69075)/(-1375) - ((-2)/11)/(11/(-11)). Factor -3/5*l**4 - 9522/5*l**2 - 146004/5*l - a - 276/5*l**3.
-3*(l + 23)**4/5
Let b(c) be the first derivative of -153 - 5/4*c**4 - 5*c**3 + 15*c + 5/2*c**2. Factor b(d).
-5*(d - 1)*(d + 1)*(d + 3)
Let i = -40458 + 40461. Let a(s) be the first derivative of -16/3*s**i - 22*s**2 + s**4 - 24*s + 24. Solve a(v) = 0.
-1, 6
Suppose 2*b - 8 = -f, 4*f + 0 - 22 = -3*b. Let a be (5 + (-231)/44)*-1. Let -1/2 - 5/4*g + a*g**3 + 1/4*g**f - 3/4*g**2 = 0. Calculate g.
-1, 2
Factor -9/4*r**2 - 4900 + 210*r.
-(3*r - 140)**2/4
Let a = -333 - -338. Suppose 0 = -5*v + a, 10*n + v = 5*n + 26. Factor 1/3*h**2 + h**4 + 1/3*h**n + h**3 + 0*h + 0.
h**2*(h + 1)**3/3
Let p(i) = -140*i**3 - 2584*i**2 - 41708*i - 128336. Let h(c) = -13*c**3 - 235*c**2 - 3792*c - 11667. Let g(j) = -32*h(j) + 3*p(j). What is s in g(s) = 0?
-27, -4
Let j(w) be the second derivative of -1/150*w**5 - 1/12*w**4 - 5*w + 0 + 1/300*w**6 - 7*w**2 - 1/5*w**3. Let r(o) be the first derivative of j(o). Factor r(v).
2*(v - 3)*(v + 1)**2/5
Factor 1/2*b**2 + 75625/2 - 275*b.
(b - 275)**2/2
Let z(s) be the first derivative of 0*s + 48*s**3 - 3/4*s**4 + 95 - 864*s**2. Determine r so that z(r) = 0.
0, 24
Factor -8281 + 26649 - 6550 + 2625*n + 5*n**2 - 6588.
5*(n + 2)*(n + 523)
Let z(a) be the second derivative of -a**5/4 - 20*a**4/3 - 70*a**3/3 + 21*a + 55. Solve z(m) = 0 for m.
-14, -2, 0
Let z be (-32)/(-48)*((-858)/77)/(-13). Let -2/7*o**3 + 6/7*o + z + 0*o**2 = 0. Calculate o.
-1, 2
Let o(f) be the second derivative of -f**4/3 + 12*f**3 - 130*f**2 + 974*f. Solve o(i) = 0.
5, 13
Let a = -39629/4 + 9908. Let t(s) be the second derivative of -s**3 + 0 + 22*s + a*s**4 - 3/10*s**5 + 3/4*s**2 + 1/20*s**6. Determine y, given that t(y) = 0.
1
Let p = 290/7 + -1111/28. Let z(v) = -v**3 - 201*v**2 + 602*v - 2038. Let x be z(-204). Factor -1/4*o**x + p - 3/2*o.
-(o - 1)*(o + 7)/4
Let m = -1888011 - -15104089/8. Solve m*p**5 + 0*p - 1/8*p**4 - 1/8*p**3 + 1/8*p**2 + 0 = 0.
-1, 0, 1
Let d = -473 - -476. Suppose -41*q + 12 = d*b - 44*q, 4*q + 21 = 5*b. Factor 32/5 - 2*u**4 + 2/5*u**b + 16*u + 10*u**2 - 2*u**3.
2*(u - 4)**2*(u + 1)**3/5
Let q(x) = -3*x**3 - 21*x**2 + 19*x + 40. Let c(t) = 4*t**3 - t. Let z(p) = 2*c(p) + 2*q(p). Let z(v) = 0. Calculate v.
-1, 2, 20
Let w(d) be the second derivative of 2*d + 1/48*d**4 + 0*d**2 - 1/24*d**3 + 8. Factor w(z).
z*(z - 1)/4
Factor 2/7*i**2 + 92*i + 7406.
2*(i + 161)**2/7
Let a(c) = c**3 + c**2 + c - 1. Let f(q) = 7*q**4 - 98*q**3 + 189*q**2 - 85*q - 31. Let n(z) = -45*a(z) - 5*f(z). Determine y, given that n(y) = 0.
-2/7, 1, 2, 10
Let p(k) = 58*k**3 + 114*k**2 + 56*k - 16. Let z(j) = -11*j**3 - 22*j**2 - 11*j + 3. Let o(x) = -3*p(x) - 16*z(x). Determine n, given that o(n) = 0.
