u + 1)**2
Let k(q) be the second derivative of q**5/40 + q**4/12 + q**3/12 - 7*q. Determine a, given that k(a) = 0.
-1, 0
Let y be (-1)/((-1)/(-5))*2/(-5). Let b(c) be the second derivative of 0 + 1/18*c**3 - 1/12*c**4 + c + 1/30*c**5 + 0*c**y. Factor b(f).
f*(f - 1)*(2*f - 1)/3
Let a(v) = 3*v + 11. Let d be a(-5). Let x be (d/(-10))/((-6)/(-60)). Factor 2 - x*f + 5/2*f**2 - 1/2*f**3.
-(f - 2)**2*(f - 1)/2
Let h(y) = 8*y**3 - 7*y**2 + 21*y. Let v be 2*(-1)/(6/(-39)). Let a(l) = 4*l**3 - 4*l**2 + 10*l. Let n(o) = v*a(o) - 6*h(o). Find f such that n(f) = 0.
0, 1/2, 2
Let b(q) be the second derivative of 1/56*q**7 - 3/40*q**5 + 1/8*q**4 + 1/8*q**3 + 0 + 3*q - 3/8*q**2 - 1/40*q**6. Factor b(d).
3*(d - 1)**3*(d + 1)**2/4
Let c(n) be the second derivative of -1/12*n**4 + 2*n - 8*n**2 + 0 + 4/3*n**3. Factor c(b).
-(b - 4)**2
Let f(c) = -c**2 - 6*c - 2. Let q be f(-5). Let o(g) be the third derivative of 0 + g**2 - 1/30*g**5 + 1/60*g**6 + 0*g - 1/12*g**4 + 1/3*g**q. Factor o(m).
2*(m - 1)**2*(m + 1)
Let j(i) be the third derivative of 0 + 1/360*i**6 + 0*i + 0*i**3 + 0*i**4 - 2*i**2 + 1/180*i**5 - 1/315*i**7. Determine p so that j(p) = 0.
-1/2, 0, 1
Suppose -7*t - 2*t = 5*t. Suppose 0 + t*l + 2/5*l**2 + 6/5*l**4 + 2/5*l**5 + 6/5*l**3 = 0. What is l?
-1, 0
Let g = 2/29721 - -20418317/148605. Let n = g + -137. Suppose n*u**3 + 4/5*u - 1/5 - u**2 = 0. What is u?
1/2, 1
Let d(z) be the third derivative of 0*z**7 + 1/168*z**8 + 0*z**5 + 0*z**4 + 0*z - 1/60*z**6 + 2*z**2 + 0*z**3 + 0. Factor d(p).
2*p**3*(p - 1)*(p + 1)
Let w(z) be the third derivative of -z**6/60 + z**5/10 - 4*z**3/3 - 17*z**2. Factor w(i).
-2*(i - 2)**2*(i + 1)
Let s(g) = g**2 - 1. Let r(n) = 95*n**2 - 84*n + 21. Let y(v) = r(v) + 3*s(v). Factor y(t).
2*(7*t - 3)**2
Let t(w) be the second derivative of 3*w**8/560 - w**7/28 + w**6/10 - 3*w**5/20 + w**4/8 + w**3/2 + 5*w. Let u(x) be the second derivative of t(x). Factor u(y).
3*(y - 1)**3*(3*y - 1)
Factor 2/5*d + 0 + 0*d**2 - 2/5*d**3.
-2*d*(d - 1)*(d + 1)/5
Let y(t) be the second derivative of t**6/70 + 3*t**5/35 + 3*t**4/14 + 2*t**3/7 + 3*t**2/14 + 4*t. Factor y(h).
3*(h + 1)**4/7
Let x(b) be the third derivative of -6*b**2 + 0*b + 1/30*b**5 + 1/3*b**3 + 0 - 1/6*b**4. Factor x(t).
2*(t - 1)**2
Suppose 3*a + 3 + 0 = 0. Let l(t) = -t**2 - t + 1. Let s(g) = 7*g**3 + 16*g**2 + 7*g - 6. Let u(n) = a*s(n) - 4*l(n). Factor u(b).
-(b + 1)**2*(7*b - 2)
Let j(l) be the second derivative of -1/24*l**3 + 3*l + 0 - 1/48*l**4 + 1/4*l**2. Suppose j(g) = 0. What is g?
-2, 1
Let n(g) be the second derivative of -g**7/280 - g**6/60 + 4*g**3/3 - 8*g. Let p(r) be the second derivative of n(r). What is a in p(a) = 0?
-2, 0
Let b(j) be the second derivative of -3/10*j**5 + 0 + j**3 + 2*j - 3/10*j**6 + 0*j**2 + 3/4*j**4. Factor b(g).
