et v(w) = -7*w**3 + 26*w**2 + 18*w. Let b(g) = -5*c(g) - 4*v(g). Suppose b(y) = 0. What is y?
-1, 0, 9
Determine c, given that c**4 - c**5 + 16*c**3 - 2*c**3 + 56*c - 53*c**2 + 1 + 3*c**3 - 21 = 0.
-5, 1, 2
Suppose 4*n + 10 = -238. Let s = n - -249/4. Find b, given that -1/4*b**3 + 0 + 1/4*b**4 + s*b - 1/4*b**2 = 0.
-1, 0, 1
Let r(y) be the first derivative of 2*y**5/35 - 44*y**4/7 + 1290*y**3/7 + 88*y**2/7 - 3872*y/7 + 208. Solve r(w) = 0.
-1, 1, 44
Suppose 4*p - 9*p + 5 = 0. Let u be p/(-2 - (-20)/8). Factor -7*h**3 - 2*h**2 - 6*h**4 - u*h**5 + h**3 + 11 - 11.
-2*h**2*(h + 1)**3
Let y(j) be the second derivative of j**6/165 + j**5/110 - j + 153. Factor y(l).
2*l**3*(l + 1)/11
Let v = 1/2394 + 223/11970. Let b(y) be the second derivative of 0*y**2 + v*y**6 + 3*y - 1/21*y**4 - 1/147*y**7 + 0*y**3 + 1/70*y**5 + 0. Solve b(d) = 0 for d.
-1, 0, 1, 2
Let l(y) = 7*y**3 + 13*y**2 - 4*y - 16. Let k(i) = 15 - 12*i**2 + 10*i + 8*i - 15*i - 6*i**3. Let m = -1 - 2. Let r(o) = m*l(o) - 4*k(o). Factor r(w).
3*(w - 1)*(w + 2)**2
Let q(o) be the third derivative of o**6/120 + 7*o**5/15 - 59*o**4/24 + 5*o**3 - 165*o**2. Solve q(s) = 0.
-30, 1
Suppose 4*g = -4*f + 24, -f + 1 + 11 = 3*g. Suppose 50 = -i + 5*s + 57, 3*i - 3*s - 9 = 0. Factor 0 + 3/5*t**i + 0*t + 3/5*t**g.
3*t**2*(t + 1)/5
Factor 49/6*o - 25/12*o**2 + 2/3.
-(o - 4)*(25*o + 2)/12
Suppose -115 = 190*o - 148 - 347. Let -25/4 - 1/4*v**o + 5/2*v = 0. Calculate v.
5
Let d(g) be the third derivative of -g**5/120 + 15*g**4/8 - 44*g**3/3 + 78*g**2 + 3*g. Find s, given that d(s) = 0.
2, 88
Let v be (1*7 - (-990)/(-528)) + -4. Factor v - 5/4*q + 1/8*q**2.
(q - 9)*(q - 1)/8
Let k(p) = -p**2 - 177*p + 1101. Let n be k(6). Factor 0*j**2 + 1/2*j**n + 0 - 1/2*j.
j*(j - 1)*(j + 1)/2
Let t(h) be the first derivative of -2*h**6/3 - 32*h**5/5 - 22*h**4 - 112*h**3/3 - 34*h**2 - 16*h - 98. Find d such that t(d) = 0.
-4, -1
Let g be (-2)/(-10)*330/33. Suppose -10 - 5 = -5*f, g*b + 9 = 3*f. Determine i so that 2/7*i**4 + 0 + 0*i**2 + b*i + 2/7*i**3 = 0.
-1, 0
Let m be -7 - (-17 - -15 - (213/9 - 0)). Let r = -1 + 3. Find s, given that -10*s - 4/3 - m*s**r = 0.
-2/7, -1/4
Let y be 3/(-1 + 4) - 1768/20. Let c = y + 88. Factor 21/5*f**2 + 0 + 39/5*f**4 - 12/5*f**5 - 9*f**3 - c*f.
-3*f*(f - 1)**3*(4*f - 1)/5
Let l(n) be the second derivative of 0*n**5 + 0*n**2 + 0*n**3 + 0 + 0*n**4 - 6*n - 2/225*n**6 + 1/315*n**7. Factor l(u).
2*u**4*(u - 2)/15
Let y(z) = 28*z**4 + 106*z**3 + 240*z**2 - 10*z + 10. Let u(n) = -8*n**4 - 35*n**3 - 80*n**2 + 3*n - 3. Let k(b) = -10*u(b) - 3*y(b). Find p such that k(p) = 0.
-2, 0, 10
Let v(k) be the second derivative of k**4/114 + 56*k**3/57 - 3*k**2 - 8*k - 3. Find c, given that v(c) = 0.
