 - 16*i + 16. Let b(u) = -2*u**5 - u**3. Let n(l) = -5*b(l) + 5*c(l). Factor n(q).
5*(q - 2)**4*(q + 1)
Factor 3*y**2 + 5441596 - 9912*y + 0*y**2 + 3340663 - 594947.
3*(y - 1652)**2
Let g be (25/(-10))/(-11 + (-39)/(-4)). Find x such that -15*x**5 - 51*x**4 - 318/5*x**3 - 174/5*x**g - 3/5 - 39/5*x = 0.
-1, -1/5
Let z(c) be the first derivative of -c**8/1680 - 3*c**7/560 - c**6/180 + 76*c**3/3 + 35. Let i(w) be the third derivative of z(w). Factor i(g).
-g**2*(g + 4)*(2*g + 1)/2
Let 0 + 347/2*n - 1/2*n**2 = 0. Calculate n.
0, 347
Let y = 2985 - 125369/42. Let h(w) be the third derivative of 3*w**2 + 0*w + 0 - y*w**4 + 4/21*w**3 - 1/105*w**5. Find s such that h(s) = 0.
-2, 1
Let l be 16/28 - (-7)/((-1176)/40). Let r(u) be the second derivative of -1/20*u**5 + 1/6*u**3 + 2*u**2 + 0 - l*u**4 - 10*u. Let r(t) = 0. Calculate t.
-4, -1, 1
Let t(c) be the third derivative of 0*c**3 + 2*c**2 + 1/210*c**5 + 1/84*c**4 + 0*c + 9. What is l in t(l) = 0?
-1, 0
Let o(c) = 2*c**3 - 76*c**2 - 333*c - 124. Let i be o(42). Factor 8 - 1/2*p**i - 15/2*p.
-(p - 1)*(p + 16)/2
Let q(r) = 2118*r + 44478. Let m be q(-21). Factor 2*u**3 + 2/7*u**4 + 32/7*u**2 + m + 24/7*u.
2*u*(u + 2)**2*(u + 3)/7
Suppose 59 - 32 = -3*i + 36. Let u = 1523/5 + -304. Suppose i*j - u*j**2 + 18/5 = 0. Calculate j.
-1, 6
Let t(f) be the first derivative of f**4/72 + f**3/6 - 7*f**2/12 - 167*f - 249. Let n(h) be the first derivative of t(h). Suppose n(a) = 0. What is a?
-7, 1
Let q(w) be the second derivative of 2*w**7/21 + 2*w**6/5 - 13*w**5/5 - 11*w**4/3 + 16*w**3 + 40*w**2 + 1736*w. What is i in q(i) = 0?
-5, -1, 2
Let j(a) be the second derivative of 2*a**6/105 + 51*a**5/35 + 14*a**4/3 + 2*a - 8083. Solve j(d) = 0 for d.
-49, -2, 0
Let m = 6233/4284 + -74/51. Let d(g) be the second derivative of m*g**7 + 0 + 1/120*g**5 - 1/18*g**3 + 1/24*g**4 - 1/60*g**6 + 0*g**2 + 4*g. Factor d(s).
s*(s - 2)*(s - 1)**2*(s + 1)/6
Let j(i) = -5*i**2 + 312*i - 598. Let v(g) = 10*g**2 - 625*g + 1195. Let d(n) = 5*j(n) + 2*v(n). Find h, given that d(h) = 0.
2, 60
Let r be (-7)/(-35) - (134/674 - 0). Let j = r + 33674/21905. Factor 2/13*v**2 + j*v + 50/13.
2*(v + 5)**2/13
Factor -1/6*t**2 - 87/2*t - 259/3.
-(t + 2)*(t + 259)/6
Suppose -22*z + 12*z + 54960 = 0. Factor 2*f**2 + 3*f**3 + 2*f**2 - 5493*f + z*f - 8 - 10 + 8*f**2.
3*(f - 1)*(f + 2)*(f + 3)
Let a(s) = 37*s - 1. Let y be a(3). Let b(w) = 4*w**2 - 18*w - 37. Let o be b(9). Find f such that -25*f**2 - o*f + y*f + 85*f - 49 = 0.
7/5
Let t(s) be the first derivative of s**5/45 - s**4/2 - 44*s**3/9 + 11*s**2 + s - 44. Let p(b) be the second derivative of t(b). Factor p(y).
4*(y - 11)*(y + 2)/3
Find z, given that 3514*z**3 - 9261147*z**2 - 1/2*z**4 + 10847890186*z - 9529871528401/2 = 0.
1757
Let c(j) = 2*j**2 - 1597*j + 1598. Let l be c(1). Factor 3/4*t + 0*t**2 - 1/2 - 1/4*t**l.
