2 - 51*m**2 - 894*m - 2. Factor k(d).
(d - 51)*(13*d + 6)/3
Let m(c) = -27*c + 918. Let p be m(34). Let i(j) be the third derivative of 0*j**4 + 0*j**3 + 0 - 1/135*j**5 + p*j - 6*j**2. Factor i(n).
-4*n**2/9
Let z(r) be the first derivative of -2*r**6/3 - 56*r**5/5 - 14*r**4 + 944*r**3/3 - 738*r**2 + 648*r + 1898. Determine w, given that z(w) = 0.
-9, 1, 2
Suppose 2/7*n**3 + 800*n + 218/7*n**2 - 2688 = 0. What is n?
-56, 3
Let x(f) be the third derivative of -f**6/90 - 4*f**5/15 - 41*f**3/6 - 123*f**2. Let d(r) be the first derivative of x(r). Factor d(b).
-4*b*(b + 8)
Let j(x) = -12*x**4 - 93*x**3 - 75*x**2 + 228*x - 180. Let o(y) = y**3 - y + 11. Let s(l) = -j(l) - 12*o(l). Factor s(q).
3*(q - 1)*(q + 4)**2*(4*q - 1)
Let r(i) be the second derivative of 9*i**7/7 - 51*i**6/10 - 3*i**5/2 + 3*i**4/4 + 17*i + 8. Suppose r(s) = 0. What is s?
-1/3, 0, 1/6, 3
Let a = 200813/45 + -4463. Let d = a + 8/9. Suppose -4/5*v**4 + d*v**3 - 2/5 - 2/5*v + 6/5*v**2 = 0. Calculate v.
-1, -1/2, 1
Let q(d) be the second derivative of 5*d**4/6 + 28*d**3/3 + 15*d**2 + 4*d + 58. Solve q(o) = 0.
-5, -3/5
Let o(v) be the second derivative of -v**6/70 - 27*v**5/35 + 19*v**4/14 + 18*v**3/7 - 111*v**2/14 + 2*v + 3574. Solve o(d) = 0.
-37, -1, 1
Let t = 68694 + -480666/7. Determine x so that 48/7 - 192/7*x - 12/7*x**3 - 51/7*x**4 + 15/7*x**5 + t*x**2 = 0.
-2, 2/5, 1, 2
Let z(a) = -6*a**2 + 28*a + 3. Let x be z(6). Let d be ((12/x)/(-4))/(7/21). Determine i, given that 3/5*i**2 + d*i + 0 = 0.
-1/3, 0
Let x(f) = -f**2 - 624*f + 1280. Let h(a) = -7*a**2 - 3738*a + 7686. Let l(j) = -6*h(j) + 39*x(j). Solve l(t) = 0.
2, 634
Let u be 4/((27 - 18) + 3). Let t(m) be the second derivative of -4/3*m**3 + 0 - u*m**4 - 2*m**2 + m. Factor t(x).
-4*(x + 1)**2
Let f(q) = 3*q**2 + 20*q - 43. Let j(w) = -2*w**2 - 21*w + 41. Let u(t) = -5*f(t) - 6*j(t). Let k be u(7). Solve -10/3 - 2/3*a**2 - k*a = 0.
-5, -1
Suppose -1/3 + 95/3*f + 1/3*f**2 - 95/3*f**3 = 0. Calculate f.
-1, 1/95, 1
Let w(p) = -4*p**4 + p**3 + p**2 - p. Let b(k) = -22*k**4 - 9*k**3 - 11*k**2 + 27*k. Let f(q) = b(q) - 5*w(q). Let f(d) = 0. Calculate d.
-4, 0, 1
Determine a, given that 125/8*a**3 - 675*a**2 - 1/8*a**4 + 11000*a - 40000 = 0.
5, 40
Let c be (30464/(-336) - -90) + (2 - (-8)/6). Let g be ((-4)/5)/((-2)/5). Factor c - 2/3*f**3 - 8/3*f**g + 2/3*f.
-2*(f - 1)*(f + 1)*(f + 4)/3
Suppose 29*b + 72*b + 47 - 249 = 0. Factor -2/3*v**3 - 2*v**b - 4/3*v + 0.
-2*v*(v + 1)*(v + 2)/3
Let a be (-344)/2666*(-31)/14. Determine x so that -2/7*x**3 - 2*x**4 + 0 + 0*x + a*x**5 + 2*x**2 = 0.
-1, 0, 1, 7
Let y(b) be the second derivative of -b**6/40 + 23*b**5/20 - 19*b**2/2 - 27*b. Let l(u) be the first derivative of y(u). Find c, given that l(c) = 0.
0, 23
Let b = -8 - -10. Let g be (1/b*-1)/((-1)/6). Factor 62*v**2 + v**g - 125*v**2 + 69*v**2 + 6 + 2 + 12*v.
