). Determine n so that 2/9*n**2 + m - 4/9*n = 0.
1
Let i(b) be the second derivative of 25*b + 0*b**6 - 3/5*b**5 - 1/2*b**4 + 0 + 1/14*b**7 + 3/2*b**3 + 3*b**2. Let i(k) = 0. Calculate k.
-1, 1, 2
Let q(a) be the second derivative of -a**9/5040 + a**7/280 - a**6/120 + a**4/12 + 11*a. Let v(u) be the third derivative of q(u). Find d, given that v(d) = 0.
-2, 0, 1
Let -75 + 10*q + 3*q**2 - 10*q**3 - 8*q**2 + 87 - 5*q**2 - 5*q**4 + 3*q**4 = 0. What is q?
-3, -2, -1, 1
Let c be 3 + 391/(-46)*(0 - -2). Let o be (-708)/210 - (-6)/c - -4. Let o*q**2 - 2/5*q + 3/5*q**3 + 0 = 0. What is q?
-1, 0, 2/3
Suppose 5*m - 21 = 2*x, 5*x = -m + 4 + 11. Suppose 5*h - m = -0. Factor 3*j - 3 + 3 - 3 + h - j**2.
-(j - 2)*(j - 1)
Let p(y) be the first derivative of -2*y**6/3 + 12*y**5/5 + 4*y**4 + 173. Factor p(z).
-4*z**3*(z - 4)*(z + 1)
Let n = -28153 - -84460/3. Factor n*d**2 + 27 + 6*d.
(d + 9)**2/3
Let n(f) be the first derivative of f**6/6 - f**4/2 + f**2/2 - 14. Determine m so that n(m) = 0.
-1, 0, 1
Let a(x) be the second derivative of 0*x**3 - 4*x + 0 - 1/4*x**4 + 3/2*x**2. Factor a(f).
-3*(f - 1)*(f + 1)
Let n be 18/(84/14) + (-28)/10. Suppose -3/5*q - n*q**2 - 2/5 = 0. What is q?
-2, -1
Let n(c) be the first derivative of c**3/2 - 3*c**2/2 - 12*c - 71. Determine v so that n(v) = 0.
-2, 4
Determine l so that 24/5*l + 64/5*l**2 + 14/5*l**5 + 0 - 24/5*l**4 - 78/5*l**3 = 0.
-2, -2/7, 0, 1, 3
Suppose 2*p - 5*a = 5, 4*p + 2 = 2*p - 2*a. Suppose p = -0*x - 4*x. Suppose 0 - 4*w - 8*w**2 + 3*w**4 - w**3 + x + 0 = 0. What is w?
-1, -2/3, 0, 2
Let p(l) = l**2 - 14*l + 5. Let s be p(16). Suppose 2*a + a - 9 = 0. Factor 3*z**3 + s - 37 - a*z.
3*z*(z - 1)*(z + 1)
Let w be 742/(-84) + 2 + -4. Let r = w + 467/42. Factor r + 2/7*m**2 + 4/7*m.
2*(m + 1)**2/7
Let y = 113 + -49. Factor 12*j**2 + y - 120*j + 16 + 16*j**2 - 5*j**3 + 17*j**2.
-5*(j - 4)**2*(j - 1)
Factor -24*c + 2*c**3 + 2*c**2 - 36 - 1/4*c**4.
-(c - 6)**2*(c + 2)**2/4
Let m(w) = -4*w**3 - 15*w**2 + 96*w - 28. Let f(s) = -55*s**3 - 210*s**2 + 1345*s - 390. Let t(d) = -6*f(d) + 85*m(d). Factor t(a).
-5*(a - 2)*(a + 4)*(2*a - 1)
Let a = -15 + 25. Solve 51*j - 5*j**2 - 31*j - 30 + a = 0 for j.
2
Let i(k) be the first derivative of k**6/70 - 3*k**5/70 - k**4/28 + k**3/7 + 10*k - 54. Let j(y) be the first derivative of i(y). Factor j(g).
3*g*(g - 2)*(g - 1)*(g + 1)/7
Suppose -26*a - 163*a = -756. Factor -4/7*p**a - 2/7*p + 0 + 6/7*p**3 + 0*p**2.
-2*p*(p - 1)**2*(2*p + 1)/7
Suppose -28*s = -23*s + 4*h - 16, -3*s = h - 4. Find o such that 0*o + 2/3*o**2 - 1/3 - 1/3*o**4 + s*o**3 = 0.
-1, 1
Let k = 9 + -5. Solve -2*h - 10*h**3 - 9*h**2 + 7*h**3 - k*h = 0 for h.