-57, 1
Factor 2/9*r**4 + 68/9*r**3 + 0 + 200*r + 230/3*r**2.
2*r*(r + 4)*(r + 15)**2/9
Suppose -367*k = 174*k. Solve 4/19*t - 10/19*t**2 + 8/19*t**3 + k - 2/19*t**4 = 0 for t.
0, 1, 2
Let d be (1/((-4)/22))/((-3)/6). Factor -48*z + 13 + 558*z**2 + 76*z + 196*z + 162*z**3 + d.
2*(z + 3)*(9*z + 2)**2
Let f(t) be the first derivative of -5*t**6/9 - 14*t**5/15 - t**4/3 + 88. Let f(c) = 0. Calculate c.
-1, -2/5, 0
Let m(j) be the first derivative of -j**6/51 - 8*j**5/85 - 3*j**4/17 - 8*j**3/51 - j**2/17 + 77. Factor m(i).
-2*i*(i + 1)**4/17
Let m(h) be the second derivative of -h**4/2 - 58*h**3/3 - 19*h**2 + 508*h. Find o, given that m(o) = 0.
-19, -1/3
Let c(p) be the third derivative of 2*p**7/735 + p**6/210 - 9*p**5/140 - 9*p**4/28 - 9*p**3/14 + p**2 - 17*p. Factor c(y).
(y - 3)*(y + 1)*(2*y + 3)**2/7
Let h(c) be the second derivative of 0 - 250/3*c**3 - 11*c - c**5 - 25/2*c**4 - 625/2*c**2 - 1/30*c**6. Factor h(m).
-(m + 5)**4
Suppose b - 3*b - 5*j + 6 = 0, 0 = 2*j. Suppose 3 = a + 2*a, 5*a + 4 = b*t. Factor -6*x + 3*x**2 + 0 + 3/2*x**t - 3/4*x**4.
-3*x*(x - 2)**2*(x + 2)/4
Let g be 39/65 - 6/10. Let d(s) be the second derivative of 0*s**3 + 0*s**2 - 1/28*s**4 + g - 3/140*s**5 - 6*s. Factor d(b).
-3*b**2*(b + 1)/7
What is k in -16/11*k**2 + 0 + 2/11*k**5 - 14/11*k**4 + 0*k + 28/11*k**3 = 0?
0, 1, 2, 4
Let j(y) be the second derivative of 0 + 0*y**2 + 1/10*y**5 - 29*y - 1/12*y**4 + 0*y**3 - 1/30*y**6. Factor j(v).
-v**2*(v - 1)**2
Let s(i) be the first derivative of -3*i**5/5 - 57*i**4/4 - 99*i**3 - 243*i**2/2 + 53. Factor s(l).
-3*l*(l + 1)*(l + 9)**2
Suppose 0 = -0*g - 5*g - 25, 4*l - 4*g = 0. Let y(u) = u**2 - 25. Let i be y(l). Factor 0 - 5/2*h**5 + h**2 + i*h + 6*h**4 - 9/2*h**3.
-h**2*(h - 1)**2*(5*h - 2)/2
Let h = -7/78 + 217/390. Let x(p) be the second derivative of -2/5*p**2 + h*p**3 + 0 + 1/15*p**4 - 7/50*p**5 + 2*p. Let x(j) = 0. What is j?
-1, 2/7, 1
Let o = -85 + 89. Determine c so that -o + 3*c**3 + 6*c**2 + 5 - 1 = 0.
-2, 0
Let u be 45/2 + -4 + (-28)/(-8). Suppose 2*l - j = -3, -u + 7 = 5*l - 5*j. Find w, given that l - 1/6*w**3 - 1/3*w**2 - 1/6*w = 0.
-1, 0
Suppose -19*n + 105 - 29 = 0. Let b(k) be the first derivative of -1 + 2/25*k**5 + 0*k + 2/15*k**3 + 0*k**2 - 1/5*k**n. Solve b(x) = 0 for x.
0, 1
Suppose -6*g + 4 = 16. Let q be ((-15)/6)/(g/4). Solve 0 + 5/2*p**2 + p**q + 7/2*p**4 + 9/2*p**3 + 1/2*p = 0.
-1, -1/2, 0
Let s = 1395 + -1395. Let n(x) be the third derivative of 0*x + 12*x**2 + 2/105*x**7 - 1/15*x**5 - 1/10*x**6 + 0 + 1/2*x**4 + s*x**3. Find k such that n(k) = 0.
-1, 0, 1, 3
Let w(v) be the third derivative of -v**8/2184 - 8*v**7/1365 - v**6/60 - v**5/65 - 254*v**2. Factor w(k).
