- 1/4*g**5 + 5/6*g**3 - 3*g - 30. Factor l(r).
-5*(r - 12)*(r - 1)*(r + 1)
Let j(k) = -k**4 - 7*k**3 - 182*k**2 - 756*k - 962. Let h(v) = -v**4 + v**3 - v**2 - 2*v - 1. Let u(f) = -4*h(f) + 2*j(f). Let u(a) = 0. What is a?
-4, -3, 20
Let i = -106 - 24. Let b = -127 - i. Factor 21*h - b*h**2 + 2*h + 10*h.
-3*h*(h - 11)
Suppose 9*c + 69 = 87. Factor -130*b**4 - 10*b**3 - c*b**3 - 3*b**5 - 18*b**5 + 82*b**4.
-3*b**3*(b + 2)*(7*b + 2)
Let l = -913 + 916. Let k be 8/40*0*(-3)/l. Factor 8/11*d**2 - 2/11*d**5 + 0 - 6/11*d**4 + k*d + 0*d**3.
-2*d**2*(d - 1)*(d + 2)**2/11
Let b(x) be the second derivative of 11*x**5/4 - 3565*x**4/12 + 1435*x**3/3 + 320*x**2 - 3074*x. Factor b(t).
5*(t - 64)*(t - 1)*(11*t + 2)
Let d(o) be the third derivative of o**8/84 - 12*o**7/35 + 6*o**6/5 + 418*o**5/15 + 121*o**4/2 + 2838*o**2. Solve d(w) = 0 for w.
-3, -1, 0, 11
Let c(j) be the first derivative of 2*j**5/85 - 27*j**4/34 + 100*j**3/51 - 869. Factor c(n).
2*n**2*(n - 25)*(n - 2)/17
Let c(j) be the first derivative of 5*j**4/36 + 2*j**3/3 + 56*j - 68. Let v(r) be the first derivative of c(r). Factor v(s).
s*(5*s + 12)/3
Let d = 384277 + -3458492/9. Factor -d*m**2 - 2/9*m**3 + 1/9 + 2/9*m.
-(m - 1)*(m + 1)*(2*m + 1)/9
Let c(o) be the third derivative of o**8/840 - 8*o**7/525 - 13*o**6/300 + 76*o**5/75 + o**4/5 - 48*o**3/5 + 24*o**2 + 18. Solve c(j) = 0 for j.
-4, -1, 1, 6
Let f(w) be the third derivative of -1/30*w**5 + 1/96*w**4 + 0*w + 0 + 1/3*w**3 - 26*w**2 - 1/480*w**6. Factor f(z).
-(z - 1)*(z + 1)*(z + 8)/4
Let c(u) be the first derivative of u**8/560 - u**6/40 + u**5/20 + 76*u**3/3 - 40. Let k(i) be the third derivative of c(i). Suppose k(x) = 0. What is x?
-2, 0, 1
Let j(n) be the third derivative of 4/3*n**3 + 0 + 0*n - 1/30*n**5 + 34*n**2 - 1/4*n**4. Find k such that j(k) = 0.
-4, 1
Let g = 33 - 19. Let v be 180/35 - 2/g. Factor -2*b**v - 28*b**3 + 7*b**4 - 18*b + 78*b**2 + 4 + 5*b**4 - 46*b**2.
-2*(b - 2)*(b - 1)**4
Let p(b) be the second derivative of -3*b**5/20 + 3*b**3/2 - 3*b**2 - 917*b. Factor p(n).
-3*(n - 1)**2*(n + 2)
Let b be (23 + -29)*(-46)/483. Factor b - 8/7*a + 8/7*a**3 + 0*a**2 - 4/7*a**4.
-4*(a - 1)**3*(a + 1)/7
Factor -92/5 + 6/5*d**3 - 16*d**2 - 178/5*d.
2*(d + 1)**2*(3*d - 46)/5
Let a(z) be the third derivative of -4/15*z**3 + 1/15*z**4 + 2 - 1/150*z**5 + 0*z + 9*z**2. Factor a(d).
-2*(d - 2)**2/5
Let 0 + 0*w**4 - 116/7*w**3 + 4/7*w**5 + 400/7*w + 0*w**2 = 0. Calculate w.
-5, -2, 0, 2, 5
Let x(j) be the second derivative of j**6/10 - 17*j**4/4 + 18*j**3 - 30*j**2 + 570*j. Factor x(u).
3*(u - 2)**2*(u - 1)*(u + 5)
Let b(z) be the first derivative of z**5/4 + 175*z**4/16 + 475*z**3/4 - 175*z**2/8 - 715*z/2 + 1977. Solve b(w) = 0.
