a*k + 137 - 142 - k - k**2.
-(k - 5)*(k - 1)
Factor -5108/3*t**2 + 680/3*t + 20*t**3 + 0.
4*t*(t - 85)*(15*t - 2)/3
Let d(g) = -282*g**3 + 225*g**2 + 2655*g + 33. Let z(x) = 35*x**3 - 28*x**2 - 332*x - 4. Let n(w) = -4*d(w) - 33*z(w). Factor n(v).
-3*v*(v - 4)*(9*v + 28)
Let i(w) = 4*w**4 - 86*w**3 + 66*w**2 + 446*w + 266. Let s(q) = 11*q**4 - 172*q**3 + 116*q**2 + 892*q + 533. Let o(r) = 10*i(r) - 4*s(r). Factor o(p).
-4*(p - 3)*(p + 1)**2*(p + 44)
Factor 6 - 3/2*p**3 - 12*p + 15/2*p**2.
-3*(p - 2)**2*(p - 1)/2
Let p(i) be the first derivative of -i**5 + 135*i**4/4 - 385*i**3 + 3025*i**2/2 - 227. Factor p(u).
-5*u*(u - 11)**2*(u - 5)
Suppose -258*o + 421 + 9 = -86. Find z, given that -4/7*z - 8/7*z**3 - 20/7*z**o + 8/7 = 0.
-2, -1, 1/2
Let r(j) be the third derivative of -11/60*j**6 + 149*j**2 + 0*j**3 + 0 + 1/12*j**4 + 2/15*j**5 + 0*j + 2/35*j**7. Determine x, given that r(x) = 0.
-1/6, 0, 1
Let p(o) = -31*o**3 + 2*o**2 + 4*o + 3. Let v be p(-1). Suppose -v*n = -2*n - 60. Determine k, given that -26/7*k + 30/7*k**n - 4/7 = 0.
-2/15, 1
Let p(n) = 39*n + 3. Let a be p(4). Let j be (-43)/(7826/(-1848)) + 4/(-26). Suppose -j + 5*q**3 - 184*q + 9*q**2 + a*q + q**2 - 20 = 0. What is q?
-3, -1, 2
Let r(h) be the second derivative of 9*h - 3*h**2 + 5/48*h**4 + 0 + 29/12*h**3. Determine v, given that r(v) = 0.
-12, 2/5
Factor -1957*f + 142 + 14*f**2 + 152 - 15*f**2 + 923 + 741.
-(f - 1)*(f + 1958)
Factor 2/19*n**4 + 50/19*n**2 + 20/19*n**3 + 0 + 0*n.
2*n**2*(n + 5)**2/19
Let c(i) = -9*i + 9. Let f be c(-16). Let 264 - 4*a**3 + 93*a + 31*a**3 - f*a**2 - 279 = 0. Calculate a.
1/3, 5
Suppose -70*b = 77543 - 77683. Determine c, given that 2/5*c**5 + 16/5 + 22/5*c**3 - 12/5*c**4 - 24/5*c - 4/5*c**b = 0.
-1, 1, 2
Factor 33 + 50760*w**2 - 4*w**5 + 0*w**5 + 94*w - 50678*w**2 + 12*w**3 - 11*w**4 + 2*w**5.
-(w - 3)*(w + 1)**3*(2*w + 11)
Let g be 45/(-15)*((-35616)/441)/16. Find j, given that -g*j + 8/7*j**2 + 26/7 = 0.
1/4, 13
Let p(x) = x**3 + 37*x**2 + 171*x - 462. Let a be p(-31). Factor -20 - 11/2*z**a - 27*z**2 - 42*z.
-(z + 2)**2*(11*z + 10)/2
Solve 4600*w**2 - 9205*w**2 + 33*w + 4602*w**2 + 306 = 0.
-6, 17
Let x(m) be the second derivative of -m**4/20 - 351*m**3/10 + 8*m - 85. Determine u, given that x(u) = 0.
-351, 0
Let h(g) be the third derivative of 3*g**8/728 - 2*g**7/39 - 49*g**6/195 - 4*g**5/39 - 259*g**2. Find u such that h(u) = 0.
-2, -2/9, 0, 10
Let n(p) be the third derivative of 0*p + 1/6*p**4 + 8*p**3 + 0 - 1/15*p**5 + 47*p**2. Factor n(m).
-4*(m - 4)*(m + 3)
Let m(v) be the first derivative of -4*v**3/3 + 2098*v**2 + 6425. What is t in m(t) = 0?
0, 1049
Let f be 91/26 + (-30)/10. Let k(y) be the second derivative of 50*y + f*y**3 - 3/20*y**5 - y**2 + 1/30*y**6 + 1/12*y**4 + 0. Suppose k(z) = 0. Calculate z.