-(t - 1)**2*(t + 2)/4
Let k(b) be the second derivative of -b**4/54 - 40*b**3/27 - 400*b**2/9 + 26*b - 6. Suppose k(h) = 0. What is h?
-20
Let c be 6/(-18) + ((-80)/9)/(-16). Solve -c + 0*g + 0*g**3 - 2/9*g**4 + 4/9*g**2 = 0 for g.
-1, 1
Let d(p) = p**2 + 3*p - 5. Let h be d(-5). Find v such that 29*v - h*v**4 + v**4 + 27*v - 48*v + 12*v**2 = 0.
-1, 0, 2
Suppose 17*m + 241 - 292 = 0. Determine b, given that -65*b**4 + 0*b**2 + 5*b - 4580*b**m - 30*b**5 + 5*b**2 + 4545*b**3 = 0.
-1, -1/2, 0, 1/3
Let s(g) be the second derivative of -1/5*g**5 + 3 + 0*g**2 + 19*g - 4/3*g**4 - 2*g**3. Suppose s(b) = 0. What is b?
-3, -1, 0
Let g(k) = -36*k**2 + k - 1. Let v be g(1). Let h(r) = r**3 + 37*r**2 + 34*r - 72. Let d be h(v). Find b, given that -5/3*b**3 + 4/3*b - 8/3*b**2 + d = 0.
-2, 0, 2/5
Suppose 0 = 2*h - 5*a - 29, -2*h + 4850 = 3*a + 4861. Find c such that 17/2*c - 1/2*c**h + 19 = 0.
-2, 19
Let y(h) be the first derivative of 4*h**3/33 - 73*h**2/11 + 72*h/11 - 11489. Factor y(s).
2*(s - 36)*(2*s - 1)/11
Suppose 8*t = 11*t - 2*f - 2216, -5*f - 2201 = -3*t. Let l = t + -740. Factor 0 - 1/2*r**l - 1/4*r.
-r*(2*r + 1)/4
Factor -56*r**3 - 22*r**3 + 2520 + 10632*r + 2*r**3 + 15650*r**2 - 49*r**3 + 1948*r.
-5*(r - 126)*(5*r + 2)**2
Let y = -178 + 180. Factor -y*p**2 - 12*p + 9*p**2 - 8 - 3*p**2 + 16.
4*(p - 2)*(p - 1)
Suppose -3*c = -3*i + 21, 15*c - 19 = 10*c - i. Factor 64/5 - 16/5*r + 1/5*r**c.
(r - 8)**2/5
Let w(b) = -6*b**2 - 235*b - 36. Let h(d) = -2*d**2 + 60*d - 327. Let y be h(6). Let m be w(y). Factor 126/5*v + 2/5*v**m + 98/5 + 6*v**2.
2*(v + 1)*(v + 7)**2/5
Suppose 3 = -4*d - 5*t, 5*d = -3*t + 3 + 3. Let u be (-7)/((-42)/36)*d/99. Factor -6/11 + 4/11*a + u*a**2.
2*(a - 1)*(a + 3)/11
Let r(p) = p**3 - 4*p**2 - 15*p - 40. Let q be r(7). Suppose -22 = 3*b - 5*i - q, -2*b + i = 4. What is y in -8/5*y**4 + b + 18/5*y**3 + 0*y - 4/5*y**2 = 0?
0, 1/4, 2
Factor -282*r**3 - 375 + 61*r**2 - 840*r + 186*r**3 - 550*r**2 - 3*r**4 - 69*r**2.
-3*(r + 1)**2*(r + 5)*(r + 25)
Let o = -115 - -119. Let h(v) = 3*v**4 + 84*v**3 - 3178*v**2 + 48664*v - 279841. Let s(p) = -p**4 + 2*p**3 + p**2 + p. Let t(q) = o*s(q) + h(q). Solve t(d) = 0.
23
Determine n so that -48/7 - 12648/7*n - 52272/7*n**4 + 417384/7*n**3 - 830019/7*n**2 = 0.
-1/132, 4
Let j(w) be the second derivative of 1/18*w**3 + 1/4*w**2 - 7*w - 1/18*w**4 + 1/180*w**6 - 1/60*w**5 + 2. Factor j(c).
(c - 3)*(c - 1)*(c + 1)**2/6
Let f(x) be the second derivative of 3*x**5/22 + 7*x**4/11 - 4*x**3/11 - 86*x**2 - 140*x. Let i(a) be the first derivative of f(a). Suppose i(o) = 0. What is o?
-2, 2/15
Let n(o) be the second derivative of -8*o**6/57 - 3*o**5/95 + 13*o**4/38 - o**3/57 - 6*o**2/19 - 295*o. Let n(x) = 0. Calculate x.
