t b(u) be the first derivative of -9 - 3/2*u**2 - 1/24*u**6 + 5/12*u**4 + 0*u - 1/12*u**5 + 0*u**3. Let v(m) be the second derivative of b(m). Factor v(x).
-5*x*(x - 1)*(x + 2)
Suppose -51*u = -54*u + 3. Let v be u - (6 - (270/24 + -6)). Find g such that -1/4*g**2 + v - 1/8*g + 1/8*g**3 = 0.
-1, 1, 2
Let l = -248 + 288. Factor -14*o - 66*o + 25 - 89*o**4 + 90*o**2 + 94*o**4 - l*o**3.
5*(o - 5)*(o - 1)**3
Suppose 0 = -90*s + 93*s + 12. Let i(k) = -15*k**2 - 19*k + 22. Let l(t) = 3*t**2 + t - 1. Let o(g) = s*l(g) - i(g). Factor o(x).
3*(x - 1)*(x + 6)
Let b(s) be the third derivative of -s**8/420 - 104*s**7/525 - 431*s**6/200 - 1429*s**5/300 + 313*s**4/15 - 24*s**3 - 7*s**2 + 149*s. Let b(d) = 0. What is d?
-45, -4, 1/2
Suppose 252*g = 233 + 523. Find x, given that 42/11*x + 36/11 - 40/11*x**g - 20/11*x**2 - 2/11*x**5 - 16/11*x**4 = 0.
-3, -2, -1, 1
Let j(a) be the first derivative of -a**5/45 + 5*a**4/12 - 19*a**3/9 + 73*a**2/18 - 10*a/3 + 5823. Let j(u) = 0. What is u?
1, 3, 10
Let i(t) be the first derivative of -t**3/27 - 14*t**2/9 + 20*t/3 - 1142. Find x such that i(x) = 0.
-30, 2
Let g(c) = 4*c**4 + 40*c**3 - 1364*c**2 + 7618*c - 10188. Let t(q) = 4*q**2 - q - 2. Let x(b) = g(b) + 2*t(b). Factor x(d).
4*(d - 7)**2*(d - 2)*(d + 26)
Factor 122*x + 740/3 - 2/3*x**2.
-2*(x - 185)*(x + 2)/3
Let n = 1482283/3 + -494081. Factor 14 - n*r - 2/3*r**2.
-2*(r - 1)*(r + 21)/3
Suppose -1326675/8*l - 1/8*l**3 + 294079625/8 + 1995/8*l**2 = 0. Calculate l.
665
Let o be (-19437)/342 + (57 - 0). Find y such that -o*y**3 + 121/3 - 77/6*y - 10/3*y**2 = 0.
-11, 2
Let a be 5/(-4) - (-549)/36. Factor -8 + 36*t - 79*t + 37*t + a*t**3 - 2*t**4 + 32*t - 30*t**2.
-2*(t - 4)*(t - 1)**3
Let h(o) = o**2 - 55*o - 6048. Let c be h(-55). Let r(u) be the first derivative of 4 + 8/27*u**3 + 0*u**c + 2/45*u**5 + 5/18*u**4 + 0*u. Factor r(s).
2*s**2*(s + 1)*(s + 4)/9
Suppose -n + 2*n = -2*k + 36, 4*n = -5*k + 156. Determine v so that 78*v + 13 + 26*v + n*v**3 - 5*v**4 - 37 - 111*v**2 - 2*v**3 - 6*v = 0.
2/5, 1, 3, 4
Let c be 2/(-4)*(2 + -2). Let y = 4857/2 + -2428. Factor c - 3/4*m**3 + 0*m - 1/4*m**4 - y*m**2.
-m**2*(m + 1)*(m + 2)/4
Let o(l) = -58*l - 1329. Let i be o(-23). Let h(d) be the third derivative of 0*d + 0*d**3 - 13*d**2 - 7/12*d**i + 5/12*d**4 + 0. Determine m so that h(m) = 0.
0, 2/7
Let x(l) be the second derivative of 21*l + 0*l**2 + 3/4*l**4 + 1/10*l**6 - 9/20*l**5 - 1 - 1/2*l**3. Factor x(t).
3*t*(t - 1)**3
Factor 1690377*d**2 + 5219465*d**2 + 15048*d + 8 + 166480*d**2.
2*(1881*d + 2)**2
Suppose 110*x = -29414 + 116314. Suppose x = 7*r + 769. Factor 0 + 2/7*o**r - 4/7*o**2 - 16/7*o.
2*o*(o - 4)*(o + 2)/7
Let r(b) be the first derivative of -2*b**3/33 + 2*b**2/11 - 2*b/11 - 2263. Solve r(l) = 0 for l.
