + 16 = g - 0*x. Let f be 2 - (0 - 24*g/(-108)). Factor -2/3*s + f*s**2 + 0.
2*s*(s - 3)/9
Let q be 3*1 + (8 - 7). Suppose y = -6*k + 3*k + 10, q*y = -5*k + 12. Factor -15*b**3 - 6*b**k - 2*b**5 + b**3 - 14*b**2 - 4*b**4 - 4*b - 4*b**3.
-2*b*(b + 1)**3*(b + 2)
Let i(x) be the second derivative of x**7/630 + x**6/180 - 7*x**2/2 + 32*x. Let y(f) be the first derivative of i(f). Let y(t) = 0. What is t?
-2, 0
Let x = -53 + 98. Let z be (-2 - 1)*(96/x)/(-4). Let 2/5*d**2 + z + 8/5*d = 0. Calculate d.
-2
Let d(c) = c**3 + 5*c**2 - 8*c - 10. Let h be d(-5). Factor 5*g**4 + 32*g - h*g**2 - 9*g**3 + 20*g + 88*g - 120 - 6*g**3.
5*(g - 2)**3*(g + 3)
Let d be 120/(-140) - (4 + -10 - -4). Factor -d*t + 8/7*t**2 - 2/7*t**4 + 0 + 2/7*t**3.
-2*t*(t - 2)*(t - 1)*(t + 2)/7
Let i(d) = d**3 + 45*d**2 - 92*d + 61. Let z(y) = -44*y**2 + 92*y - 60. Let p(o) = -4*i(o) - 5*z(o). Find v such that p(v) = 0.
1, 2, 7
Let i(z) be the first derivative of z**7/98 + z**6/35 - z**4/14 - z**3/14 - z - 7. Let d(m) be the first derivative of i(m). Solve d(t) = 0.
-1, 0, 1
Let r(y) be the first derivative of -121*y**4/2 - 2618*y**3/3 + 241*y**2 - 22*y - 188. Find j such that r(j) = 0.
-11, 1/11
Let i = -17950/11 + 1632. Solve 4/11*r**2 - i*r - 4/11*r**4 + 2/11*r**5 + 0 + 0*r**3 = 0 for r.
-1, 0, 1
Factor -37/3*w + 0 - 1/6*w**2.
-w*(w + 74)/6
Let -4/3*s**4 + 80/9*s**2 + 64/9*s**3 + 256/9 - 4/9*s**5 - 128/3*s = 0. Calculate s.
-4, 1, 2
Factor -2/3*m**3 - 32258/3*m + 508/3*m**2 + 0.
-2*m*(m - 127)**2/3
Suppose -6*h - 8 = -8*h. Determine r, given that 1 + 9*r**4 - 20*r - h*r**4 - 10*r**3 + 4 - 10*r**3 + 30*r**2 = 0.
1
Let x(c) be the first derivative of 310*c**3/3 + 5*c**2/2 + 66. What is m in x(m) = 0?
-1/62, 0
Let c(f) be the first derivative of -f**3/5 + 9*f**2/10 + 12*f/5 + 516. Factor c(q).
-3*(q - 4)*(q + 1)/5
Let d(j) be the third derivative of -1/840*j**7 + 0*j**3 + 10*j**2 + 0*j + 0 + 0*j**4 + 0*j**5 - 1/480*j**6. Factor d(y).
-y**3*(y + 1)/4
Let f be (-12)/(-22) + 1040/715. Find l, given that 3/7*l + 0 - 3/7*l**f = 0.
0, 1
Let x = 13 - 10. Let t be (3/(-8 - -2))/(2 - x). What is y in 1/2*y**2 + 0 - 1/2*y - 1/2*y**4 + t*y**3 = 0?
-1, 0, 1
Let u be (17*(-22)/(-561))/(4/3). Let t = -6 + 13/2. Factor -u*l**2 + 0 + t*l.
-l*(l - 1)/2
Suppose 5*j - 308 = n, -4*j + 238 = -2*n - 3*n. Suppose -j*a = -52*a. Suppose -4/5*b - 2/5 + 4/5*b**3 + a*b**2 + 2/5*b**4 = 0. Calculate b.
-1, 1
Suppose -51*o + 56*o = -m + 18, -3*o = m - 12. Determine h so that 0*h**2 + 0*h + 1/4*h**m + 0 = 0.
0
Let y(j) be the second derivative of -j**5/40 - j**4/12 + j**3/12 + j**2/2 + 167*j. Factor y(d).
-(d - 1)*(d + 1)*(d + 2)/2
Suppose -n = -z - 9, -3*n + 5*z = -0 - 37. Let o = 3/5 - -11/15. Find j, given that 0*j - o*j**2 - 11/3*j**n + 0 + j**5 + 4*j**3 = 0.
0, 2/3, 