rivative of -f**6/120 + f**5/80 + f**4/24 - 53*f + 67. Let p(q) be the first derivative of x(q). Factor p(s).
-s**2*(s - 2)*(s + 1)/4
Let w(n) be the second derivative of n**5/60 + n**4/12 - 8*n**3 + 90*n**2 - 947*n. Suppose w(u) = 0. What is u?
-15, 6
Let j = 336 + -231. Let u be 10/j*1 - (-2)/(-21). Factor 4/5*x**4 + 2/5*x**5 - 4/5*x**2 + 0 - 2/5*x + u*x**3.
2*x*(x - 1)*(x + 1)**3/5
Suppose z = 52 - 49, -3*z = k + 2304. Let m = k + 2316. Suppose 0*f**2 + 0 - 2/19*f**m + 2/19*f**4 + 0*f = 0. What is f?
0, 1
Suppose 0 = 4*p - 7*p - 4*t + 16, -4*t = p - 8. Suppose g + 4*i + 6 = 0, p*g + 1 + 1 = -5*i. Factor 6*x - 15*x + 2*x**2 + 3*x**g + 5 - x.
5*(x - 1)**2
Factor -128/17*f + 264/17 - 2/17*f**2.
-2*(f - 2)*(f + 66)/17
Suppose 2 = -4*b - 2*n, -2*b + 21 = -4*b - 5*n. Determine j, given that -127*j**b - 152*j**2 - 3*j**4 - 30*j**3 + 228*j**2 - 24*j = 0.
-8, -1, 0
Let w = -664231/2 - -332117. Find f such that -1/4*f + w - 1/4*f**2 = 0.
-3, 2
Let b be (-2 - (-57)/6)*1/(-30)*-15. Factor b + 5/4*q**2 + 5/4*q**3 - 25/4*q.
5*(q - 1)**2*(q + 3)/4
Suppose -4*k - 28 = -4*m, 4*m - 5*k + 14 = 43. Let -4 + 209*z**2 - m - 244*z**2 - 45*z = 0. What is z?
-1, -2/7
Let w(q) = 7*q + 13. Let v be w(17). Let a = 132 - v. What is m in 2/9*m**2 + a + 4/9*m = 0?
-2, 0
Suppose -450 = -n - 5*n. Let u = -71 + n. Factor -24*l**2 - 12 + 32*l + 3*l**u + l**4 - 7*l**3 + 7*l**3.
4*(l - 1)**3*(l + 3)
Let c(b) be the second derivative of b**8/2240 - b**7/280 - 13*b**4/12 + 2*b**3/3 - 96*b. Let n(d) be the third derivative of c(d). Factor n(g).
3*g**2*(g - 3)
Let z = 244752 - 244749. Let 0*h**z + 0 - 32/9*h**2 - 2/9*h**5 + 32/9*h + 8/9*h**4 = 0. What is h?
-2, 0, 2
Let 16/3*b**3 + 192*b + 0 + 12*b**4 - 208*b**2 - 4/3*b**5 = 0. What is b?
-4, 0, 1, 6
Find h, given that 73 + 115*h - 82*h**2 + 77*h**2 + 2267 = 0.
-13, 36
Let c(d) = d**3 - d. Let j(w) be the second derivative of 13*w**5/5 - 65*w**4/4 + 203*w**3/6 - 30*w**2 + 8*w - 6. Let f(u) = 3*c(u) + j(u). Factor f(m).
5*(m - 2)*(m - 1)*(11*m - 6)
Let y(o) = 41*o**2 + 338*o + 1260. Let m(u) = 31*u**2 + 333*u + 1259. Let j(r) = -4*m(r) + 3*y(r). Factor j(d).
-(d + 4)*(d + 314)
Let u be (-36)/(-10) - 36/(-90). Suppose u*d = 5 + 3. Factor -1 + 2*x**2 + d*x - 3*x**2 + 4.
-(x - 3)*(x + 1)
Let u be (((-156)/(-15) - 10)/(4/(-5)))/(4/(-28)). Let -u*d**4 + 3*d**2 - 11/4*d**3 + 11/4*d + 1/2 = 0. Calculate d.
-1, -1/2, -2/7, 1
Let t(u) be the third derivative of 0 + 15*u**2 + 1/63*u**7 + 0*u**3 + 0*u**4 + 1/5*u**5 - 1/1008*u**8 - 11/120*u**6 - 2*u. Factor t(s).
-s**2*(s - 4)*(s - 3)**2/3
Let n(h) be the first derivative of h**3/9 + 68*h**2/3 - 92*h + 5682. Solve n(x) = 0.