1
Let x = 64 + -65. Let z(h) = -h**4 + 2*h**3 + h**2 - h. Let d(k) = 6*k**4 + 2*k**2 - 4*k - 8. Let o(m) = x*d(m) - 4*z(m). Factor o(u).
-2*(u - 1)*(u + 1)*(u + 2)**2
Factor 2208/5*r - 3/5*r**2 + 2211/5.
-3*(r - 737)*(r + 1)/5
Suppose 0 = -602*t - 58*t. Let s be (11/(-55))/((-1)/2). Factor 2/5*h - s*h**3 + 0*h**2 + t.
-2*h*(h - 1)*(h + 1)/5
Let v(t) = 2*t - 12. Let s be v(7). Let a be (-5)/s*(-6)/5. What is x in -5*x**4 + 7*x**3 - a*x**3 + x**3 = 0?
0, 1
Let j be (-4)/6*6/(-16)*(65 - 57). Let c(r) be the third derivative of -7/8*r**4 + 0 + 5*r**j - 3/2*r**3 + 0*r - 1/4*r**5 - 1/40*r**6. Factor c(z).
-3*(z + 1)**2*(z + 3)
Let b(w) = -35*w**3 - 970*w**2 + 3095*w - 10. Let u(y) = -11*y**3 - 324*y**2 + 1032*y - 3. Let i(f) = 3*b(f) - 10*u(f). Factor i(d).
5*d*(d - 3)*(d + 69)
Let o(h) = -h**3 + 5*h**2 - 3. Let w(f) be the first derivative of -37 - 3*f**3 + 0*f**2 + 1/4*f**4 + 7*f. Let l(t) = -7*o(t) - 3*w(t). Factor l(r).
4*r**2*(r - 2)
Let m(z) = -2*z**2 + 9*z + 1. Let g(h) = -2456*h + 1 + 2456*h + h**2. Let n(u) = 5*g(u) + m(u). Solve n(a) = 0.
-2, -1
Let o = 2431 - 2960. Let a = o - -531. Factor 27/8*t + 3/4 + 9/4*t**4 + 3/8*t**5 + 6*t**a + 21/4*t**3.
3*(t + 1)**4*(t + 2)/8
Suppose 0 = -2*r + 2*k - 2 - 0, 15 = r + 3*k. Let i(c) = c + 58. Let x be i(0). Determine l so that -l**r + 28 - x + 30 + l = 0.
-1, 0, 1
Let y(r) = r**2 - r + 1. Let n(j) = 7*j**2 - 7*j - 17. Let g(a) = n(a) - 3*y(a). Let i be g(10). Suppose 335*w**3 - 3*w**2 - i*w**3 - 2*w**2 = 0. What is w?
-1, 0
Solve 3/2*r**2 - 57 + 51/2*r = 0.
-19, 2
Let v be (-310)/50 + 6 + 388/(-10). Let m be (6 + 410/(-65))/(6/v). Solve 2*p**m + 3/2*p**3 - 5/2*p - 1 = 0.
-2, -1/3, 1
Let h = -344 - -348. Factor 134*l + 100*l**3 - 108*l**2 - 24 - 6058*l**4 + 6051*l**h - 95*l**2.
-(l - 12)*(l - 1)**2*(7*l - 2)
Suppose 5*v - 8 = -96*j + 94*j, -4*v = 3*j - 12. Suppose -3/2*k**4 - 1/2*k**2 - 3/2*k**3 + v*k + 0 - 1/2*k**5 = 0. Calculate k.
-1, 0
Let u(d) = d**4 - 3*d**3 - 2*d**2 + 1. Let g(j) = 2*j**5 - 429*j**4 + 409*j**3 - 18*j**2 + 9. Let q(t) = 2*g(t) - 18*u(t). Factor q(b).
4*b**3*(b - 218)*(b - 1)
Let k(f) be the first derivative of 6*f - 11/2*f**2 + 4/3*f**3 + 1/4*f**4 - 147. Find t such that k(t) = 0.
-6, 1
Let c(a) = a**2 - 34*a + 66. Let n be c(32). Let d(v) be the third derivative of 0 + 2*v**n + 0*v + 1/16*v**4 - 1/160*v**5 - 1/4*v**3. Factor d(f).
-3*(f - 2)**2/8
Let n(w) be the second derivative of -w**4/3 - 572*w**3/3 + 1152*w**2 + 9364*w. Solve n(l) = 0.
-288, 2
Let u be (6/15)/((-21)/2940). Let d be (185/35 - 5)/((-32)/u). Factor 1/5*n**2 + 3/10*n**4 + 9/10*n - n**3 - d + 1/10*n**5.
(n - 1)**3*(n + 1)*(n + 5)/10
Factor -1/3*v**2 + 139/3*v - 274/3.