-1, 1, 2
Let m(l) = -l + 8. Let y be m(5). Let n = -11098 + 11100. Factor 104/9*a + 625/9*a**y - 4/9 - 725/9*a**n.
(a - 1)*(25*a - 2)**2/9
Let o(t) be the second derivative of -2*t**6/135 - 2*t**5/3 + 23*t**4/3 + 480*t**3 - 10368*t**2 - 6794*t. Determine a, given that o(a) = 0.
-24, 9
Let g(i) = -4*i**2 + 16*i - 4. Let z(u) = 4*u**2 - 144*u + 399*u - 129*u + 5 - 141*u. Let c(k) = -3*g(k) - 4*z(k). Find q such that c(q) = 0.
1, 2
Factor 23*l**4 - 497*l**3 - 4*l**4 - 13*l - 67*l + 17*l**3 + 6*l**4 - 396*l**2.
l*(l - 20)*(5*l + 2)**2
Let q = -244405 + 244414. Find l, given that -q*l**2 + 1/8*l**3 - 1728 + 216*l = 0.
24
Let y be (-31 - -4)/((-6900)/25760). What is t in -784/5*t - y*t**2 + 0 - 12*t**3 - 2/5*t**4 = 0?
-14, -2, 0
Factor 0 + 6*z**4 + 1/4*z**5 + 11*z**3 + 0*z + 0*z**2.
z**3*(z + 2)*(z + 22)/4
Let v(m) = 16*m**3 - 536*m**2 + 460*m - 20. Let g(a) = 5*a**3 - 178*a**2 + 155*a - 6. Let r(f) = -10*g(f) + 3*v(f). Factor r(c).
-2*c*(c - 85)*(c - 1)
Suppose -2*n = -3*p + 698 + 283, 3*n + 2*p = -1491. Let j = -493 - n. Suppose 94/5*s**j + 16/5 - 92/5*s - 18/5*s**3 = 0. What is s?
2/9, 1, 4
Let u = -40762 - -40765. Solve -9/7*k**5 - 186/7*k**2 - 24/7 - 108/7*k - 60/7*k**4 - 153/7*k**u = 0.
-2, -1, -2/3
Let q(f) be the third derivative of 0 - 1/420*f**5 + 0*f + 17/168*f**4 + 183*f**2 + 3/7*f**3. Factor q(s).
-(s - 18)*(s + 1)/7
Let y be 1 - (2742/84 + 2). Let u = y + 246/7. Factor 3/4*k - 3/4*k**4 + u*k**2 + 3/4*k**5 - 3/4 - 3/2*k**3.
3*(k - 1)**3*(k + 1)**2/4
Let f = 33/104 - 443/1560. Let a(c) be the second derivative of 0 + 4*c - 2/5*c**5 - 4*c**3 - 11/6*c**4 - f*c**6 - 9/2*c**2. Let a(y) = 0. What is y?
-3, -1
Let k(w) = -w**2 + 3*w + 57. Let n be k(-6). Find a, given that -2*a**3 + 24 + 50*a**n - 9 + 216*a**2 - 9*a - 108*a = 0.
-5, 1/4
Let b(v) = -v**2 + 14*v - 272. Let o be b(0). Let s = o - -5714/21. Let -4/21*g + s + 2/21*g**2 = 0. What is g?
1
Let a(n) be the second derivative of -21/2*n**3 + 21/10*n**6 + 51/20*n**5 - 6*n**2 + 20*n - 17/4*n**4 + 2/7*n**7 + 2. Suppose a(h) = 0. What is h?
-4, -1, -1/4, 1
Let a = -689 - -774. Suppose 76 = -3*i + a. Factor 10/3*h + 4/3 + 2*h**2 - 2/3*h**4 - 2/3*h**i.
-2*(h - 2)*(h + 1)**3/3
Let v(u) be the second derivative of -u**6/150 - 19*u**5/50 + 89*u**4/60 + 57*u**3/5 - 72*u**2 + u - 1491. Let v(w) = 0. What is w?
-40, -3, 2, 3
Let q(o) be the first derivative of 3*o**4/4 + 295*o**3 + 32412*o**2 - 65712*o + 1146. Factor q(a).
3*(a - 1)*(a + 148)**2
Suppose 80 = -66*z + 476. Let m(d) be the third derivative of 0*d**5 + 1/240*d**z + 0*d**3 + 0*d + 0 - 1/48*d**4 + 18*d**2. Suppose m(p) = 0. What is p?
-1, 0, 1
Factor -17/4*y + 1/4*y**2 + 1/4*y**3 + 15/4.