-138, 2
Let c = -14240 - -14243. Let w(t) be the first derivative of -8/3*t**3 + 23 + 0*t - c*t**4 - t**2 - 1/3*t**6 - 8/5*t**5. Factor w(y).
-2*y*(y + 1)**4
Let m(i) = 11*i**3 + 1660*i**2 - 8*i. Let z(h) = -h**3 + 34*h**2 + h. Let v(r) = -m(r) - 8*z(r). Solve v(k) = 0 for k.
-644, 0
Let l(d) be the second derivative of -3/4*d**2 - 1/2*d**3 + 0 - 1/8*d**4 - 4*d. Solve l(u) = 0.
-1
Let f(z) = -z - 10. Let o(q) = -2*q**3 - 16*q**2 + 43*q + 30. Let u(g) = 5*f(g) + o(g). Factor u(v).
-2*(v - 1)**2*(v + 10)
Let d(f) be the first derivative of f**5/55 + 2*f**4/11 + 6*f**3/11 - 27*f/11 - 668. Solve d(p) = 0 for p.
-3, 1
Suppose -54 = -26*h + 50. Suppose 0 = 4*p + 4*w, -11*w = 4*p - 6*w + h. Find c such that 0 + 5/2*c**3 + 3/2*c**2 + 0*c - c**p = 0.
-1/2, 0, 3
What is g in -463*g**4 + 1 - 1 + 100*g**3 + 464*g**4 + 0 - 101*g**2 = 0?
-101, 0, 1
Let o(a) be the first derivative of -a**4/12 - 53*a**3/9 + 28*a**2/3 + 36*a + 689. Factor o(u).
-(u - 2)*(u + 1)*(u + 54)/3
Let w(g) be the third derivative of 128/15*g**3 - 45*g**2 + 1/300*g**5 + 4/15*g**4 + 0 - 2*g. Find a such that w(a) = 0.
-16
Let n(i) be the first derivative of i**5/120 - 5*i**4/48 + 7*i**2 - 106. Let x(r) be the second derivative of n(r). Factor x(a).
a*(a - 5)/2
Let o(y) be the first derivative of -4*y**3/3 + 40*y**2 + 276*y + 1445. Factor o(b).
-4*(b - 23)*(b + 3)
Factor -8/3*a**2 - 38/3*a + 10/3.
-2*(a + 5)*(4*a - 1)/3
Let o(j) = 4*j**4 + 302*j**3 - 1256*j**2 - 292*j + 1462. Let n(x) = x**3 - 2*x**2 + 23. Let h(v) = -10*n(v) + o(v). Determine g, given that h(g) = 0.
-77, -1, 1, 4
Let y(c) be the third derivative of -11*c**7/1365 + 67*c**6/390 - 4*c**5/65 + 3*c**2 + 464*c. Factor y(b).
-2*b**2*(b - 12)*(11*b - 2)/13
Let h = -23629 - -23629. Let s(c) be the third derivative of h - 1/480*c**5 + 0*c - 1/24*c**3 + 19*c**2 + 1/64*c**4. Solve s(z) = 0 for z.
1, 2
Let v be 136/(-392)*3 + 5. Let f = v - 26/49. Factor -3/7*u**3 - 36/7*u + 18/7*u**2 + f.
-3*(u - 2)**3/7
Let h(s) be the first derivative of -2*s**5/5 + 7*s**4/2 + 4804. Find a such that h(a) = 0.
0, 7
Suppose -2*f + j + 1 = 0, -f + 2*j + 3*j = 13. Suppose 32*v**2 - 67*v**f + v**3 + 39*v**2 - 3*v**3 = 0. Calculate v.
0, 2
Let g(c) be the third derivative of 1/420*c**5 + 0 - 1/168*c**6 + c**2 + 1/735*c**7 + 6*c - 1/14*c**3 + 5/168*c**4. Factor g(j).
(j - 1)**2*(j + 1)*(2*j - 3)/7
Let s be 3/(-4) + 14*91/56. Factor -4*y**2 - 17*y + 11*y + s*y.
-4*y*(y - 4)
Let k be 70/24*(-5 + 8007/925). Let b = k - -1/370. Let -32/9 - 2*l**4 + b*l**3 - 176/9*l**2 + 128/9*l = 0. Calculate l.
2/3, 2
Factor 5/3*h**3 - 20525*h**2 + 84255125*h - 345867288125/3.
5*(h - 4105)**3/3
Let h(d) be the first derivative of -7*d**5/3 + 143*d**4/12 - 122*d**3/9 + 4*d**2 + 545. Let h(z) = 0. What is z?
0, 2/7, 4/5, 3
Let w(r) be the first derivative of 111*r**4/4 + 212*r**3/15 - 2*r**2/5 - 9834. Suppose w(d) = 0. What is d?
