 - 1)/7
Let n(a) be the first derivative of -6 + 11/6*a**3 + 9/4*a - 1/2*a**4 + 1/20*a**5 - 3*a**2. Factor n(l).
(l - 3)**2*(l - 1)**2/4
Let d(a) be the first derivative of a**6/42 - a**4/14 + a**2/14 + 118. Factor d(s).
s*(s - 1)**2*(s + 1)**2/7
Let a(l) be the first derivative of -20*l**3 - 15 + 0*l + 10*l**2 - 6*l**5 + 65/4*l**4 + 5/6*l**6. Find h, given that a(h) = 0.
0, 1, 2
Let c = -4107 + 4112. Factor 0 + 1/9*w**c + 0*w**2 + 0*w + 1/9*w**4 - 2/9*w**3.
w**3*(w - 1)*(w + 2)/9
Let c(y) be the third derivative of y**8/168 - y**7/49 + 3*y**6/140 - y**5/210 + 65*y**2. Factor c(d).
2*d**2*(d - 1)**2*(7*d - 1)/7
Let c = 133 - 131. Let h(n) = n**2 + 7*n + 5. Let s be h(-7). Let a(z) = z**2 + z. Let f(v) = -2*v**2 - 2*v. Let k(r) = c*f(r) + s*a(r). Factor k(y).
y*(y + 1)
Find j, given that -28*j**3 - 3*j**5 - 57*j + 60*j**3 + 9*j**2 + 8*j**4 + 21*j**2 + 28*j**3 + 4*j**4 - 42 = 0.
-2, -1, 1, 7
Suppose 0 = -5*j - k + 40, j + 5*k - 10 = -2. Suppose g - 3*g = -j. Let p(n) = n**2 - 2*n. Let b(v) = 2*v. Let i(t) = g*b(t) + 5*p(t). What is y in i(y) = 0?
0, 2/5
Let i(p) be the third derivative of -1/60*p**6 + 0*p + 1/12*p**4 + 0 + 1/105*p**7 - 1/30*p**5 - 34*p**2 + 0*p**3. Suppose i(f) = 0. Calculate f.
-1, 0, 1
Let v(s) be the second derivative of -s**7/105 + s**6/30 + s**5/10 + s**2/2 + 8*s. Let h(d) be the first derivative of v(d). Determine b so that h(b) = 0.
-1, 0, 3
Let t(v) be the second derivative of 0*v**3 + 0 - 1/15*v**6 + 1/6*v**4 + 1/21*v**7 - 1/10*v**5 + 0*v**2 - 6*v. Factor t(h).
2*h**2*(h - 1)**2*(h + 1)
Let t be 1*2/(-1) + (6 - 1). Factor 47 + 192*n - 55 - 127 - 12*n + 5*n**4 - 30*n**2 - 20*n**t.
5*(n - 3)**2*(n - 1)*(n + 3)
Factor -3*l + 14*l**2 - 119*l**3 + 131*l**3 + 21*l**2.
l*(l + 3)*(12*l - 1)
Let h = 3148 - 18881/6. Suppose -h*s**2 + 0*s + 1/6*s**3 + 0 = 0. What is s?
0, 7
Let o(n) = -2*n**2 + 2*n - 1. Let j(m) = -15*m**2 - 423*m + 141. Let u(s) = j(s) - 3*o(s). Solve u(g) = 0.
-48, 1/3
Let f(t) be the second derivative of t**7/252 - t**6/90 + t**4/36 - t**3/36 - 14*t - 2. What is m in f(m) = 0?
-1, 0, 1
Let z(y) be the third derivative of -y**8/1680 - y**7/1050 + y**6/300 + y**5/150 - y**4/120 - y**3/30 + 55*y**2. Factor z(f).
-(f - 1)**2*(f + 1)**3/5
Let y(q) be the third derivative of -5*q**2 + 1/45*q**5 + 0*q - 2/9*q**3 + 0 + 0*q**4. Factor y(s).
4*(s - 1)*(s + 1)/3
Let p(q) = -3*q + 17. Let y(v) = -v + 9. Let f(k) = -2*p(k) + 5*y(k). Let n be f(-9). Factor 9 - 4*s**2 - 6*s + 5*s**n + 0*s**2.
(s - 3)**2
Let j(k) = -42*k**2 + 33*k + 24. Let m(d) = -5*d**2 + 4*d + 3. Let b(c) = -2*j(c) + 17*m(c). Factor b(u).
-(u - 3)*(u + 1)
Let d be 13 - (-11)/((-11)/11). Factor 0 - 8/5*m - 12/5*m**d.
-4*m*(3*m + 2)/5
Let d(x) be the second derivative of x**6/10 - 21*x**5/5 + 83*x**4/2 + 210*x**3 + 675*x**2/2 + 223*x. Solve d(j) = 0.