-4, -1, 0
Let p(v) be the first derivative of 2*v**3/21 - 33*v**2/7 + 232*v/7 + 2966. What is m in p(m) = 0?
4, 29
Let r be (-1672)/114*(-140)/616. Let 0 + 2/3*i**3 - r*i - 8/3*i**2 = 0. What is i?
-1, 0, 5
Let i(y) = -15*y + 78. Let g be i(5). What is x in 20*x**2 + 120 - 36*x**2 - 44*x - 8*x**3 + 12*x**g = 0?
-3, 2, 5
Let n = 216633/433286 + 5/216643. Factor -3025/2 - n*x**2 + 55*x.
-(x - 55)**2/2
Factor 349*r**2 + 1 + 875*r**5 + 368*r**4 + 5 + 77*r - 811*r**5 - 279*r**3 + 915*r**3.
(r + 2)*(r + 3)*(4*r + 1)**3
Let y = 62831/27 + -2327. Let s(m) be the second derivative of 0*m**3 - y*m**4 + 0*m**2 - 2/45*m**6 + 0 - 1/9*m**5 - 4*m. Factor s(p).
-4*p**2*(p + 1)*(3*p + 2)/9
Let i(x) = x + 1. Let o = 450 + -454. Let s(a) = 2*a**2 - 8*a + 22. Let u(y) = o*i(y) + s(y). Let u(c) = 0. What is c?
3
Let a = 503321/5 - 100987. Let l = 324 + a. Factor 3/5 - l*z + 3/5*z**2.
3*(z - 1)**2/5
Let p(u) = u**3 - 9*u**2 + 20*u - 10. Let d be p(6). Let n(t) be the first derivative of 1/3*t**3 - 11 + 25*t - 5*t**d. Solve n(j) = 0 for j.
5
Let r be (((-7)/4)/(-7))/50. Let v = r + 149/200. Factor 3/2*o**2 - 3/2*o**3 - v*o**5 + 3/4 + 9/4*o - 9/4*o**4.
-3*(o - 1)*(o + 1)**4/4
Suppose -327*t + 2*t**2 - 576*t + 25*t + 18*t = 0. What is t?
0, 430
Let x = -241 - -245. Factor v - 41*v**x + 4*v**2 + 39*v**4 - v - 2*v**3.
-2*v**2*(v - 1)*(v + 2)
Let w be (39/((-6786)/145))/(70/(-8)). Let n(b) be the first derivative of w*b**3 - 11 + 9/7*b**2 + 16/7*b. Factor n(k).
2*(k + 1)*(k + 8)/7
Let b be -8*19/228 - 136/(-51). Factor 27/5 - 18/5*g + 3/5*g**b.
3*(g - 3)**2/5
Let u = 182 + -182. Let q(i) be the first derivative of -23 + 5/2*i**4 + 0*i**2 + 5/3*i**3 + u*i + i**5. Factor q(d).
5*d**2*(d + 1)**2
Suppose -1507*p = -1515*p + 2976. Let a be (p/36 + -10)*(-6)/(-4). Factor -1/2*q + 0*q**2 + a*q**3 + 0.
q*(q - 1)*(q + 1)/2
Factor 3/4*j**4 + 0 - 27/4*j**2 + 6*j**3 + 0*j.
3*j**2*(j - 1)*(j + 9)/4
Suppose -8*b**2 - 124/5*b - 4/5*b**3 - 24 = 0. Calculate b.
-5, -3, -2
Suppose 84*j + 1/2*j**4 + 21/4*j**3 - 27 - 251/4*j**2 = 0. Calculate j.
-18, 1/2, 1, 6
Let r(g) be the second derivative of g**5/70 - 9*g**4/14 + 8*g**3 + 28*g**2 - 10*g - 92. Determine p so that r(p) = 0.
-1, 14
Suppose 0 = -519*v + 920 + 3232. Determine q, given that -v*q - 6*q**2 + 40/3 + 2/3*q**3 = 0.
-2, 1, 10
Suppose 18 = 63*n - 54*n. Let o be 104/63 - (n + (-80)/45). What is y in 8/7 + 2/7*y**2 + o*y = 0?
-4, -1
Let f(y) be the second derivative of y**6/105 - 9*y**5/35 + 17*y**4/14 + 10*y**3/3 - 663*y + 3. Factor f(c).
2*c*(c - 14)*(c - 5)*(c + 1)/7
Let l be (-3 + 2)*45/(-13500). Let o(j) be the third derivative of -l*j**6 + 1/75*j**5 + 0*j + 0*j**4 + 0*j**3 - 17*j**2 + 0. Factor o(v).
-2*v**2*(v - 2)/5
Suppose 9*o = 18, -4*f = -0*f + 3*o - 4046. Let t = f + -4037/4. Factor -t*r**3 + 3/4*r + 9/4 - 9/4*r**2.