-22, -13, -1, 1
Let -1650/7*y + 3/7*y**2 + 226875/7 = 0. What is y?
275
Let i(d) be the third derivative of d**6/1260 + 3*d**5/140 - 11*d**4/42 + 38*d**3/3 - 83*d**2. Let y(x) be the first derivative of i(x). Factor y(p).
2*(p - 2)*(p + 11)/7
Let n be (2 - (9 + 1)) + 8. Let d(k) be the second derivative of n*k**2 + 1 + 1/4*k**5 + 5/3*k**3 - 7*k + 5/4*k**4. Suppose d(g) = 0. What is g?
-2, -1, 0
Let p = 8469 - 8455. Let l(b) be the first derivative of -30*b**2 - p*b**3 + 16 - 24*b - 9/4*b**4. Factor l(k).
-3*(k + 2)**2*(3*k + 2)
Let b(v) be the first derivative of 1/3*v**3 + 16*v - 4*v**2 - 98. Factor b(u).
(u - 4)**2
Let k(c) be the third derivative of -7*c**2 + 4 + 4/3*c**3 + 0*c + 1/30*c**5 - 5/12*c**4. Let k(q) = 0. Calculate q.
1, 4
Let r(f) be the third derivative of -f**7/6300 + 4*f**6/225 - 64*f**5/75 + 77*f**4/6 - 4*f**2 - 5. Let y(x) be the second derivative of r(x). Factor y(n).
-2*(n - 16)**2/5
Let q = -1011001029/770360 - 22/96295. Let l = -1312 - q. Factor -15/8*y**2 + 0 + 0*y - l*y**3.
-3*y**2*(y + 5)/8
Let w(d) = 4*d**2 + 8*d + 1. Suppose i - 8 = -5. Let r be w(i). Factor -51*g**2 - r*g - 32 + 65*g**2 - 47*g.
2*(g - 8)*(7*g + 2)
Let m(s) = 2*s**3 + 18*s**2 - 76*s - 276. Let r(z) = -5*z**3 - 33*z**2 + 153*z + 551. Let d(g) = 9*m(g) + 4*r(g). Find o, given that d(o) = 0.
-2, 7, 10
Suppose -83*f + 175 - 46 = -203. Let u(l) be the first derivative of 0*l - 5/16*l**f + 5/4*l**2 + 5/12*l**3 + 20. Let u(b) = 0. What is b?
-1, 0, 2
Let v(f) = 24*f - 35. Let q be v(5). Let w = 87 - q. Factor -14*x**2 - x**3 + 39*x + 2*x**3 - 21 - x**w - 4*x**3.
-3*(x - 1)**2*(x + 7)
Let s be (4*87/(-580))/((-5)/((-110)/3)) + 6. Determine f so that 8/5 + 24/5*f - 6/5*f**3 - 34/5*f**2 + s*f**4 = 0.
-2, -1/4, 1, 2
Let l(g) = g**2 - 420*g - 1851. Let j(b) = -b**2 - 35*b + 1. Let c(k) = -6*j(k) - l(k). Determine v so that c(v) = 0.
-123, -3
Let z be (4/10 + 14/(-35))/1. Suppose 12*i - 7*i - 3*p = 0, 3*i - 5*p = 0. Determine o so that z*o**2 + 0*o**4 + 0 + 1/5*o**5 + i*o - 1/5*o**3 = 0.
-1, 0, 1
Let m = 501 - 441. Find y such that 22*y**3 + 18*y**3 + 39*y + 24*y**2 + 19*y**3 - 183*y - m*y**3 = 0.
0, 12
Suppose 46*p - 94 = 194 + 34. Let k(h) be the third derivative of 0 + 0*h**3 + 5/6*h**4 + p*h**2 - 1/15*h**5 + 0*h. Suppose k(a) = 0. What is a?
0, 5
Let s(g) = -4*g + 176. Let b be s(44). Suppose 14 = -3*r + 11, b = -z - 5*r - 2. Factor -27/5 + 9/5*d + 3/5*d**2 - 1/5*d**z.
-(d - 3)**2*(d + 3)/5
Let s(w) be the second derivative of -w**4/16 - 213*w**3/4 - 136107*w**2/8 - 2270*w. Factor s(f).
-3*(f + 213)**2/4
Let o(g) = -33*g - 502 - 55*g + 2222*g**2 - 2225*g**2. Let m(b) = -3*b**2 - 90*b - 501. Let s(v) = -5*m(v) + 6*o(v). Let s(r) = 0. Calculate r.
-13
Let p(z) = z - 24. Let i be p(-7). Let j = i - -35. Factor -19*c**4 + 2*c + 4*c**3 - 4*c**2 + 39*c**4 - c**2 - 21*c**j.
