/10
Suppose 0 = 3*k - 3*o - o - 22, -3*o + 3 = k. Let a be k/33 - 1884/(-44). Factor 5 - 78*m**2 - 18*m - 7*m + a*m**2 + 5.
-5*(m + 1)*(7*m - 2)
Factor -5007059 - 5*o**3 - 2146*o + 2870*o**2 + 5006343 - 3*o**3.
-2*(o - 358)*(o - 1)*(4*o + 1)
Let 2/7*i**2 + 547058/7 - 2092/7*i = 0. Calculate i.
523
Let v be (-50306412)/(-351) + 1/(-9). Find s such that 2*s**2 + 5*s**3 + 9169*s - 2*s**3 - 407*s**2 + 9056*s + v - 416698 = 0.
45
Factor 0*p + 0*p**2 + 6/7*p**4 + 0 - 2/7*p**5 + 108/7*p**3.
-2*p**3*(p - 9)*(p + 6)/7
Let f(j) be the first derivative of j**6/36 + 5*j**5/24 + 5*j**4/12 - 4*j**3/3 - 6*j + 119. Let m(w) be the third derivative of f(w). Find d such that m(d) = 0.
-2, -1/2
Let n(i) be the third derivative of 2 + 5/96*i**6 - 1/8*i**5 + 1/168*i**7 + 0*i + 0*i**3 + 0*i**4 + 10*i**2. Solve n(c) = 0 for c.
-6, 0, 1
Let q(o) = 66*o**2 + 11*o - 45. Let c(u) = 428*u**2 + 72*u - 292. Let h = 207 - 239. Let w(b) = h*q(b) + 5*c(b). Factor w(z).
4*(z + 1)*(7*z - 5)
What is c in -1/2*c**2 + 28 + 5*c = 0?
-4, 14
Let t(f) be the first derivative of -4*f**3/27 + 94*f**2/3 + 1144*f/9 + 353. Factor t(k).
-4*(k - 143)*(k + 2)/9
Let o(j) be the first derivative of 0*j**2 + 1/30*j**6 + 14*j - 5 + 1/10*j**5 + 1/12*j**4 + 0*j**3. Let n(r) be the first derivative of o(r). Factor n(x).
x**2*(x + 1)**2
Let f(u) be the first derivative of 0*u - 1/330*u**5 + 13*u**2 + 0*u**3 + 13 - 7/132*u**4. Let r(h) be the second derivative of f(h). Factor r(x).
-2*x*(x + 7)/11
What is i in -970*i**2 - 192 + 972*i**2 + 6*i + 35*i - i = 0?
-24, 4
Let s(c) = -208845*c**3 - 1844*c**2 + 12. Let n(b) = b**3 - 4*b**2 + b + 3. Let a(u) = -4*n(u) + s(u). Factor a(m).
-m*(457*m + 2)**2
Let l(x) be the first derivative of x**9/6804 + x**8/1260 - 2*x**7/945 + 38*x**3/3 + 2*x + 27. Let j(s) be the third derivative of l(s). Factor j(y).
4*y**3*(y - 1)*(y + 4)/9
Let q(p) be the first derivative of -p**4/44 + 7*p**3/33 + 7*p**2/11 - 48*p/11 + 1256. What is h in q(h) = 0?
-3, 2, 8
Let n(i) be the second derivative of 2 + 1/36*i**4 + 4/9*i**3 + 0*i**2 - i - 2/15*i**5 - 1/90*i**6. Find l, given that n(l) = 0.
-8, -1, 0, 1
Let q(g) = g**3 + 6*g**2 + 6*g + 8. Let a be q(-5). Let -294*o - 3*o**a - 111*o**2 + o**3 + 69*o**2 + 259 - 945 = 0. What is o?
-7
Let c(y) be the second derivative of -10*y**2 - 5/48*y**4 + 0 + 164*y - 25/12*y**3. Suppose c(q) = 0. Calculate q.
-8, -2
Let s(w) be the third derivative of w**5/12 - 695*w**4/6 + 2770*w**3/3 - 2*w**2 + 251*w + 1. Solve s(d) = 0.
2, 554
Suppose 0 = -d + 5*z - 23, -5*z = -2*d + 2049 - 2070. Factor 14 - 27/2*w - 1/2*w**d.
-(w - 1)*(w + 28)/2
Let z(i) be the second derivative of -34*i + 15/8*i**2 - 1/32*i**4 - 3/16*i**3 + 2. Factor z(w).
-3*(w - 2)*(w + 5)/8
Suppose -2*x = 5*n + 25, x + 25 = 5*x - 5*n. Factor -c**5 + 5 - 2*c**2 - 2*c**3 + 9*c - 3*c**4 + 2*c**5 + x*c**3 - 8*c**3.