-(v - 137)*(v - 2)/3
Let t = -127869 - -127869. Factor -2/15*l**4 + 4/5*l**3 + 16/15*l - 8/5*l**2 + t.
-2*l*(l - 2)**3/15
Suppose 2772 = -j + 12*j. Let c be (-3 - 2/(-2))*j/(-336). Solve 1/4*k**4 + 0*k - c*k**2 + 0 + 1/4*k**3 = 0 for k.
-3, 0, 2
Let m(l) be the third derivative of 0 - 1/10*l**4 - 1/100*l**5 - 53*l**2 - 3/10*l**3 + 0*l. Factor m(t).
-3*(t + 1)*(t + 3)/5
Let x(m) be the third derivative of -33/10*m**6 + 0*m + 0*m**3 + 279*m**2 + 2/5*m**7 + 0 - 121/15*m**5 + 0*m**4 - 1/84*m**8. Determine h so that x(h) = 0.
-1, 0, 11
Suppose 2*d = -3*r + 21 - 7, 2*r - 9 = -d. Let j = -22 - -52. Factor 16*s**2 - 40*s**2 - 36*s**2 - 5*s**r + j*s**3 + 40*s.
-5*s*(s - 2)**3
Let o(p) be the first derivative of 0*p + 0*p**2 + 16/9*p**3 + 135 + 1/18*p**6 + 1/2*p**4 - 3/5*p**5. Factor o(j).
j**2*(j - 8)*(j - 2)*(j + 1)/3
Suppose -21176/7*b**2 + 402/7*b**3 + 13944*b - 2/7*b**4 - 10976 = 0. Calculate b.
1, 4, 98
Let x(r) be the first derivative of -15/2*r**2 - 4*r**3 + 0*r + 226 + 3/4*r**4. Factor x(q).
3*q*(q - 5)*(q + 1)
Let r = 1232/669 + -1349/1338. Determine b, given that -r*b**2 + 1/6*b**3 + 7/6*b - 1/2 = 0.
1, 3
Let p(o) = 3*o**4 - o**3 - 1. Let l(i) = -2*i**4 - 13*i**3 + 53*i**2 - 76*i + 37. Let w(d) = -l(d) - p(d). Let w(f) = 0. What is f?
1, 2, 9
Let q be (-5)/(-3) - (-252)/189. Let o(k) be the third derivative of 0*k**q + 0*k**4 + 0*k + 0 - 1/510*k**5 + 11*k**2 - 1/1020*k**6. Factor o(d).
-2*d**2*(d + 1)/17
Let q(w) be the first derivative of w**3/6 + 1197*w**2/4 + 598*w + 2070. Factor q(r).
(r + 1)*(r + 1196)/2
Let r(h) be the second derivative of 0*h**4 + 1/195*h**6 + 0*h**3 + 0 + 2/65*h**5 - 61*h + 0*h**2. Determine a, given that r(a) = 0.
-4, 0
Suppose 0 = -5*k - z + 2*z + 47, 0 = 3*k + z - 33. Suppose 0*d + d - 5*o + 22 = 0, k = 2*o. Determine r, given that 4*r**2 - 2*r + 10*r + 4 + 3 - d = 0.
-1
Let x(o) be the second derivative of -o**6/60 - 11*o**5/5 - 121*o**4 - 10648*o**3/3 - 18*o**2 - 80*o. Let m(i) be the first derivative of x(i). Factor m(l).
-2*(l + 22)**3
Let i(b) be the first derivative of b**3/5 - 1344*b**2/5 + 602112*b/5 - 2469. Let i(t) = 0. Calculate t.
448
Let b be 5/((-30)/18) - 615/(-200). Let a(i) be the second derivative of 3*i + 0*i**2 + 0 - 1/4*i**3 + b*i**5 + 1/24*i**4 - 1/60*i**6. Factor a(y).
-y*(y - 3)*(y - 1)*(y + 1)/2
Let a(m) be the first derivative of m**5/2 + 7415*m**4/2 + 10996445*m**3 + 16307727935*m**2 + 24184360527605*m/2 - 6190. Suppose a(r) = 0. What is r?
-1483
Let n = -85053/4 - -21265. Let g(x) be the second derivative of -n*x**4 - 8*x**2 + 0 + 8*x**3 + 1/8*x**5 + x. Factor g(o).
(o - 4)**2*(5*o - 2)/2
Suppose 7*v - 14 = -0*v. Let h = 443 + -441. Find x, given that h*x - 8/5*x**v + 2/5*x**3 - 4/5 = 0.
1, 2
Let s(j) be the second derivative of j**4/108 + 13*j**3/9 + 169*j**2/2 + 88*j + 7. Factor s(g).
(g + 39)**2/9
Let