-3*(r - 1)*(r + 1)*(r + 3)/4
Let m be ((-3)/(-30))/(18/3645). Let h = m + -227/12. Factor 1/3*f**2 + h*f + 1.
(f + 1)*(f + 3)/3
Let c be ((3 + 1)*-1)/(((-12656)/(-294))/(-113)). Factor -9 - 17/2*b**3 + c*b + 3/2*b**4 + 19/2*b**2.
(b - 3)**2*(b + 1)*(3*b - 2)/2
Factor -3/2*c**3 - 80*c + 24 + 49/2*c**2.
-(c - 12)*(c - 4)*(3*c - 1)/2
Let u = -270 + 258. Let f be (u/15)/((-33)/(-5) + -7). Factor 2/9*o**f - 8/9 - 2/3*o.
2*(o - 4)*(o + 1)/9
Suppose -88 = -252*p + 230*p. Let d(t) be the third derivative of 0 + 1/540*t**5 - 1/54*t**p - 8*t**2 + 2/27*t**3 + 0*t. Factor d(j).
(j - 2)**2/9
Suppose 6*d - 10*d - 3*f + 18 = 0, 3*d + 3*f - 12 = 0. Factor 3*z**3 - d - 1 - 6*z**2 - 39*z - 23.
3*(z - 5)*(z + 1)*(z + 2)
Let v be (2810/176 - -2) + (-363)/968. Let c = v - 144/11. Solve 3/2*u**4 + 0 - 9/2*u**3 + c*u - 3/2*u**2 = 0.
-1, 0, 1, 3
Let x = -30195 + 30243. Let w(g) be the second derivative of 3*g**4 + 1/30*g**6 + 3/5*g**5 + 0*g**3 + x*g + 0*g**2 + 0. Solve w(o) = 0 for o.
-6, 0
Let b(d) be the first derivative of 0*d**4 + 8/5*d**5 - 22/3*d**3 + 46 - 4*d - 9*d**2. Solve b(m) = 0 for m.
-1, -1/2, 2
Let r(d) be the third derivative of d**6/1800 - d**5/100 - 7*d**4/120 - 11*d**3/3 + 4*d**2 + 3. Let j(o) be the first derivative of r(o). Factor j(k).
(k - 7)*(k + 1)/5
Suppose -25*k - 2*k + 116 = 2*k. Let n(p) be the third derivative of 35*p**2 + 0 + 1/30*p**6 + 1/30*p**5 + 0*p**k + 0*p + 0*p**3 + 1/105*p**7. Factor n(z).
2*z**2*(z + 1)**2
Find d such that 679 + 42*d**2 + 92*d - 335 - 344 - 2*d**3 = 0.
-2, 0, 23
Factor 405*w**2 - 709/7*w**3 - 2832/7*w - 4/7.
-(w - 2)**2*(709*w + 1)/7
Let s = 496 + -484. Let z be 4/s*0 - 40/(-25). Determine a so that z*a - 6/5 - 2/5*a**2 = 0.
1, 3
Suppose 28*s = 191 + 677. Suppose s = -6*r + 43. Factor -3*w**4 + 0 + 0*w + 1/2*w**5 - 4*w**r + 6*w**3.
w**2*(w - 2)**3/2
Solve -35/3*q + 32 + 1/3*q**2 = 0 for q.
3, 32
Let x(j) be the first derivative of -3*j**4/4 - j**3 + 18*j**2 - 4738. Find d such that x(d) = 0.
-4, 0, 3
Let s(a) = -2*a + 115*a**2 - 116*a**2 - 4*a - 6. Let p be s(-4). Let 2/5*r + 3/5*r**3 - r**p + 1/5*r**4 + 0 - 1/5*r**5 = 0. What is r?
-2, 0, 1
Let k(u) = -u**3 - 4*u**2 + 22*u + 9. Let h(y) = y**3 - 8*y**2 - 11*y + 11. Let d be h(9). Let m be k(d). Factor 5*o**2 + 2*o**4 + 3*o**4 - 21*o**m + 11*o**2.
5*o**2*(o - 1)*(o + 1)
Suppose -400352*m + 400323*m + 0 + 0 = 0. Factor -1/5*v**3 + m*v + 0 - 8/5*v**2.
-v**2*(v + 8)/5
Determine h, given that 1164*h**2 - 2443*h**2 + 6*h + 1204*h**2 = 0.
0, 2/25
Let a(n) be the second derivative of 2*n**6/15 + 3*n**5 - 73*n**4/3 + 38*n**3 + 5588*n. Solve a(v) = 0 for v.
-19, 0, 1, 3
Suppose -65*g = 42*g - 321. Let x be (2 - g) + 13 + 160/(-15). Factor -16/5*y**2 - 