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Let c(p) be the second derivative of -p**7/945 + p**6/135 - p**5/45 + p**4/27 - p**3/27 - p**2/2 + p. Let k(n) be the first derivative of c(n). Factor k(s).
-2*(s - 1)**4/9
Let i be ((-6)/4)/((-6)/(-8)) + 3. Factor 3/2*p + 1/2*p**2 + i.
(p + 1)*(p + 2)/2
Let h be ((-66)/(-24) - 3)*(-1 - 1). Factor h*g**2 + 0 - 1/2*g**3 + g.
-g*(g - 2)*(g + 1)/2
Let s(f) be the third derivative of 0*f + 0*f**4 + 0 + 0*f**3 - 2*f**2 - 1/80*f**6 + 1/140*f**7 + 0*f**5. Find r such that s(r) = 0.
0, 1
Factor 56*x**5 + 48*x**5 - x**2 - 4*x**2 + 5*x**4 + 5*x**3 - 109*x**5.
-5*x**2*(x - 1)**2*(x + 1)
Let v(h) be the first derivative of h**3/7 - 3*h**2/14 - 2. Factor v(a).
3*a*(a - 1)/7
Let k(i) = i**2 - 18*i - 110. Let w be k(-5). Find f, given that -4/5*f**w + 2*f**3 + 4/15 + 2/3*f**2 - 6/5*f - 14/15*f**4 = 0.
-2, -1, 1/3, 1/2, 1
Let g = -257/3 - -86. Let m(t) be the first derivative of 2/3*t**3 + 6/5*t**5 + 0*t**2 + 2 + 3/2*t**4 + 0*t + g*t**6. Let m(k) = 0. What is k?
-1, 0
Factor -3*l**2 - 48/7*l - 12/7.
-3*(l + 2)*(7*l + 2)/7
Let j(n) be the second derivative of -n**10/15120 + n**9/3780 - n**8/3360 - n**4/6 - 3*n. Let d(b) be the third derivative of j(b). Solve d(p) = 0 for p.
0, 1
Let d(a) be the third derivative of a**6/24 - a**5/4 - 15*a**4/8 - 25*a**3/6 - 16*a**2. Factor d(v).
5*(v - 5)*(v + 1)**2
Let m = 39/133 - 1/133. Let 3/7*a**2 + 0 + m*a + 1/7*a**3 = 0. What is a?
-2, -1, 0
Let g(k) be the second derivative of -k**4/84 + k**3/14 - k**2/7 + 11*k. Factor g(q).
-(q - 2)*(q - 1)/7
Let u = -23 - -41. Solve -k**2 + 12 + u*k + 4*k**2 + 15 = 0.
-3
Suppose -7*c = -0*c - 14. Let t(z) be the second derivative of -1/18*z**4 - 1/9*z**3 + 0 + 0*z**2 - c*z. Let t(m) = 0. What is m?
-1, 0
Let x = -2 + 5. Let p(d) be the second derivative of 2*d + 0 + 0*d**x - 1/3*d**2 + 1/18*d**4. Determine i so that p(i) = 0.
-1, 1
Suppose 7*p = 4 + 10. Let m be (2/(-14))/(6/(-7)). Find v, given that -1/6*v**p + m*v + 0 = 0.
0, 1
Let b = 97 - 467/5. Factor -b*j**5 - 8/5*j**3 + 0 + 0*j - 24/5*j**4 + 0*j**2.
-2*j**3*(3*j + 2)**2/5
Let p(q) = 3*q**3 + 2*q**2 - 16*q + 5. Let x(i) = 10*i**3 + 6*i**2 - 48*i + 16. Let z(j) = 8*p(j) - 3*x(j). Suppose z(r) = 0. Calculate r.
-2, 2/3, 1
Let k(q) be the second derivative of 5*q**4/4 - 2*q**3 + 6*q**2/5 + 52*q. Determine a, given that k(a) = 0.
2/5
Let y(x) = -3*x**4 + 17*x**3 - 13*x**2 - 16*x + 17. Let d(j) = j**4 + j**3 - j**2 + 1. Let l(m) = -d(m) + y(m). Suppose l(c) = 0. What is c?
-1, 1, 2
Let b = 1374 - 17858/13. Factor -2/13*o**2 + b + 2/13*o.
-2*(o - 2)*(o + 1)/13
Let d be ((-12)/27)/(-17 + 15). What is v in d*v**2 + 0 + 4/9*v = 0?
-2, 0
Let q = 7 - 4. Let -6*o**q + 3*o + o + 2*o - 3*o**4 + 3*o**2 = 0. Calculate o.
-2, -1, 0, 1
Factor 0 - 1/5*a**2 + 2/5*a.
-a*(a - 2)/5
Let m be (35/(-21))/5*(-12)/2. Factor 1/3 + 1/3*q**m + 2/3*q.