(y - 3)*(y - 1)*(y + 5)/4
Let d be (-2)/(-3) - (-178)/3 - 3. Let y be 8/40 - d/(-15). Factor -8*u**y + 3261*u - 4*u**5 + 12*u**3 - 3261*u.
-4*u**3*(u - 1)*(u + 3)
Let t(b) = -28*b - 105. Let z be t(-12). Let w be (-11)/(z/(-12)) - (-1)/(-7). Solve 0*p**2 + 0 - w*p**4 + 0*p + 9/7*p**3 = 0 for p.
0, 3
Let o = -6500 + 6504. Let r(l) be the first derivative of 5/2*l**2 - 10/3*l**3 - 5/4*l**o - 3 + 10*l. Factor r(m).
-5*(m - 1)*(m + 1)*(m + 2)
Let t = 1058/1419 - -278/473. Let 2/3*b**3 + 0 + 0*b - t*b**2 = 0. What is b?
0, 2
Let p = -15623 + 15627. Let k(o) be the second derivative of 13*o + 4/55*o**5 + 0 - 5/66*o**p + 1/33*o**3 + 0*o**2 - 4/165*o**6. Factor k(s).
-2*s*(s - 1)*(2*s - 1)**2/11
Factor 624/5*p - 168/5*p**2 - 608/5 + 4/5*p**3.
4*(p - 38)*(p - 2)**2/5
Let u = 2/245 - 4673/2205. Let m = -17/9 - u. Factor 2/9*w + 0 + m*w**3 + 4/9*w**2.
2*w*(w + 1)**2/9
Let a(p) be the third derivative of 2/3*p**3 + 43*p**2 - 2/3*p**4 + 2/5*p**5 + 0 + 2/105*p**7 - 2/15*p**6 + 0*p. Find m such that a(m) = 0.
1
Suppose -11*r + 126 + 72 = 0. Suppose 11*t**3 + r - 2*t**3 - 27*t - 2*t**2 - t**3 - 5*t**3 = 0. Calculate t.
-3, 2/3, 3
Let x = -1657 - -1657. Let k(h) be the third derivative of h**2 - 1/270*h**5 + x*h + 0 - 1/54*h**4 + 1/9*h**3. Determine b so that k(b) = 0.
-3, 1
Let t = -11042/35 + 22189/70. Factor -1/2*a**2 + t - a.
-(a - 1)*(a + 3)/2
Let j be (-4)/11 - ((26 - 8466/231) + 10). Factor -j*t - 12/7 + 4/7*t**2.
2*(t - 2)*(2*t + 3)/7
Determine l so that -107/3 + 1/3*l**3 + 215/3*l - 109/3*l**2 = 0.
1, 107
Determine f, given that -37*f**3 + 8 - 464*f - 136*f**3 + 458*f**2 + 59*f**3 = 0.
1/57, 2
Let s(i) be the second derivative of i**5/110 - i**4/11 - 27*i**3/11 - 130*i**2/11 + 1187*i. Factor s(u).
2*(u - 13)*(u + 2)*(u + 5)/11
Let s(w) be the second derivative of w**4/108 - 7*w**3/18 - 23*w**2/9 - 3*w + 256. Factor s(d).
(d - 23)*(d + 2)/9
Let x(f) be the second derivative of -5*f**8/1344 + f**7/42 - f**6/32 - 79*f**2/2 + 3*f + 18. Let q(c) be the first derivative of x(c). Solve q(k) = 0.
0, 1, 3
Let u = -34 - -36. Solve 195*y**u - 48*y - 36*y**2 - 18*y**4 - 87*y**2 - 3*y**5 - 3*y**3 = 0 for y.
-4, 0, 1
Let s(z) = -5*z**2 - 13*z - 3. Let u(p) be the first derivative of 8*p**3 + 31*p**2 + 14*p - 120. Let h(a) = 14*s(a) + 3*u(a). Factor h(n).
2*n*(n + 2)
Let q(l) be the first derivative of 1/35*l**5 - 8/21*l**3 + 1/21*l**4 - 8/7*l**2 - 33*l + 10. Let m(o) be the first derivative of q(o). Solve m(w) = 0 for w.
-2, -1, 2
Factor -190 - 3379*v**2 - 3374*v**2 + 105*v + 6748*v**2.
-5*(v - 19)*(v - 2)
Let k(o) = -2*o**3 - 8*o**2 + 22*o + 9. Let f be k(-6). Solve 12*g**2 + 11*g**2 + f*g**2 - 118 - 175*g - 41*g**2 = 0 for g.
-2/3, 59
Let a(i) be the second derivative of -i**4/48 + 7*i**3/8 - 45*i**2/4 - 16*i + 1. Let a(d) = 0. Calculate d.
6, 15
Determine l so t