-1, -2/5, 1/2, 3/4
Suppose -4*l + 30 = -18. Let t be (l/18)/(0 - 4/(-18)). Find n such that -2*n + 16*n**2 - 9*n - n**3 - t*n**3 + 8 - 9*n = 0.
1, 2
Let m(v) = 5*v**4 + 13*v**3 + 8*v**2 - 3*v. Let n = 473 + -472. Let h(k) = -k**3 - k**2 + k. Let z(w) = n*m(w) + 3*h(w). Suppose z(a) = 0. What is a?
-1, 0
Factor 142/5*z - 28 - 2/5*z**2.
-2*(z - 70)*(z - 1)/5
Determine x so that 97/2*x**4 - 201*x**3 + 103*x**2 + 401/2*x + 1/2*x**5 - 303/2 = 0.
-101, -1, 1, 3
Let f(j) be the third derivative of -j**8/112 + j**7/70 + 17*j**6/40 + 19*j**5/20 - 2*j**4 - 10*j**3 + 2922*j**2. Solve f(x) = 0 for x.
-2, -1, 1, 5
Let i(m) be the first derivative of m**6/21 - 8*m**5/35 - 3*m**4/14 + 20*m**3/21 + 8*m**2/7 - 164. Suppose i(d) = 0. What is d?
-1, 0, 2, 4
Let h(k) be the second derivative of -k**5/100 - 7*k**4/20 - 49*k**3/10 + 171*k**2/2 - 2*k - 19. Let i(t) be the first derivative of h(t). Factor i(y).
-3*(y + 7)**2/5
Suppose -5*l + 4074*a + 6 = 4075*a, -4*l = 3*a + 15. Determine n, given that -289/4*n + 17/2*n**2 - 1/4*n**l + 0 = 0.
0, 17
Let z be 2595782/3234 - (-2)/33. Let b = 805 - z. Let 2/7 + 57/7*f**2 - 8*f**3 - 19/7*f + b*f**4 = 0. Calculate f.
1/4, 1, 2
Find o, given that -224/3*o - 2/3*o**4 - 28/3*o**3 - 130/3*o**2 - 40 = 0.
-6, -5, -2, -1
Let v = 28 - 8. Let i be v/(-150) - (-188)/60. Factor 0*c**2 + 0*c**i - 1/6*c**4 + 0*c + 0.
-c**4/6
Let p(n) = 13*n**2 - 65*n + 5. Let k = -291 + 296. Let f be p(k). Factor -3/10*x**3 + 1/10*x**f + 0 - 1/5*x**2 + 0*x**4 + 0*x.
x**2*(x - 2)*(x + 1)**2/10
Let c(u) = -55*u**2 - 732*u + 135424. Let t(r) = -41*r**2 - 733*r + 135424. Let z(d) = 3*c(d) - 4*t(d). Determine q, given that z(q) = 0.
368
Let g = -4336 - -8673/2. Let a(k) be the first derivative of 0*k**5 + g*k**4 + 0*k**2 + 0*k - 1/3*k**6 + 0*k**3 + 6. What is s in a(s) = 0?
-1, 0, 1
Suppose 114 = 11*p + 136. Let d(v) = -v**2 - 2*v - 1. Let r(g) be the second derivative of g**3/3 + g**2 - g. Let c(t) = p*d(t) - 3*r(t). Factor c(m).
2*(m - 2)*(m + 1)
Let o = 189927 - 949591/5. Solve -2/5*z**2 - 18/5*z + o = 0 for z.
-11, 2
Let a(m) = -101*m**2 - 483*m + 476. Let l(z) = 228*z**2 + 966*z - 951. Let u(q) = 9*a(q) + 4*l(q). Suppose u(i) = 0. Calculate i.
1, 160
Let h(k) = -936*k**2 + 1800*k + 8. Let m(z) = z**3 - 932*z**2 + 1806*z + 6. Let r(i) = -3*h(i) + 4*m(i). Factor r(p).
4*p*(p - 228)*(p - 2)
Let m(g) be the second derivative of g**4/6 + g**3/3 - g**2 + 18*g. Let o be m(1). Factor 5*x**o + 9*x + 16 - 16 + x.
5*x*(x + 2)
Let p(d) be the first derivative of 4*d**5/35 + 928*d**4/7 + 861184*d**3/21 + 1511. Factor p(g).
4*g**2*(g + 464)**2/7
Suppose -5*g + 143 = 113. Let m be (16/g)/(((-16)/12)/(-2)). Factor -4*l**5 - 7*l**m - 9*l**4 + 214*l*