-1, 15
Let w be 4 + 0/4 + 14/(-12). Let q(h) be the first derivative of -2/3*h - w*h**4 + 1/6*h**2 - 7/18*h**6 + 16/9*h**3 - 3 + 26/15*h**5. Let q(z) = 0. Calculate z.
-2/7, 1
Let o(c) be the third derivative of -1/21*c**4 + 0*c - 1/105*c**5 + 0*c**3 + 0 - 12*c**2. Solve o(r) = 0 for r.
-2, 0
Let x = 35 - 33. Determine g, given that -10*g - g**2 + 0*g**2 - 4*g**x - 5 + 0*g**2 = 0.
-1
Factor 18*v - 180 - 3*v**2 - 6*v - 3*v**3 + 192.
-3*(v - 2)*(v + 1)*(v + 2)
Let t = -73553/7 - -10508. Factor -1/7*b**2 + t + 2/7*b.
-(b - 3)*(b + 1)/7
Suppose 10 = -5*d + o, 5*d - 4*o = -5 - 5. Let j be (-106)/(-20) - (4 + 7/d). Factor -21/5*n**4 + 0 - 12*n**2 - j*n - 54/5*n**3 - 3/5*n**5.
-3*n*(n + 1)*(n + 2)**3/5
Let g(r) = 76*r - 25. Let x be g(4). Suppose 280*w - 5 = x*w. Suppose 1/4*u**3 + 0*u + 0 + 1/4*u**4 - 1/4*u**w - 1/4*u**2 = 0. What is u?
-1, 0, 1
Let q(c) = -14*c**2 - 1. Let z be q(-1). Let w = 19 + z. Factor 5*t + 8*t**2 - 8*t**3 + 20*t**w + 3*t - 28*t**2.
4*t*(t - 1)*(t + 1)*(5*t - 2)
Let d(h) be the first derivative of 3*h**4/32 - 97*h**3/8 - 591*h**2/16 - 297*h/8 + 345. Suppose d(n) = 0. Calculate n.
-1, 99
Suppose -y + 4*w - 18 = 0, -16 = 2*y - 59*w + 55*w. Factor 2/11*b**3 + 24/11 + 14/11*b**y + 32/11*b.
2*(b + 2)**2*(b + 3)/11
Let v(o) be the second derivative of -o**7/14 - o**6/5 - 3*o**5/20 + 6*o - 7. Suppose v(k) = 0. Calculate k.
-1, 0
Suppose -227*j = -211*j - 32. Solve 2*o**3 - 18/5*o**j - 2/5*o**4 - 4/5 + 14/5*o = 0 for o.
1, 2
Determine i so that 68*i**2 - 44*i**2 - 39*i**2 + 3*i**3 - 42*i = 0.
-2, 0, 7
Let h(w) be the third derivative of -2*w**7/105 - w**6/30 + 4*w**5/15 + 2*w**4/3 - w**2 - 112*w. Find m, given that h(m) = 0.
-2, -1, 0, 2
Let q(g) be the third derivative of 7*g**6/24 + 19*g**5/2 + 685*g**4/24 + 25*g**3 + g**2 + 43*g. Factor q(h).
5*(h + 1)*(h + 15)*(7*h + 2)
Let i = -2475 - -2477. Find c such that -2/5*c + 1/5*c**i + 1/5 = 0.
1
Let x(f) be the second derivative of -f**5/45 + f**4/9 + 2*f**3/27 - 2*f**2/3 + 153*f. Factor x(r).
-4*(r - 3)*(r - 1)*(r + 1)/9
Let o(n) be the first derivative of -2*n**5/3 - 131*n**4/3 - 6968*n**3/9 - 1352*n**2/3 + 354. Solve o(p) = 0 for p.
-26, -2/5, 0
Let t(v) be the third derivative of -5*v**8/448 - 3*v**7/280 - 175*v**2. Determine f so that t(f) = 0.
-3/5, 0
Let d be (14 - 8)/(3/14). Factor 10*y**3 - d*y**2 - 5*y**4 + 10*y + 10*y**3 + 3*y**2 + 0*y**4.
-5*y*(y - 2)*(y - 1)**2
Let n(x) = x**4 + x**3 + 4*x**2 + 2*x + 1. Let g(a) = -4*a**4 + 2*a**3 - 9*a**2 - 5*a - 5. Let f(m) = -g(m) - 5*n(m). Determine o so that f(o) = 0.
-5, -1, 0
Suppose 3*q = -5*w - 2, -4*w + 5*q + 28 = -0*q. Suppose -67 = -11*k - 1. Find v such that -k*v + v**3 - 6*v**w - 2*v**3 - v**3 - 2 = 0.