-2*k**2*(k + 1)**2*(k + 6)/13
Let i(y) = 13*y**4 + 28*y**3 + 9*y**2 - 10*y. Let o(p) = 12*p**4 + 27*p**3 + 9*p**2 - 9*p. Let j(m) = 3*i(m) - 4*o(m). Let j(z) = 0. What is z?
-2, -1, 0, 1/3
Suppose -b - 5*s + s = -14, 2*s = -2*b + 10. Let p = -18 + 56/3. Determine j, given that 0*j + 0 - p*j**b = 0.
0
Suppose 20 - 36 = 8*p. Let m(a) = 6*a + 17. Let x be m(p). Factor -2/5*r**3 + 2/5*r**4 - 2/5*r**2 + 0*r + 0 + 2/5*r**x.
2*r**2*(r - 1)*(r + 1)**2/5
Suppose 0 = 4*j + 3*k - 17, -4*j + 8 = 4*k - 8. Suppose -3*z = j*z. Let z + 0*x + 1/2*x**2 = 0. Calculate x.
0
Let d(u) be the third derivative of 3*u**7/10 - u**6 - 83*u**5/420 - u**4/84 + 464*u**2. What is x in d(x) = 0?
-1/21, 0, 2
Let f = 274/462805 + 1/11334. Let v(d) be the third derivative of -f*d**7 + 0*d + 0*d**4 + 5*d**2 + 0 + 0*d**5 + 1/420*d**6 + 0*d**3. Find r such that v(r) = 0.
0, 2
Let v be 132/15 - 4/5. Let y(w) be the third derivative of 0*w - 1/1470*w**7 + 0 - 4*w**2 + 0*w**4 + 0*w**5 - 1/2352*w**v + 0*w**3 + 0*w**6. Solve y(a) = 0.
-1, 0
Let h(j) be the third derivative of j**9/241920 - j**8/20160 + j**7/5040 + j**5/20 - 5*j**2. Let t(z) be the third derivative of h(z). Factor t(x).
x*(x - 2)**2/4
Factor 90/23*s + 4 - 2/23*s**2.
-2*(s - 46)*(s + 1)/23
Factor 2/5 - 2/5*k**2 + 2/5*k**3 - 2/5*k.
2*(k - 1)**2*(k + 1)/5
Let g(u) be the first derivative of -3/2*u + 1/8*u**4 + 1/2*u**3 - 1/4*u**2 - 18. Factor g(y).
(y - 1)*(y + 1)*(y + 3)/2
Let d = -2005 + 2005. Factor -1/2*a**5 - 2*a**2 + 0*a**3 + 3/2*a**4 + d*a + 0.
-a**2*(a - 2)**2*(a + 1)/2
Let s(q) be the second derivative of q**5/45 - q**4/9 + 2*q**3/9 - 7*q**2/2 + 8*q. Let d(i) be the first derivative of s(i). Determine u, given that d(u) = 0.
1
Let l(h) be the first derivative of -h**4/60 - h**3/15 + 21*h - 10. Let g(b) be the first derivative of l(b). What is r in g(r) = 0?
-2, 0
Factor -64/13 - 64/13*n - 2/13*n**3 - 20/13*n**2.
-2*(n + 2)*(n + 4)**2/13
Let s(w) be the third derivative of w**5/60 + 31*w**4/24 - 75*w**2. Solve s(z) = 0 for z.
-31, 0
Let p be ((-144)/352*-11)/(12/8). Factor 3*j**p - 3*j - 3/2*j**4 + 0 + 3/2*j**2.
-3*j*(j - 2)*(j - 1)*(j + 1)/2
Let z(s) be the first derivative of -s**7/280 + s**6/90 - s**5/120 - 19*s**3/3 - 5. Let w(d) be the third derivative of z(d). Solve w(g) = 0.
0, 1/3, 1
Let 0 + 20/11*d**4 - 2/11*d**5 + 120/11*d**2 - 74/11*d**3 - 72/11*d = 0. What is d?
0, 2, 3
Let x = 393/7 + -56. Let w(l) be the first derivative of 0*l - 4 + 2/21*l**3 + x*l**2 - 1/14*l**4 - 2/35*l**5. Solve w(i) = 0 for i.
-1, 0, 1
Let t be (7/21 - (-3)/(-9))/(-2). Factor 4/7*u**2 + t*u - 6/7*u**3 + 0*u**4 + 2/7*u**5 + 0.
2*u**2*(u - 1)**2*(u + 2)/7
Let g be 8/(-32)*(0 - 4) - -3. Let i(h) be the second derivative of 0 - h**3 - 1/6*h**g + 0*h**2 + 9*h. Solve i(m) = 0.
-3, 0
Let u(g) be the first derivative of g**2 + 1/6*g**6 + 0*g - 11/60*g**5 + 5 - 1/30*g**4 + 2/15*g**3. Let z(t) be t