-2/5, 0, 2/111
Let f(o) be the first derivative of -283*o**3 + 2 - 108*o + 9/4*o**6 + 144/5*o**5 - 315*o**2 + 507/8*o**4. Suppose f(j) = 0. What is j?
-6, -1/3, 2
Let p(w) be the third derivative of -w**7/504 + w**6/72 + w**5/3 + w**4/24 + 3*w**3 + 165*w**2. Let o(k) be the second derivative of p(k). Factor o(l).
-5*(l - 4)*(l + 2)
Let b be (-126)/98 + (-6847)/(-4879). Solve b*m**2 + 4/17*m + 0 = 0 for m.
-2, 0
Let p be (1 + -3)/((2*-1)/(-652 + 654)). Factor -1/4*h**3 + 0 + 3*h**p + 0*h.
-h**2*(h - 12)/4
Factor 0 - 1/4*u**2 - 1/8*u**3 + 0*u.
-u**2*(u + 2)/8
Let f(u) = -27*u**2 + 1586*u + 531. Let m(d) = -410*d**2 + 23792*d + 7966. Let g(w) = -46*f(w) + 3*m(w). What is k in g(k) = 0?
-1/3, 132
Let u(a) = 2*a**3 + 92*a**2 + 675*a + 84. Let i be u(-9). Factor 32/3*v**2 + 0 - 1/3*v**i - 256/3*v.
-v*(v - 16)**2/3
Let t(c) be the first derivative of 76/21*c**3 + 0*c - 1/7*c**4 - 122 + 0*c**2. Determine k so that t(k) = 0.
0, 19
Let w = 3/252188 + 882655/252188. Determine a, given that 2 - w*a**2 + 3/2*a**4 + 26/3*a - 26/3*a**3 = 0.
-1, -2/9, 1, 6
Let w(i) be the first derivative of 11*i**7/210 - i**6/6 - i**5/15 - i**2/2 - 6*i + 121. Let t(l) be the second derivative of w(l). Factor t(c).
c**2*(c - 2)*(11*c + 2)
Suppose -4*n + 2*w = -20, 10 = 2*n - 2*w + 5*w. Suppose -5*k + 3*v + 9 = 0, -3*k - k + n*v = -15. Factor 4*c**2 + 0*c - 4*c + 64 - 28*c + k*c**2.
4*(c - 4)**2
Let g = -285 - -287. Solve 16 + 4*c - 5*c**g - 11*c**2 + 1158*c**3 - 1162*c**3 = 0 for c.
-4, -1, 1
Determine f so that 88 - 2*f**3 - 5535*f**2 + 171*f + 5547*f**2 - 69*f = 0.
-4, -1, 11
Let m be ((-37888)/(-12432))/(5/(31 - 1)). Factor 6/7*b**2 - m*b - 88/7.
2*(b - 22)*(3*b + 2)/7
Suppose 4 = g - 0. Factor -23*q**3 - 35*q**4 - 9*q - 16*q**3 - 2*q**4 + 28*q**g - 39*q**2.
-3*q*(q + 1)*(q + 3)*(3*q + 1)
Find u such that 16/15*u**5 - 1042/15*u**4 + 0 + 2048/15*u - 3712/3*u**2 + 5846/5*u**3 = 0.
0, 1/8, 1, 32
Let 43/3*h**3 + 800/3 + 1280/3*h + 174*h**2 + 1/3*h**4 = 0. Calculate h.
-20, -2, -1
Let f(b) be the second derivative of 3*b**5/160 + 19*b**4/32 + 37*b**3/8 + 21*b**2/2 + 2624*b. Let f(n) = 0. What is n?
-14, -4, -1
Factor 0 - 1/4*j**3 + 75/4*j - 5/2*j**2.
-j*(j - 5)*(j + 15)/4
Let v(x) be the second derivative of -x**4/3 - 20*x**3/3 - 42*x**2 - 5954*x. Find a such that v(a) = 0.
-7, -3
Suppose -167/4*n**3 + 5/4*n**4 + 1641/4*n**2 - 4005/4*n + 675/2 = 0. What is n?
2/5, 3, 15
Let c(q) be the first derivative of 0*q - 7/2*q**2 - 1/12*q**5 - 5/12*q**4 + 5/2*q**3 - 6. Let b(r) be the second derivative of c(r). Let b(u) = 0. What is u?
-3, 1
Let x be (-2*(-172)/(-14))/((-92)/69*(-2025)/(-630)). Factor 22/15 + 16/3*d**2 + x*d - 8/15*d**3.
-2*(d - 11)*(2*d + 1)**2/15
Suppose 5*h - 87 = -3*v, 0 = -4*h - 613 + 637. Let a(j