(c - 5)*(c - 1)*(c + 1)**3
Let c = -11109 - -11129. Let h(k) be the second derivative of -c*k - 1/2*k**5 + 0 + 0*k**3 - 5/12*k**4 - 1/6*k**6 + 0*k**2. Determine i so that h(i) = 0.
-1, 0
Let l be (-712 + 722)*(-3 + 332/110). Factor -2/11*h + 4/11 + l*h**3 - 4/11*h**2.
2*(h - 2)*(h - 1)*(h + 1)/11
Let o(a) = a**3 + 41*a**2 + 17*a - 19. Let c be o(-41). Let d = c + 720. Factor 3*b**2 - 4 + 2*b**3 - 4/3*b + 1/3*b**d.
(b - 1)*(b + 2)**2*(b + 3)/3
Let w(d) be the third derivative of -1/260*d**6 + 0*d - 13*d**2 + 17/156*d**4 + 8/39*d**3 - 11/195*d**5 + 0. Suppose w(b) = 0. Calculate b.
-8, -1/3, 1
Let p(j) = -14*j**2 - 1086. Let h(w) = 4*w**2 + w + 361. Let b(a) = -20*h(a) - 6*p(a). Suppose b(y) = 0. What is y?
-11, 16
Let r(u) be the first derivative of -5/22*u**4 - 4/11*u**3 + 0*u + 0*u**2 - 38 - 2/55*u**5. Factor r(i).
-2*i**2*(i + 2)*(i + 3)/11
Let l(r) be the first derivative of 50/3*r**3 - 20*r**2 - 24 - 5/4*r**4 - r**5 + 0*r. Factor l(c).
-5*c*(c - 2)*(c - 1)*(c + 4)
Let c(n) = 3*n**3 - 8*n**2. Let s(g) = 5*g**3 - 13*g**2. Let w be (-190)/(-25) + 2/30*6. Let x(b) = w*c(b) - 5*s(b). Determine k, given that x(k) = 0.
0, 1
Let s be 5/7 + 2 + 78/273. Determine h so that 175*h + 30*h**s + 249*h + 45 + 185*h**2 - 40*h - 84*h = 0.
-3, -1/6
Let c = -2418 + 2425. Let j(l) be the third derivative of c*l**2 - 1/180*l**5 + 1/9*l**3 + 0*l - 1/72*l**4 + 0. Factor j(v).
-(v - 1)*(v + 2)/3
Let i(z) = -z**3 + 45*z**2 - 419*z + 100. Let w be i(32). Let p(u) be the first derivative of -15 + w*u**4 - 8*u**3 - 4*u + 8*u**2 - 4/5*u**5. Factor p(r).
-4*(r - 1)**4
Let u(v) = -322*v**3 + 104*v**2 + 508*v + 226. Let a(x) = -697*x**3 + 209*x**2 + 1015*x + 451. Let h(y) = -6*a(y) + 13*u(y). Factor h(n).
-2*(n - 29)*(n + 4)*(2*n + 1)
Let x(d) be the third derivative of d**8/3360 - d**7/1680 - d**6/360 + 53*d**3/6 + 36*d**2. Let t(r) be the first derivative of x(r). What is v in t(v) = 0?
-1, 0, 2
Let z(j) be the second derivative of -j**8/2184 + j**6/156 - j**4/39 - 21*j**2/2 - 62*j. Let c(o) be the first derivative of z(o). Solve c(v) = 0 for v.
-2, -1, 0, 1, 2
Suppose 4*z - 10 = 2*u, 5*u - 2*u = 3*z - 9. Let a be (3/18)/((-10)/(-15)). Factor 0*k + a*k**z - 1.
(k - 2)*(k + 2)/4
Let f be 0 + 6/(-81)*-3. Let h be 65/(-143) - (-1215)/495. Factor f*w**h + 0 + 2/9*w.
2*w*(w + 1)/9
Let a(f) be the first derivative of -4/35*f**5 + 15 + 4/21*f**3 + 0*f - 1/7*f**4 + 2/7*f**2. Let a(v) = 0. Calculate v.
-1, 0, 1
Let o(f) be the second derivative of -8*f + 5/24*f**4 - 43/12*f**3 - 9/2*f**2 + 0. Find x, given that o(x) = 0.
-2/5, 9
Let b be 0/(2 - 0) + 5822 + -5822. Determine u so that 10/9*u**2 - 2/9*u**4 - 8/9*u**3 + 0*u + b = 0.
