third derivative of l**7/210 + 11*l**6/30 + 17*l**5/12 + 7*l**4/4 + 7469*l**2. Suppose n(a) = 0. Calculate a.
-42, -1, 0
Let y be 1/(-2)*76/2128*-42. Let y*u**3 + 0 + 0*u + 1/4*u**4 + 1/2*u**2 = 0. Calculate u.
-2, -1, 0
Suppose -4*r + 5 = -c, -5*c = r - 22 + 5. Factor 0*t + 24 + 36*t**r - 12*t - 69*t**2 - 8*t + 29*t**2.
-4*(t - 1)*(t + 6)
Let n(v) be the first derivative of v**6/3 + 76*v**5/5 - 3*v**4/2 - 224*v**3/3 + 76*v**2 + 2319. Let n(b) = 0. Calculate b.
-38, -2, 0, 1
Let n(g) = -3*g**2 + 2904*g - 714436. Let b(c) = -9*c**2 + 8718*c - 2143307. Let h(t) = 4*b(t) - 11*n(t). Factor h(i).
-3*(i - 488)**2
Let k(j) = -3*j**3 + j**2. Let w be k(-1). Let d be (-27)/(-54)*(1 + 3). Find b such that 3 - 1 - 2*b**2 + w*b - 6 + b**d = 0.
2
Let l be (-45)/9*(-6 + 8 - (-15)/(-5)). Factor 3/2*p**l + 3/2*p**4 + 3*p**2 - 9/2 + 15/2*p - 9*p**3.
3*(p - 1)**3*(p + 1)*(p + 3)/2
Let n be 4/30*(-2115)/(-1128)*5. Let -5/2 - 35/4*z - n*z**4 - 45/4*z**2 - 25/4*z**3 = 0. Calculate z.
-2, -1
Let k be (-3 + -1)/((-4)/9). Factor 3 + k + 7*n**2 + 22*n - 3*n**2 + 2*n**2.
2*(n + 3)*(3*n + 2)
Suppose 0 = -1861*v + 847 + 4004 - 1129. Solve -2*x - 31/3*x**v + 0 - 37/3*x**3 + 7/3*x**5 - 5/3*x**4 = 0 for x.
-1, -2/7, 0, 3
Let o(k) be the first derivative of -k**3 - 729*k**2/2 + 688. Determine z so that o(z) = 0.
-243, 0
Let a(y) = -y**3 - 28*y**2 - 68*y - 90. Let w be a(-27). Let n = 1019 - w. Let -16/3*k + 4*k**4 - 4/3 + 16/3*k**3 - 8/3*k**n = 0. What is k?
-1, -1/3, 1
Let s(v) be the third derivative of v**6/24 - 65*v**4/24 - 10*v**3 - 852*v**2 + 1. Factor s(c).
5*(c - 4)*(c + 1)*(c + 3)
Suppose 0 = -3*q + 149 - 2. Let t = 102 - q. Let -3*c**4 + t*c**3 + 3*c**2 - 53*c**3 = 0. Calculate c.
-1, 0, 1
Suppose -7*j + 84 = 154. Let x be ((-3)/(-54))/(j/(-150)). Factor -1/3*f + 1/6*f**4 + 0 - 2/3*f**3 + x*f**2.
f*(f - 2)*(f - 1)**2/6
Let d(w) be the first derivative of w**3/3 - 9*w**2/2 + 3*w - 2. Let b be d(9). Suppose 3*u + u**3 - b*u**2 - 1 - u + u = 0. Calculate u.
1
Let k(s) be the first derivative of -2/15*s**3 + 18 - 2/5*s + 2/5*s**2. Factor k(w).
-2*(w - 1)**2/5
Let j(o) = 2*o**3 - 63*o**2 + 5*o - 7. Let p be 6/4*70/(-5)*1. Let l(y) = y**3 + y**2 + y + 1. Let r(a) = p*l(a) - 3*j(a). Factor r(n).
-3*n*(n - 6)*(9*n - 2)
Let h = 76456 - 76454. Let g = 689/2 - 338. Let -g*r**h - 1 + 15/2*r = 0. What is r?
2/13, 1
Factor -800/3 - 1208/9*k - 4/9*k**2.
-4*(k + 2)*(k + 300)/9
Determine f, given that 9/4*f**2 - 1/4*f**3 + 0 - 9/2*f = 0.
0, 3, 6
Let r = 67/7 + -127/14. Let x(c) be the third derivative of 16*c**2 - 1/20*c**5 - 1/4*c**4 - r*c**3 + 0 + 0*c. Factor x(z).
-3*(z + 1)**2
Let w(l) be the first derivative of 3*l**3/4 + 111*l**2/2 + 1369*l - 1191. Factor w(f).
(3*f + 74)**2/4
Suppose 2*o = 5*o - 6. Suppose 4*h**2 - 21 + 9 - 3*h + 0*h + 3*h**3 + 8*h**o = 0. Calculate h.