-3*g*(g - 1)*(g + 1)*(3*g + 2)
Let q(r) be the first derivative of 5 - 2/3*r - 1/3*r**3 - 5/6*r**2. Let q(g) = 0. Calculate g.
-1, -2/3
Let n(u) = -36*u**2 - 9*u. Suppose 3*j - 12 = 9. Let g(t) = -24*t**2 - 6*t. Let m(q) = j*g(q) - 5*n(q). Solve m(p) = 0.
-1/4, 0
Let t(h) = h + 8. Let f be t(-5). Let c = -2 - -6. Suppose 8*m**f - 2*m + m**4 + 4*m**c - m**2 + 2*m**2 = 0. What is m?
-1, 0, 2/5
Let u be (-1)/4 - 146/(-72) - 0. Suppose 5*f - 3*f = 6. Find y such that -4/9*y**2 + 2/9*y**4 + 2/9 + u*y**f - 8/9*y - 8/9*y**5 = 0.
-1, 1/4, 1
Let n = -4 - -10. Let d(i) = -i**2 + 9*i - 14. Let f be d(n). Find y, given that 2/7*y**3 + 0 + 2/7*y**f + 0*y + 0*y**2 = 0.
-1, 0
Let d(c) = -c**2 + 6*c + 9. Let o be d(8). Let n = -7 - o. Solve 0 + n*h + 2/7*h**2 = 0 for h.
0
Let h be (3/60*4)/1. Suppose 0 + h*s**2 + 0*s = 0. Calculate s.
0
Suppose 4*k = 0, 5*k - 1 = -3*i + 17. Factor g**3 - 2 + 3*g + 4*g**3 + 3*g - i*g**2 - 3*g**3.
2*(g - 1)**3
Let g(r) be the third derivative of r**8/10080 + r**7/1260 - r**5/60 + r**2. Let n(t) be the third derivative of g(t). Factor n(o).
2*o*(o + 2)
Let u = -1034 + 1037. Factor 0*x + 1/4*x**2 + 3/4*x**u + 0.
x**2*(3*x + 1)/4
Determine u so that 32/5*u**4 + 128/5*u**5 + 22/5*u**2 - 72/5*u**3 - 2/5*u + 0 = 0.
-1, 0, 1/4
Let -4/3*y**3 + 8/3*y - 10/3*y**2 + 2 = 0. What is y?
-3, -1/2, 1
Suppose 2*u + 6 = 5*u. Let k(c) be the first derivative of 1/5*c**u + 1/10*c**4 + 0*c - 3 + 4/15*c**3. Suppose k(l) = 0. Calculate l.
-1, 0
Factor 0 - 4/5*g - 6/5*g**2 - 2/5*g**3.
-2*g*(g + 1)*(g + 2)/5
Let s(v) = v**3 - 2*v**2 + 3*v - 3. Let t be s(2). Let n be (1 + 1 - 1)*t. Find h such that -h + h**2 + 1 - h**4 + h**n - 1 = 0.
-1, 0, 1
Suppose 2*l - 4*l + p + 4 = 0, -3*p = l + 12. Let l*i + 1/2*i**4 - i**2 - 1/2*i**3 + 0 = 0. What is i?
-1, 0, 2
Let u(z) be the second derivative of z**4/90 + 2*z**3/45 - 2*z. Let u(l) = 0. Calculate l.
-2, 0
Let l(k) be the second derivative of k**7/63 - k**5/15 + k**3/9 - 11*k. Factor l(i).
2*i*(i - 1)**2*(i + 1)**2/3
Let b(h) = 4*h - 6. Let n(m) = m**2 + 7*m - 13. Let a be -1*(-2 + 3)*2. Let q(y) = a*n(y) + 5*b(y). Determine r, given that q(r) = 0.
1, 2
Let k(f) be the first derivative of 25/8*f**6 + 3*f - 23/4*f**3 + 57/16*f**4 - 3 + 33/4*f**5 - 3*f**2. Determine i so that k(i) = 0.
-1, 2/5
Suppose -2 = -3*j + 4. Let q = j - 0. Let -4*x**3 - 2*x**4 + 6*x**2 - x**3 + 4 + q*x + 3*x**3 + 8*x = 0. What is x?
-1, 2
Let n(c) = c**3 - 3*c**2 - 2*c - 5. Let j be n(4). Let b(o) be the second derivative of -1/5*o**2 + 2*o - 1/10*o**4 + 0 + 1/5*o**j + 1/50*o**5. Factor b(w).
2*(w - 1)**3/5
Let a(p) be the third derivative of 1/60*p**4 + 0*p + 0*p**3 + 0 + 2*p**2 + 1/300*p**6 + 1/75*p**5. What is l in a(l) = 0?