(q + 1)**2/3
Suppose -5*t + 9 + 1 = 0. Let o = 4 - t. Let -h**2 + h**o - 6*h**2 + 3 + 3*h**4 = 0. Calculate h.
-1, 1
Let -n - 9 + n**3 - 2*n**2 + 5 + 6 = 0. What is n?
-1, 1, 2
Let k = -17 + 32. Let d = 18 - k. Determine w, given that 0*w**2 - 1/3*w**d + 0 + 1/3*w = 0.
-1, 0, 1
Let k(n) be the third derivative of n**5/270 - n**4/36 + n**2. Factor k(q).
2*q*(q - 3)/9
Let o(j) = -2*j. Let q be o(-2). Factor q*w + w - w**2 - 4*w + 2.
-(w - 2)*(w + 1)
Let o(q) be the third derivative of 0*q**3 - 9*q**2 + 0*q**4 - 1/105*q**7 + 0 + 1/30*q**6 + 0*q**5 + 0*q. Factor o(l).
-2*l**3*(l - 2)
Solve 4/3*k**4 + 0 - 4*k**3 + 8/3*k**2 + 0*k = 0 for k.
0, 1, 2
Let p be 99/27 + 4/(-6). Let 2*k**3 - 2*k**4 - 8*k**p + 3*k + 5*k = 0. Calculate k.
-2, 0, 1
Let k(d) be the first derivative of -2/3*d**3 - 3 - 1/2*d**2 + 0*d - 1/4*d**4. Factor k(r).
-r*(r + 1)**2
Let k(w) = -w + 3. Let b be k(3). Suppose b = 5*z + 17 - 52. Factor -4*t**3 + 3*t**4 + z*t**3 + 0*t**4 - 3*t**5 + 4*t**5 + t**2.
t**2*(t + 1)**3
Let w(m) = m + 19. Let f be w(-15). Factor -4/3*g**2 + 0 + 2*g**3 - 2/3*g**f + 0*g.
-2*g**2*(g - 2)*(g - 1)/3
Let d be 2/10*(-20)/(-6). Let g = d - 1/3. Factor 1/3 + g*c**2 - 2/3*c.
(c - 1)**2/3
Let v(w) be the second derivative of -w**5/50 - w**4/30 + 4*w**2 - 2*w. Let m(b) be the first derivative of v(b). Find j such that m(j) = 0.
-2/3, 0
Factor 0*m - m**3 + 0*m**2 + 1/3*m**4 + 0.
m**3*(m - 3)/3
Let l be (2*(-1)/2)/(-1). Let f(d) = -d**4 + d**3 - d**2 - d - 1. Let r(o) = o**5 - o**4 - o**3 - o**2 - 1. Let p(c) = l*r(c) - f(c). Let p(m) = 0. What is m?
-1, 0, 1
Solve 26 + 4*w**2 - 13 + 4*w - 17 - 4*w**3 = 0.
-1, 1
Let u(r) be the third derivative of -r**7/42 - 11*r**6/180 - r**5/15 + 7*r**4/24 - 2*r**2. Let m(g) be the second derivative of u(g). Factor m(j).
-4*(3*j + 1)*(5*j + 2)
Suppose 5*g = -0*f - 2*f + 1, 3*g - 4*f + 15 = 0. Let l = 2 - g. Determine j so that l*j**4 + j**4 - 5*j**4 - j**2 - j**3 + 3*j**2 = 0.
-2, 0, 1
Let l(m) be the third derivative of 0 + 1/150*m**5 + 1/20*m**4 + 0*m - m**2 + 2/15*m**3. Factor l(g).
2*(g + 1)*(g + 2)/5
Suppose -2/5*m**3 + 0 + 2/5*m + 0*m**2 = 0. Calculate m.
-1, 0, 1
Let k = 31 + -27. Let h(m) be the first derivative of 0*m + k + 1/12*m**2 - 1/18*m**3. Factor h(a).
-a*(a - 1)/6
Let s be (1 - -3) + 4 + (-774)/99. What is b in s*b - 2/11*b**3 - 2/11 + 2/11*b**2 = 0?
-1, 1
Let d(m) = -15*m**2 - 15*m - 9. Let i(p) = -7*p**2 - 8*p - 5. Let f(j) = -4*d(j) + 9*i(j). Let f(c) = 0. What is c?
-3, -1
Let w(j) = -j**2 - 5*j + 6. Let c be w(-6). Let k(r) be the first derivative of 2/5*r**5 + 1/6*r**6 + 1/4*r**4 + 0*r + c*r**2 + 2 + 0*r**3. Factor k(d).
d**3*(d + 1)**2
Let j(g) be the third derivative of 2*g**7/21 - 16*g**6/15 + 4*g**5/5 + 45*g**2. Factor j(h).