-1
Determine r so that 1/2*r**2 + 0 + 7/2*r = 0.
-7, 0
Let i(d) be the second derivative of -d**5/160 - d**4/96 + d**3/24 + 16*d - 1. Suppose i(s) = 0. What is s?
-2, 0, 1
Suppose 21 = 5*z - 24. Suppose -z = -g - 5. Factor -16/9*m**3 + 0 + 0*m + 32/9*m**g + 2/9*m**2.
2*m**2*(4*m - 1)**2/9
Suppose -5*s = -406 + 1071. Let v = s - -400/3. Factor -2/3*i**3 + v*i**4 + 1/3*i + 1/3*i**5 + 1/3 - 2/3*i**2.
(i - 1)**2*(i + 1)**3/3
Let n(g) = -g + 9. Let z be n(3). Factor 2*r**3 + z*r**2 - r - 4*r**2 + r.
2*r**2*(r + 1)
Suppose 11 - 1 = 5*u. Suppose -u*c + 5 + 9 = 0. Determine r, given that 6*r**4 + 36*r**3 - c*r**5 + 11*r**5 - 2*r**2 + 8*r + 30*r**2 + 14*r**4 = 0.
-2, -1, 0
Let q(b) be the first derivative of 9*b**3 - 42*b**2 + 196*b/3 + 17. Determine y so that q(y) = 0.
14/9
Let h(j) = -4*j**4 + 43*j**3 + 7*j**2 - 40*j - 3. Let p(f) = 4*f**4 - 42*f**3 - 6*f**2 + 40*f + 2. Let m(a) = -2*h(a) - 3*p(a). Factor m(i).
-4*i*(i - 10)*(i - 1)*(i + 1)
Let l(v) = -2*v**5 + 28*v**4 - 71*v**3 + 67*v**2 - 21*v + 1. Let n(y) = -y**5 + 2*y**4 - y**3 - y**2 - 1. Let b(p) = -l(p) - n(p). What is j in b(j) = 0?
0, 1, 7
Let r be (1/1)/((-3)/156). Let v be ((-20)/r)/5*4. Factor 0 - v*p + 30/13*p**3 - 2/13*p**2 - 38/13*p**4 + 14/13*p**5.
2*p*(p - 1)**3*(7*p + 2)/13
Let v(b) be the third derivative of b**5/150 + 17*b**4/30 + 11*b**3/5 + b**2 + 3. Suppose v(q) = 0. What is q?
-33, -1
Factor 0*o**2 + 4*o**4 - 4*o**2 - 2*o**4 - 4*o**2.
2*o**2*(o - 2)*(o + 2)
Let w(a) be the third derivative of a**6/120 - a**5/5 + 2*a**4 + 25*a**3/6 - 3*a**2. Let x(v) be the first derivative of w(v). Factor x(z).
3*(z - 4)**2
Suppose -12 + 22 = 5*u. Factor h**3 + 125 - h**2 + 40*h**2 + 75*h - 24*h**u.
(h + 5)**3
Let j(n) = -3*n**3 - 1. Let t be j(-1). Suppose 0 = -8*o + 3*o + 5*v + 40, 5*o - 2*v - 43 = 0. Solve 2*b + o*b**2 - 7*b**t + b**3 - b = 0 for b.
-1, 0
Let v(a) be the third derivative of 0 + 0*a**3 + 0*a - 1/15*a**5 + a**2 + 1/20*a**6 - 1/105*a**7 + 0*a**4. Factor v(s).
-2*s**2*(s - 2)*(s - 1)
Let v be 3 - 0 - (4/(-6) + 2101/573). Let 7/2*d**3 + 10/3*d**2 + v + 1/12*d**5 + 4/3*d**4 + 13/12*d = 0. What is d?
-13, -1, 0
Let y(u) be the third derivative of u**5/120 + 3*u**4/8 + 27*u**3/4 - u**2 - 9*u. Suppose y(s) = 0. Calculate s.
-9
Let c be 12/14*(-7)/(-2). Factor -32*a**4 - 4*a**5 + 4*a**c + 36*a**4 - 7*a**2 + 3*a**2.
-4*a**2*(a - 1)**2*(a + 1)
Let w(j) = -j**2 + 15*j + 57. Let r be w(18). Suppose -2*n + 4 = 2*n + 2*m, -4*n + r*m = -24. Determine i, given that 0*i**2 + 3/4*i - 1/4*i**n + 1/2 = 0.
-1, 2
Let q(f) be the second derivative of -f**6/40 + 9*f**5/80 - f**4/16 - 3*f**3/8 + 3*f**2/4 + 24*f. Determine r, given that q(r) = 0.
-1, 1, 2
Let y(x) be the first derivative of -1/10*x**4 - 16 + 4/5*x + 0*x**3 + 3/5*x**2. Find m such th