-1, 0
Let v(a) be the first derivative of -a**6/4 + 9*a**5/5 - 39*a**4/8 + 6*a**3 - 3*a**2 - 55. Let v(i) = 0. What is i?
0, 1, 2
Let k(o) be the third derivative of o**6/40 + o**5/20 - o**4/4 + 11*o**2. Factor k(v).
3*v*(v - 1)*(v + 2)
Let g(c) be the third derivative of -c**8/420 + c**6/30 + c**5/15 + c**3/3 - 4*c**2. Let n(x) be the first derivative of g(x). Solve n(w) = 0 for w.
-1, 0, 2
Suppose 2*j = -3*f + 13, 7*j = -4*f + 6*j + 14. Let 0*r**2 + 0*r**4 + 0*r**f + 0 + 0*r + 1/3*r**5 = 0. Calculate r.
0
Let g(m) be the second derivative of -3*m + 0*m**2 - 1/540*m**6 + 0 + 1/6*m**3 + 1/90*m**5 - 1/36*m**4. Let t(i) be the second derivative of g(i). Factor t(c).
-2*(c - 1)**2/3
Let d = 3 - -1. Let l(i) be the third derivative of 0 - i**2 - 1/240*i**6 - 1/120*i**5 + 0*i + 0*i**3 + 0*i**d. Let l(c) = 0. Calculate c.
-1, 0
Let b be (((-8)/(-90))/(-1))/(12/(-120)). Factor -b - 26/9*p**2 - 8/3*p - 2/9*p**4 - 4/3*p**3.
-2*(p + 1)**2*(p + 2)**2/9
Let q(p) be the third derivative of p**8/10080 - 13*p**7/12600 - p**6/300 + p**5/60 - p**2. Let i(w) be the third derivative of q(w). Let i(z) = 0. Calculate z.
-2/5, 3
Let c = -2/29 + 35/87. Let f(x) be the first derivative of -2*x**2 - 4 - c*x**3 - 4*x. Factor f(s).
-(s + 2)**2
Let y = 1718/91 - 212/13. Find o, given that y*o**3 + 24/7*o**2 + 0 + 8/7*o = 0.
-2/3, 0
Let i(b) be the first derivative of b**3/6 - b**2/4 - b - 13. Suppose i(m) = 0. Calculate m.
-1, 2
Let r be ((-55)/(-10))/((-1)/10). Let h be (-10)/r + (-24)/(-110). Factor -2/5*k**3 + 0 + 2/5*k + h*k**4 - 2/5*k**2.
2*k*(k - 1)**2*(k + 1)/5
Factor -2/17*v + 0 - 2/17*v**2.
-2*v*(v + 1)/17
Let j(m) = -m**2 + 7*m - 6. Let r be j(4). Factor 12 + 2*u**2 - 20 + r.
2*(u - 1)*(u + 1)
Let k(o) be the second derivative of -5*o**4/24 - 5*o**3/12 - 2*o. Determine g so that k(g) = 0.
-1, 0
Let i be 48/18*18/8. Let -v**2 - v + 3 + 5 - i = 0. Calculate v.
-2, 1
Let b be 9/(-60) + (-6)/(-15). Determine n, given that -b*n**2 + 5/4*n**4 + 1/4*n**5 - 2*n + 7/4*n**3 - 1 = 0.
-2, -1, 1
Let h(l) be the third derivative of -l**7/630 - l**6/40 - 2*l**5/15 - 2*l**4/9 + 14*l**2. Factor h(f).
-f*(f + 1)*(f + 4)**2/3
Suppose -3*q = -5*x - 233, 2*x + 2*q = 6*x + 186. Let t = 65 + x. Factor -14*j**3 - t*j - 32*j**2 - 4 + 6*j - 9*j.
-2*(j + 1)**2*(7*j + 2)
Suppose 2*y + 2*y - 12 = 0. Let q(t) be the second derivative of 0 + 4/45*t**6 + 0*t**2 + 1/18*t**4 + 1/6*t**5 + t + 0*t**y. Find i such that q(i) = 0.
-1, -1/4, 0
Suppose 2*b + 5 = c, -c - 17 = -6*c + 2*b. Let k(v) be the second derivative of 0 - 1/6*v**2 + c*v - 1/36*v**4 + 1/9*v**3. Factor k(u).
-(u - 1)**2/3
Let h be (50/90)/(15/18). Let r(t) be the first derivative of -1/6*t**6 + 1/2*t**2 + 1 - h*t**3 + 0*t + 2/5*t**5 + 0*t**4. Suppose r(m) = 0. Calculate m.
-1, 0, 1
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