-4, -1, 1
Let i(d) be the second derivative of -d**5/15 + 344*d**4/9 + 2*d**3/9 - 688*d**2/3 + d - 11610. What is b in i(b) = 0?
-1, 1, 344
Let t(k) be the first derivative of -3*k + 39/4*k**2 - 46 - 11/2*k**3. Factor t(f).
-3*(f - 1)*(11*f - 2)/2
Let w(s) = 119*s**2 + 5452*s + 63845. Let z(p) = 237*p**2 + 10871*p + 127690. Let y(b) = 13*w(b) - 6*z(b). Factor y(c).
5*(5*c + 113)**2
Let a = -256 + 280. Suppose 0 = -3*t + 4*t - 2. Suppose 12*z**3 + a*z + 0*z**2 + t*z**4 + 14 + 26*z**2 - 6 = 0. What is z?
-2, -1
Let 27929*x + 99 + 665*x**3 + 3977 + 8697*x**2 + 10434*x + 17*x**4 + 318 = 0. Calculate x.
-13, -2/17
Let v(i) be the third derivative of -i**7/735 + i**6/21 + 15*i**5/7 + 625*i**4/21 + 625*i**3/3 + 50*i**2 - i. Factor v(a).
-2*(a - 35)*(a + 5)**3/7
Factor -147023 - 4*x**3 - x**3 - 90*x**2 - 325*x + 147443.
-5*(x - 1)*(x + 7)*(x + 12)
Let k(h) be the second derivative of -7/4*h**4 + 3*h**3 - 9/80*h**6 + 0 + 1/112*h**7 - 3*h**2 + 38*h + 3/5*h**5. Factor k(v).
3*(v - 2)**4*(v - 1)/8
Let v(r) be the first derivative of -r**3/3 - 3*r**2/8 + 517*r/4 + 9686. Solve v(p) = 0.
-47/4, 11
Suppose -2*s - 35 + 39 = 0. Let y be 1 + -3 - (-36)/18. Suppose -1/4*k**s + 0 + 1/4*k**4 + 0*k + y*k**3 = 0. What is k?
-1, 0, 1
Let n(l) = -2*l**2 - 22*l - 11. Let y be n(-9). Determine v, given that -5*v**4 + 348*v**5 + y*v**3 - 748*v**5 + 5*v**2 + 375*v**5 = 0.
-1, -1/5, 0, 1
Let x(i) = 20*i**4 + 42*i**3 + 3*i**2 - 75*i - 42. Let z(n) = -17*n**4 - 39*n**3 - 3*n**2 + 73*n + 42. Let f(o) = 6*x(o) + 7*z(o). Factor f(u).
(u - 21)*(u - 2)*(u + 1)**2
Let m be (234/(-63) - -4)*119. Find a such that -31*a**3 - m*a**3 - 7*a**3 + 96*a**2 - 16*a + 20*a**3 - 112*a**5 - 276*a**4 = 0.
-2, -1, 0, 1/4, 2/7
Let c(t) = 1. Let h(q) = -9*q**4 - 84*q**3 + 98*q**2 + 1372*q - 2420. Let w(u) = 19*c(u) + h(u). Factor w(n).
-(n + 7)**2*(3*n - 7)**2
Let y(i) = -10*i**3 - 1480*i**2 - 2845*i. Let t(u) = 3*u**3 + 423*u**2 + 813*u. Let l(n) = 25*t(n) + 7*y(n). Factor l(b).
5*b*(b + 2)*(b + 41)
Let c(k) = -10*k**3 + k**2 + k - 1. Let v(a) = 28*a**3 - 15*a**2 - 27*a - 13. Let l(b) = -3*c(b) - v(b). Factor l(o).
2*(o + 2)**3
Find p, given that -2*p**2 - 1/4*p**3 - 19/4*p - 3 = 0.
-4, -3, -1
Let n(g) = -2*g**2 - 24*g - 4. Let i be n(15). Let r be i/(-165) + (-4)/3. Factor -6/5*y**3 + 2*y**4 + 0*y - 2/5*y**5 + 0 - r*y**2.
-2*y**2*(y - 3)**2*(y + 1)/5
Let c = 1496/9651 + 75/6434. Factor c*i + 1/6*i**5 - 1/3*i**2 - 1/3*i**3 + 1/6*i**4 + 1/6.
(i - 1)**2*(i + 1)**3/6
Let z(d) be the third derivative of 0*d**3 - 5 + 29/24*d**6 + 0*d - 65/4*d**5 - 1/42*d**7 - 375/8*d**4 - 3*d**2. What is p in z(p) = 0?
-1, 0, 15
Let d = 280363 - 280363. Factor d*r - 9*r**2 + 0 - 1/2*r**3.