(v + 2)**3
Let q(p) be the second derivative of -2*p**5/25 + 4579*p**4/30 - 3431*p**3/15 - 1144*p**2/5 - 1294*p. Determine m, given that q(m) = 0.
-1/4, 1, 1144
Let c(t) be the first derivative of 5/14*t**4 + 4/3*t**3 - 72 + 13/7*t**2 + 8/7*t. Factor c(m).
2*(m + 1)**2*(5*m + 4)/7
Let j(r) = r**3 + 37*r**2 - 44*r - 131. Let l be j(-38). Let g = 99 - l. Let 9/5*k + 1/5*k**3 - 4/5 - 6/5*k**g = 0. What is k?
1, 4
Factor 5/9*m - 14/9 + 1/9*m**3 + 8/9*m**2.
(m - 1)*(m + 2)*(m + 7)/9
Suppose 146 + 94 = 6*s. Find h such that 5*h - 21*h - 36*h**3 + s*h**2 + 0*h**3 - 2*h**5 + 14*h**4 = 0.
0, 1, 2
Let t(d) be the first derivative of -2*d**7/105 - d**6/15 + d**5/15 + d**4/3 + 49*d**2/2 - 67. Let n(h) be the second derivative of t(h). What is w in n(w) = 0?
-2, -1, 0, 1
Let c = 3031/286 - 14/143. Let q(a) be the first derivative of a**4 + 4*a + 37 + 7*a**3 + c*a**2. Factor q(z).
(z + 1)*(z + 4)*(4*z + 1)
Let q(c) = -31*c**3 + 46*c**2 - 36*c. Let o(f) = 4*f**3 - 2*f**2 + f. Let b(r) = 35*o(r) + 5*q(r). Solve b(m) = 0.
0, 1, 29/3
Let s(z) be the first derivative of 12*z + 21/5*z**5 - 1/2*z**6 - 4 - 24*z**2 + 25*z**3 - 57/4*z**4. Factor s(i).
-3*(i - 2)**2*(i - 1)**3
Suppose -5*r - 10 = o, -5*o + r - 550 = -578. Factor 0 + 16/9*b**2 + 0*b - 2/9*b**o - 34/9*b**3 + 20/9*b**4.
-2*b**2*(b - 8)*(b - 1)**2/9
Suppose 17*i = 3*i + 70. Suppose -3*l + 18 = 2*m, -m - 10*l + 23 = -i*l. Factor 120/13*n - 2/13*n**4 - 74/13*n**2 - 72/13 + 20/13*n**m.
-2*(n - 3)**2*(n - 2)**2/13
Let a(m) be the second derivative of 2*m**4/7 - 50*m**3/21 + 8*m**2/7 + 2*m - 352. Suppose a(i) = 0. What is i?
1/6, 4
Find k such that -2/7*k**3 + 36/7 - 58/7*k + 24/7*k**2 = 0.
1, 2, 9
Let s be (-1 + -4 + 3)*(-3)/2. Suppose -2*n**5 + 14*n**s - 12*n**3 + 0 - 4*n**4 + 4*n**2 + 0 = 0. Calculate n.
-2, -1, 0, 1
Let v(i) = i**2 + 8*i - 3. Let f be v(-7). Let t be f*(-3 + 4/4). Factor 20 + 18*u**2 + 14*u**2 + 20*u + t*u**2 - 47*u**2.
5*(u + 2)**2
Factor -4/3*n**2 - 2/15*n**3 - 14/15*n + 12/5.
-2*(n - 1)*(n + 2)*(n + 9)/15
Let x(p) be the first derivative of -2*p**5 + 13/2*p**4 - 4*p**2 - 36 + 0*p - 8/3*p**3. Factor x(z).
-2*z*(z - 2)*(z - 1)*(5*z + 2)
Let a = 2096/327 - -28/109. Let t(v) be the first derivative of -12 + a*v**3 - 16*v - 16*v**2. Suppose t(u) = 0. What is u?
-2/5, 2
Let n be (3/4 - (-5 - -5))*12. Suppose -3*o = -2*v - n, v - o + 17 = 3*o. Factor 62 + 82 - 2*j**2 + v*j**2 - 24*j.
(j - 12)**2
Let s be 7 + -12 + 968/66 + -9*1. Suppose 2/3*l**5 + 0 + 2/3*l**4 + 0*l - s*l**3 - 2/3*l**2 = 0. Calculate l.
-1, 0, 1
Let -100/3 + 2*u**2 + 5*u - 1/3*u**3 = 0. What is u?
-4, 5
Let m be (2080/39)/(-4)*(-3)/(-2). Let a be (20 + m)/(12/4). Factor a + 16/9*p**2 - 8/3*p - 2/9*p**3.