-5, 0, 1
Let r(p) be the first derivative of 0*p + 5*p**2 + 95/4*p**4 + 65/3*p**3 + 87 - 35/2*p**6 - 13*p**5. Determine t, given that r(t) = 0.
-1, -1/3, -2/7, 0, 1
Let g = 1 - -47. Let j be (g/66)/((-1)/4*-1). Determine i so that 12/11*i**4 - 28/11*i**3 - 18/11*i - 2/11*i**5 + 4/11 + j*i**2 = 0.
1, 2
Let b be 5 + 85/(-15) + (-12452)/(-30). Let u = 415 - b. Factor 3/5*j**2 + u*j**3 - 6/5*j + 0.
3*j*(j - 1)*(j + 2)/5
Let h(a) be the second derivative of a**5/30 + 7*a**4/9 + 40*a**3/9 + 3*a + 194. Suppose h(s) = 0. Calculate s.
-10, -4, 0
Suppose 0 = r + 26*r - 270. Factor -r*g**2 + 8 + 17 + 4*g**2 + 4*g**2 + g**2.
-(g - 5)*(g + 5)
Let l(u) be the second derivative of -u**4/15 + 3644*u**3/15 - 1659842*u**2/5 - 447*u + 1. Suppose l(z) = 0. What is z?
911
Let q(i) be the third derivative of i**5/210 - 239*i**4/6 - 3347*i**3/21 - i**2 - 2551. Suppose q(d) = 0. Calculate d.
-1, 3347
Let m(i) be the third derivative of -i**6/300 + 2*i**5/25 + i**4/60 - 44*i**3/5 - 142*i**2 - 6*i + 2. Factor m(z).
-2*(z - 11)*(z - 4)*(z + 3)/5
Suppose -3*c = -2*r - 2, -3*r + 7*r = -c + 24. Let p(b) = -b**2 - 2*b + 24. Let q be p(c). Factor q + 0*z - 2/3*z**2 - 2/3*z**3 + 2/3*z**4 + 2/3*z**5.
2*z**2*(z - 1)*(z + 1)**2/3
Suppose 99*z - 102*z = 5*j - 47, 4*z = -2*j + 44. Let a(c) be the second derivative of 35*c + 3/8*c**j + 0*c**2 - 3/40*c**5 - 1/2*c**3 + 0. Factor a(q).
-3*q*(q - 2)*(q - 1)/2
Let x(z) = -z**3 - 90*z**2 - 52*z - 4678. Let a be x(-90). Solve -a*i + 0 + 3/2*i**4 + 6*i**2 - 11/2*i**3 = 0.
0, 2/3, 1, 2
Let d(b) = -b**2 - b + 1. Suppose 25*l - 2 + 27 = 0. Let v(u) = 3*u**2 - 8*u - 1. Let p(a) = l*v(a) - 6*d(a). What is i in p(i) = 0?
-5, 1/3
Let m = -40 - -43. Suppose g + 11 = m*d, -4*g + g - 23 = -4*d. Factor 0 + 0*p + 1/8*p**3 + 0*p**d.
p**3/8
Let c = 2216/121 - 2128/121. Factor 0 + 2/11*h**3 + c*h + 8/11*h**2.
2*h*(h + 2)**2/11
Let s(k) be the third derivative of -k**6/180 - k**5/6 - 59*k**4/36 - 5*k**3 - 2*k**2 - 850*k. Solve s(n) = 0.
-9, -5, -1
Let q be (-4 + -1)*(-4)/20*3. Suppose 12 - 52*d**3 - 61*d**3 - 15*d**4 - 46*d**3 + 180*d**3 + 3*d**5 + q*d**2 - 24*d = 0. What is d?
-1, 1, 2
Let -783*s**2 + 787*s**2 - 40 + 3*s + 9*s = 0. What is s?
-5, 2
Suppose -w + 3 + 0 = 0. Suppose -t - 28 = -5*m, 2*m - 163 = 5*t - 161. Factor 23*n**2 + 2 - w*n - 41*n**2 + n**3 + 18*n**t.
(n - 1)**2*(n + 2)
Let m(n) be the second derivative of -n**4/9 - 3182*n**3/9 + 2124*n**2 - 13396*n. Let m(a) = 0. What is a?
-1593, 2
Let j(c) be the first derivative of -c**6/240 + 7*c**5/120 - c**4/6 - 4*c**3/3 - 33*c**2/2 - c - 154. Let v(m) be the second derivative of j(m). Solve v(t) = 0.
-1, 4
Let v(u) be the first derivative of -5*u**3/3 - 285*u**2 + 575*u - 964. Factor v(f).
-5*(f - 1)*(f + 115)
Factor -1/3*i**4 - 192*i**3