4*h**2*(h - 6)*(5*h - 2)
Let w = -574 + 2897/5. Find a, given that 21/5*a**2 - 3/5*a**3 - 9*a + w = 0.
1, 3
Suppose -c = 4*j - 9 - 20, -2*c = 6. Suppose j*i - 12 = 2*i. Factor -8/7*w**i + 2/7*w**3 - 4/7 + 10/7*w.
2*(w - 2)*(w - 1)**2/7
Suppose -7*n + 10*n = 6. Factor n*x**2 + 0*x**3 - 2*x**3 + 2 - 6*x + 4*x**2.
-2*(x - 1)**3
Let y be -1 + (-190)/(-198) + 122/549. Factor -16/11*g**2 + 0*g + 0 + y*g**5 - 12/11*g**4 + 24/11*g**3.
2*g**2*(g - 2)**3/11
Find j, given that 5/2*j + 5*j**2 + 0 + 5/2*j**3 = 0.
-1, 0
Let s be ((-6)/1)/((-2)/1). Let 6*d**2 - 3*d + 4*d + 0*d**2 + 2*d - 6 - 3*d**s = 0. What is d?
-1, 1, 2
Let k = 229 - 227. Factor -16/5*o + 8/5 + k*o**2 - 2/5*o**3.
-2*(o - 2)**2*(o - 1)/5
Let u = 109 - 871/8. Let h(x) be the first derivative of 1 - 3/4*x**2 + 1/2*x**3 - u*x**4 + 1/2*x. What is c in h(c) = 0?
1
Let d be (5/3)/(5/6). Let m(h) be the first derivative of -3*h**d - 1/2*h**4 + 2 - 2*h - 2*h**3. What is l in m(l) = 0?
-1
Suppose -7*b = -2*b - 5*y + 30, 5*y = -2*b - 19. Let a be b/(-14)*(-2)/(-2). Factor 0*k**2 + 2*k**4 + 0*k + 0 + a*k**3 + 3/2*k**5.
k**3*(k + 1)*(3*k + 1)/2
Let z(h) be the first derivative of 5*h**3/3 - 55*h**2/2 + 50*h - 20. Find y such that z(y) = 0.
1, 10
Let m(b) be the second derivative of -b**5/4 + 5*b**4/6 + 5*b**3/6 - 5*b**2 + 10*b. Determine s, given that m(s) = 0.
-1, 1, 2
Let v be -2 + 4 - 0/(-3). Suppose v*m**2 + 0*m**4 + 0*m**2 + 4*m**3 + 2*m**4 = 0. What is m?
-1, 0
Let y = 46 - 68. Let h be 14/44 + (-4)/y. Factor h*l**2 - 1/2 + 0*l.
(l - 1)*(l + 1)/2
Let l be (7/(-2) + 3)/((-3)/12). Suppose -8/7 + 8/7*g - 2/7*g**l = 0. Calculate g.
2
Let j(z) be the first derivative of -z**6/2520 + z**4/168 + z**3 + 1. Let m(g) be the third derivative of j(g). What is d in m(d) = 0?
-1, 1
Determine h, given that 0*h**4 + 1/7*h**5 - 2/7 + 2/7*h**2 + 3/7*h - 4/7*h**3 = 0.
-2, -1, 1
Let o(k) be the first derivative of 9*k**4/2 + 8*k**3 + k**2 - 4*k - 18. Find a such that o(a) = 0.
-1, -2/3, 1/3
Let t(k) be the first derivative of k**4/28 + k**3/21 - k**2/14 - k/7 - 21. What is g in t(g) = 0?
-1, 1
Let b = 20 + -10. Let n = b + -10. Solve -2/11*l**4 + n*l**2 + 0*l + 0*l**3 - 2/11*l**5 + 0 = 0.
-1, 0
Let q be (4/1)/((-18)/(-3)). Let 4/3*s - q*s**2 - 2/3 = 0. What is s?
1
Let p(f) be the first derivative of f**6/8 + 3*f**5/20 - 3*f**4/16 - f**3/4 - 7. Factor p(y).
3*y**2*(y - 1)*(y + 1)**2/4
Let a(s) = s**3 + 8*s**2 - 9*s + 4. Let y be a(-9). Suppose -9 = -y*d - 1. Factor -p**2 + 3*p**2 - 2 + 0*p**d.
2*(p - 1)*(p + 1)
Let h(m) be the first derivative of m**5/390 - 5*m**2/2 - 4. Let n(g) be the second derivative of h(g). Suppose n(c) = 0. Calculate c.
0
Factor 0 + 4/11*l + 2/11*l**3 - 6/11*l**2.
2*l*(l - 2)*(l - 1)/11
Let h