-2, -1, 0
Factor 3195*h**4 + 5*h**3 - 4*h - 2*h**3 - 3194*h**4.
h*(h - 1)*(h + 2)**2
Let r(i) be the third derivative of i**7/735 - i**6/140 - i**5/70 + 11*i**4/84 - 2*i**3/7 + 79*i**2. Factor r(u).
2*(u - 3)*(u - 1)**2*(u + 2)/7
Let o(f) = 3*f**3 + 5*f**2 + f. Let l(b) = -b**3 - b**2 - b. Let n(x) = 2*l(x) + 2*o(x). Solve n(r) = 0 for r.
-2, 0
Let h = 66 - 64. Let u(k) = -12*k**3 - 38*k**2 - 42*k - 18. Let j(a) = -a**2 - a + 1. Let b(f) = h*j(f) + u(f). Find o, given that b(o) = 0.
-4/3, -1
Let q = 1137 + -51163/45. Let o(k) be the first derivative of -2/5*k**2 - q*k**3 - 1 - 6/5*k. Factor o(w).
-2*(w + 3)**2/15
Suppose u + 19 - 2 = 5*w, 3*u - 3*w + 3 = 0. Factor 6*f**u - 12*f**3 - 2*f**4 + f**4 + 4*f**4.
3*f**3*(f - 2)
Let m(b) be the first derivative of b**6/14 + 3*b**5/35 - 3*b**4/28 - b**3/7 + 72. Let m(n) = 0. Calculate n.
-1, 0, 1
Factor 2/5*d**3 + 112/5*d - 104/5 - 34/5*d**2.
2*(d - 13)*(d - 2)**2/5
Let x(c) be the third derivative of -1/42*c**7 - 5/6*c**4 - 34*c**2 + 0*c + 0 + 1/12*c**5 + 0*c**3 + 1/6*c**6. Factor x(s).
-5*s*(s - 4)*(s - 1)*(s + 1)
Suppose 40 + 4/3*m**2 - 124/3*m = 0. What is m?
1, 30
Let w be ((-1)/(-770))/(9/1917). Let s = w - -1/110. Solve -4/7 + s*v**2 + 2/7*v**4 + 6/7*v - 6/7*v**3 = 0 for v.
-1, 1, 2
Suppose 2 = -74*i + 75*i. Solve -v**3 - 365 - 243*v + 19*v**i + 81 - 445 - 46*v**2 = 0.
-9
Suppose -47*j = -51*j. Let z(v) be the first derivative of -2/27*v**3 + j*v + 2/45*v**5 - 1/18*v**4 + 6 + 1/9*v**2. Determine h so that z(h) = 0.
-1, 0, 1
Suppose 0 = -5*x + 2*r + 80 + 130, -3*x = 3*r - 105. Let b be (17/(-15) - 1)/((-24)/x). Let 16/9*o + 2/9*o**2 + b = 0. What is o?
-4
Let s = 413 + -408. Let u(n) be the third derivative of 1/240*n**5 + 0*n**3 + 0*n**4 - s*n**2 + 0*n + 0. Determine b, given that u(b) = 0.
0
Let f(z) be the third derivative of -5/3*z**4 - 40/3*z**3 + 0 + 7/12*z**5 - 5*z**2 + 0*z - 1/24*z**6. Let f(o) = 0. What is o?
-1, 4
Let y(w) be the third derivative of 3*w**7/70 + w**6/10 - w**5/4 - w**4/4 - 37*w**2 - w. What is d in y(d) = 0?
-2, -1/3, 0, 1
Let m(a) = -a**2 - a + 1. Let j(r) = -4*r**2 - 20*r + 2. Let k(o) = j(o) - 2*m(o). Suppose k(t) = 0. Calculate t.
-9, 0
Let r(g) = -2*g**2 + 7*g + 3. Let y(h) = -h**2 - h - 1. Let k(x) = r(x) - 5*y(x). Let o be k(-6). Solve -19*a**3 - 4*a**2 + o*a**3 - 27*a**3 + 2*a**4 = 0.
-1, 0, 2
Let c(y) be the third derivative of y**6/30 - 7*y**5/30 - y**4/3 - 162*y**2. Determine i, given that c(i) = 0.
-1/2, 0, 4
Let w = -46 + 62. What is o in -21*o - 19*o + 32*o + 4*o**4 + 20*o**2 - w*o**3 = 0?
0, 1, 2
Let i(h) be the first derivative of 242*h**6/7 - 396*h**5/35 + 27*h**4/28 + 248. Let i(s) = 0. What is s?
0, 3/22
Let g(u) = -u**2 + 15*u - 14. Let l be g(14). Let o(b) = 9*b + 2. Let p be o(l). Factor -1/4 + 0*v + 1/4*v**p.
(v - 1)*(v + 1)/4
Let j(k) = -9*k**3 - 57*k**2 - 63*k + 5. Let s(z) = -11*z**3 - 55*z**2 - 62*z + 6. Let b(o) = -6*j(o) + 5*s(o). Solve b(y) = 0.