-r**2*(r + 18)/2
Suppose -3*j = -5*j + 4. Let w be (3/12)/((-2370)/240 + 11). Solve 0 + 0*f**3 - w*f**j + 0*f + 2/9*f**4 = 0.
-1, 0, 1
Suppose -60 = -124*x + 134*x. Let i be x/(-7)*(-18)/504*-49. Factor -3/4*u**2 + i*u - 3/4.
-3*(u - 1)**2/4
Let h be (-13 + 2877/210)/(2/8). Factor -2/5*d**2 + h*d - 12/5.
-2*(d - 6)*(d - 1)/5
Let f = 11070 + -11067. Let a(j) = -j**3 - j**2 + j. Let k be a(0). Factor 0*x - 4/7*x**2 - 8/7*x**f + k.
-4*x**2*(2*x + 1)/7
Let a(h) be the second derivative of -h**6/60 + 3*h**5/20 + 2*h**4/3 + 2*h - 147. Factor a(v).
-v**2*(v - 8)*(v + 2)/2
Let p be (-30)/(-1)*3/6. Let r be ((-18)/(-15))/(6/p). Factor 95*c**r + 24*c - 94*c**3 - 8*c**2 - 8*c.
c*(c - 4)**2
Let v be (15464/(-30)*(-105)/70)/322. Let r = -1/805 + v. Factor 12/5 + 3/5*p**4 - 6/5*p**3 - 9/5*p**2 + r*p.
3*(p - 2)**2*(p + 1)**2/5
Let l(a) = 4*a**3 + 46*a**2 + 6*a + 14. Let b(q) = -q**3 - 15*q**2 - 2*q - 3. Let m(u) = -10*b(u) - 3*l(u). Factor m(v).
-2*(v - 6)*(v - 1)*(v + 1)
Let w(i) be the second derivative of 27*i**4/7 + 1464*i**3 + 208376*i**2 - 4*i + 164. Solve w(k) = 0.
-854/9
Let q(d) be the third derivative of d**8/840 - 22*d**7/1575 + 11*d**6/180 - 26*d**5/225 + d**4/15 + 193*d**2 + 2*d. Find o such that q(o) = 0.
0, 1/3, 2, 3
Suppose -3*y - 3*i = -51, 8 = 3*i - 1. Suppose -8*k + 26 + y = 0. Let -11*j + 7*j - j**3 + 0*j**3 + k*j**3 = 0. Calculate j.
-1, 0, 1
Factor 0 - 1/8*m**5 - 14161/8*m**2 + 0*m - 239/8*m**4 - 14399/8*m**3.
-m**2*(m + 1)*(m + 119)**2/8
Let g = -5054 - -5054. Let u(s) be the third derivative of 0 - 1/6*s**4 - 1/30*s**5 + g*s + s**3 + 17*s**2. Solve u(j) = 0 for j.
-3, 1
Factor -6348 - 3358*r - 2/3*r**3 - 280/3*r**2.
-2*(r + 2)*(r + 69)**2/3
Let -285/2*i**3 + 0 + 369/4*i**4 + 6*i + 63*i**2 - 75/4*i**5 = 0. What is i?
-2/25, 0, 1, 2
Suppose -288/5*m**2 - 292/5*m**3 + 58 - 2/5*m**4 + 292/5*m = 0. Calculate m.
-145, -1, 1
Let r be (120/32)/(-2 + ((-1365)/(-26))/15). Solve r*o**2 - 5/2 - 1/2*o**3 + 1/2*o = 0.
-1, 1, 5
Find n such that -81/2*n - 3*n**5 - 33/2*n**2 + 87/2*n**3 - 21/2*n**4 + 27 = 0.
-6, -1, 1, 3/2
Solve 5/4*f**3 - 75/2 + 20*f**2 + 65/4*f = 0 for f.
-15, -2, 1
Let a(h) be the first derivative of -2/45*h**5 + 0*h + 1/3*h**4 + 40/9*h**2 - 20 + 8/3*h**3. Factor a(d).
-2*d*(d - 10)*(d + 2)**2/9
Let b(j) = -9*j**3 - j**2 - 9*j + 9. Let q be b(1). Let p(a) = 12*a + 123. Let u be p(q). Suppose 0*d - 2/9*d**4 + 0*d**2 + 0 + 2/9*d**u = 0. Calculate d.
0, 1
Let d(h) = 4*h**4 + 516*h**3 + 236*h**2 - 420*h. Let o(c) = -c**4 - 104*c**3 - 49*c**2 + 84*c. Let r(s) = 5*d(s) + 24*o(s). Suppose r(n) = 0. Calculate n.
-1, 0, 1, 21
Let p(j) be the first derivative of -j**5/15 - 53*j**4/6 - 104*j**3/3 - 87*j**2 + 190. Let t(c) be the second derivative of p(c). Suppose t(n) = 0. Calculate n.
-52, -1
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