-2*p*(p - 6)*(p - 2)/9
Let g(o) be the second derivative of -o**6/720 + o**5/480 + o**4/16 - 203*o**3/6 + 137*o. Let f(c) be the second derivative of g(c). Factor f(n).
-(n - 2)*(2*n + 3)/4
Let j(d) = -215*d + 212*d - 1 + 14*d**2 - 13*d**2. Let b(f) = -130*f + 2. Let l(a) = b(a) + 2*j(a). Factor l(z).
2*z*(z - 68)
Let r(n) be the first derivative of -2*n**3/3 - 90*n**2 - 9765. Factor r(x).
-2*x*(x + 90)
Suppose 25 = 5*w, 28*v + 3*w - 9 = 30*v. Solve -z**4 - 27*z**4 - 24*z - 46*z**2 - 6*z**2 - 1137 + 1137 + 104*z**v = 0 for z.
-2/7, 0, 1, 3
Solve -10*p**4 - 164*p**2 - 674/9*p**3 + 246 + 3*p - 1/9*p**5 = 0.
-82, -3, 1
Suppose -7*j = -0*j - 294. Determine s so that -47*s**2 + 137*s**2 - 47*s**2 - j*s**2 = 0.
0
Suppose -1 = 2*g - 5. Let l be (1675/10 + 3)*2. Factor 8*h**3 + 341*h**g - 12*h**4 - l*h**2 + 4*h**5.
4*h**3*(h - 2)*(h - 1)
Let o(g) be the second derivative of g**6/135 - 2*g**5/15 + 7*g**4/18 - 10*g**3/27 + 7735*g. Factor o(b).
2*b*(b - 10)*(b - 1)**2/9
Let k(n) be the third derivative of n**8/280 + 19*n**7/1050 - 19*n**6/200 - n**5/30 + 122*n**2 - 19*n. Suppose k(q) = 0. Calculate q.
-5, -1/6, 0, 2
Suppose 5*g - 5 = 20. Let f be 616/40 - (-3)/g. Factor f - 2*m + 68*m**2 - 34*m**3 + 66*m + 54*m**3.
4*(m + 1)*(m + 2)*(5*m + 2)
Suppose u + 4 = 2*h - 1, 5*h + 2*u - 26 = 0. Suppose -a + 0*y + h*y - 6 = 0, 3*y = -5*a + 16. Factor 1/2*q**a - 1/4*q**4 + 0*q - 7/8*q**3 + 0.
-q**2*(q + 4)*(2*q - 1)/8
Let n(l) be the third derivative of l**6/40 - 11*l**5/10 + 57*l**4/8 - 1234*l**2. Let n(m) = 0. Calculate m.
0, 3, 19
Let w = 197 - 195. Find q such that -13 + 69*q + 62*q**2 - 5 + 20*q**2 + 110*q**w + 105*q**3 = 0.
-1, 6/35
Let p(d) be the third derivative of d**7/420 - 13*d**6/80 - 7*d**5/20 + 5*d**4/3 - 851*d**2. Let p(x) = 0. Calculate x.
-2, 0, 1, 40
Let p(j) be the first derivative of j**6/780 - j**5/65 + 5*j**4/156 + 4*j**3/13 + 12*j**2 - 31. Let x(b) be the second derivative of p(b). Factor x(t).
2*(t - 4)*(t - 3)*(t + 1)/13
Let y(r) be the second derivative of -r**4/4 - 7*r**3 + 48*r**2 + 14450*r. Factor y(b).
-3*(b - 2)*(b + 16)
Let n(j) be the first derivative of j**4/18 - 16*j**3/3 - 51*j**2 - 156*j + 1603. Factor n(u).
2*(u - 78)*(u + 3)**2/9
What is f in 10*f**2 - 24*f**3 - 7/2*f**5 - 75/2*f**4 + 0*f + 0 = 0?
-10, -1, 0, 2/7
Let k be 5 + 492/(-60) + 11/(11/4). Find f, given that -6/5*f**2 - k*f**3 + 0*f + 2/5*f**4 + 0 = 0.
-1, 0, 3
Factor -155*d**2 + 157*d**2 - 140*d**4 + 357*d + 52 - d**5 + 119 - 33 - 80*d - 276*d**3.
-(d - 1)*(d + 1)**3*(d + 138)
Let d(j) = -j**3 + 2*j**2 + 1. Let i(g) = -3*g**4 + 291*g**3 - 7485*g**2 + 7203*g + 6. Let h(z) = -6*d(z) + i(z). Determine q so that h(q) = 0.
0, 1, 49
Factor 346120*b - 2/3*b**4 + 680*b**3 - 518162/3 - 52