-1, 0, 68
Let k(c) be the first derivative of -2*c**5/5 - c**4/2 + 2*c**3/3 + c**2 - 88. Factor k(l).
-2*l*(l - 1)*(l + 1)**2
Factor -72*p**3 + 8*p**2 - 4*p**5 - 44*p**4 + 55*p + 36 - 117*p + 138*p.
-4*(p - 1)*(p + 1)**3*(p + 9)
Let x be (5 - (0 - -3))/(-12 - -13). Find c, given that 5/2*c**4 - 10*c + 13/2*c**3 + 4 - 3*c**x = 0.
-2, 2/5, 1
Factor 2/3*a**2 + 5*a - 1/3*a**3 - 12.
-(a - 3)**2*(a + 4)/3
Let k(u) be the third derivative of u**5/240 + 5*u**4/96 + u**3/4 + 3*u**2 + 15. Factor k(v).
(v + 2)*(v + 3)/4
Let o(k) = k**3 - 8*k**2 - 20*k - 3. Let l be o(10). Let i be 1*l*(-27)/324. Determine m, given that -i*m**2 + m - 1 = 0.
2
Determine k, given that -16*k**2 - 28*k**2 + 2*k**4 - 6*k**4 + 48*k**3 = 0.
0, 1, 11
Let u(n) = n**3 + 1. Let d(j) = 12*j**3 + 40*j**2 + 108*j + 80. Let i(k) = d(k) - 8*u(k). Factor i(s).
4*(s + 1)*(s + 3)*(s + 6)
Let w(d) be the third derivative of 1/10*d**6 + 1/168*d**8 + 0*d - 2/15*d**5 + 0*d**3 - 4/105*d**7 + 0 - 17*d**2 + 1/12*d**4. Factor w(y).
2*y*(y - 1)**4
Let k(z) be the first derivative of 0*z**2 - 8/15*z**3 - 26/25*z**5 + 0*z - 1/5*z**6 - 23 - 8/5*z**4. Factor k(b).
-2*b**2*(b + 2)**2*(3*b + 1)/5
Suppose -4*w + 2 = -2*i, -2*w = -0*w - 4. Factor 12*m**2 - 4*m**i - 2279 + 2279 - 8*m.
-4*m*(m - 2)*(m - 1)
Factor -198/7*o - 6*o**2 - 2/7*o**3 + 242/7.
-2*(o - 1)*(o + 11)**2/7
Suppose -1/7*c**3 - 9/7*c**2 + 81/7*c - 135/7 = 0. Calculate c.
-15, 3
Solve 0*g - 7/4*g**2 - 9/8*g**3 + 0 + 3/4*g**4 + 1/8*g**5 = 0.
-7, -1, 0, 2
Suppose 0 = -4*y + 9*y + 70. Let d(h) = -h - 10. Let q be d(y). Factor 11*w**3 - 3*w**3 - 4*w**q - 2*w**3 - 2*w**2.
-2*w**2*(w - 1)*(2*w - 1)
Let h(j) be the second derivative of j**7/147 + j**6/21 + 3*j**5/35 - 892*j. Factor h(p).
2*p**3*(p + 2)*(p + 3)/7
Let w be 3/8 - ((-121)/88)/11. Find b such that -5/2*b + w*b**2 + 2 = 0.
1, 4
Let n(i) be the second derivative of i**8/13440 - i**7/1680 + i**4 + 3*i. Let a(h) be the third derivative of n(h). Solve a(c) = 0.
0, 3
Let i(z) be the first derivative of 12 + 1/6*z**3 - 2/3*z + 1/30*z**5 + 1/6*z**4 - 1/3*z**2. Suppose i(v) = 0. Calculate v.
-2, -1, 1
Let r(w) be the third derivative of 3*w**8/112 - w**7/14 - 11*w**6/20 + 13*w**5/5 - 3*w**4 - 63*w**2. Solve r(m) = 0.
-3, 0, 2/3, 2
Let g(h) = -5*h**4 - 80*h**3 - 470*h**2 - 1195*h - 1135. Let s(i) = 5*i**4 + 80*i**3 + 470*i**2 + 1194*i + 1137. Let t(w) = -6*g(w) - 5*s(w). Solve t(p) = 0.
-5, -3
Let a(n) be the third derivative of -1/480*n**6 + 6*n**2 + 0 + 1/12*n**3 + 1/96*n**4 - 1/120*n**5 + 0*n. Determine m, given that a(m) = 0.
-2, -1, 1
Let x be 0/(((-4)/5)/(36/90)). Let h(l) be the third derivative of 0*l + 0*l**4 + 0 - 1/180*l**5 + x*l**3 - l**2. Determine n, given