-c*(c - 2)*(c - 1)**2
Let a = 215773/172612 + -2/43153. Find u such that a - u - 1/4*u**2 = 0.
-5, 1
Let j be (-3)/((-180)/(-147)) + ((-338)/(-104))/1. Factor -4/5*x**3 - j*x**4 + 224/5 - 304/5*x + 24*x**2.
-4*(x - 2)**3*(x + 7)/5
Let -9747*g - 171/2*g**2 - 370386 - 1/4*g**3 = 0. What is g?
-114
Factor 94/9*q**2 - 2/9*q**3 + 0 - 92/9*q.
-2*q*(q - 46)*(q - 1)/9
Let t(r) be the third derivative of 131*r**2 + 2 + 5/108*r**4 - 1/270*r**5 + 2/9*r**3 + 0*r. Suppose t(n) = 0. What is n?
-1, 6
Suppose -4*q = -t - 9, -5*t = 14*q - 19*q + 30. Let c(l) = l**4 - 3*l**3 - 2*l**2 + 22*l - 8. Let a(m) = -2*m. Let f(x) = t*a(x) - c(x). Factor f(p).
-(p - 2)**2*(p - 1)*(p + 2)
Let s(u) be the second derivative of -u**7/336 - 31*u**6/80 + 47*u**5/80 - 68*u - 36. Factor s(a).
-a**3*(a - 1)*(a + 94)/8
Let v = -108/59 + 707/354. Let i(r) be the second derivative of 10/3*r**3 + 6*r + 0 + 1/2*r**5 + v*r**6 + 0*r**2 - 35/12*r**4. Find t such that i(t) = 0.
-4, 0, 1
Let w = 372 + -373. Let b be 13/(-78) + w/(-6) + 2. Factor 34/3*z + 28/3*z**b + 2*z**3 + 4.
2*(z + 1)*(z + 3)*(3*z + 2)/3
Suppose -14 + 8 = -3*d - 3*r, d + 2*r = 1. Let b be d/2*(-23)/((-207)/12). Solve -4*g**b - 9/5*g - 1/5 = 0 for g.
-1/4, -1/5
Let c(u) = 5342*u - 352570. Let a be c(66). Factor 20/3*n**a + 24*n - 32/3.
4*(n + 4)*(5*n - 2)/3
Let t(r) be the first derivative of -2/7*r**2 + 78 + 0*r + 2/21*r**3. Solve t(l) = 0 for l.
0, 2
Let i(r) = -6*r**2 - 2560*r - 816638. Let k(v) = -25*v**2 - 10241*v - 3266551. Let f(x) = -17*i(x) + 4*k(x). Solve f(a) = 0.
-639
Let h = -644929/9 - -71659. Factor 0 - 4/9*z**3 + 16/9*z - 8/9*z**2 + h*z**4.
2*z*(z - 2)**2*(z + 2)/9
Let w(m) be the first derivative of 0*m**4 + 8/3*m**3 + 76 + 0*m**2 - 4/5*m**5 - 4*m. Find v, given that w(v) = 0.
-1, 1
Solve -444*w**2 - 48 - 1352/5*w + 50*w**4 - 150*w**3 = 0 for w.
-6/5, -2/5, 5
Let y(t) = -10*t**2 + 132*t + 718. Let x(s) be the first derivative of -2*s**3 + 44*s**2 + 479*s + 25. Let k(g) = 8*x(g) - 5*y(g). Factor k(p).
2*(p + 11)**2
Let w be (-4)/(16/(-954)) + 24/48. Factor 121*y + y**4 - w*y + 115*y - y**3 - 5*y**2.
y*(y - 3)*(y + 1)**2
Let h(w) be the second derivative of 1/14*w**7 + 2/5*w**6 + 9/10*w**5 + 0*w**2 + 53*w + 1/2*w**3 + w**4 + 0. Solve h(d) = 0 for d.
-1, 0
Let z(d) = -86*d**3 - 3493*d**2 - 383616*d - 1119744. Let b(i) = -20*i**3 - 873*i**2 - 95904*i - 279936. Let s(r) = -26*b(r) + 6*z(r). Factor s(u).
4*(u + 3)*(u + 216)**2
Let x(h) be the second derivative of h**4/9 - 41*h**3/27 - 7*h**2/9 + 876*h. Find o, given that x(o) = 0.
-1/6, 7
Let q be 40/(-48) - (-17)/6. Factor 23*r**q - 48*r**2 + r + 2*r**3 + 28*r**2.
r*(r + 1)*(2*r + 1)
Let d = 1006363 - 8040783/8. Let v = -1264 + d. Determine c, given that 1/8*c**2 + 0 + v*c = 0