et d(c) be the third derivative of -1/180*c**5 + 0*c**4 + 1/18*c**3 - c**2 + r*c + 0. Factor d(g).
-(g - 1)*(g + 1)/3
Let j = -313/56 - -55/8. Factor -12/7*c**2 - 33/7*c + j.
-3*(c + 3)*(4*c - 1)/7
Let y(d) = d**2 + 6*d + 7. Let t be y(-5). Let b(f) = -f**2 - 5*f - 3. Let n be b(-2). Suppose 2*v**n + t*v - v - v - 2*v = 0. What is v?
-1, 0, 1
Let q(g) be the second derivative of 5*g**4/12 + g**3/3 + 3*g**2/2 + 3*g. Let s(j) = -j**2 - j - 1. Let y = -22 + 21. Let b(t) = y*q(t) - 6*s(t). Factor b(i).
(i + 1)*(i + 3)
Factor 2*q**4 - 5*q**2 + 0*q**4 - 3*q**3 - 3*q**3 + 3*q**2 + 6*q**2.
2*q**2*(q - 2)*(q - 1)
Let f(r) be the second derivative of -r**6/12 - 3*r**5/8 + 5*r**3/3 + 18*r + 2. Solve f(o) = 0 for o.
-2, 0, 1
Let n(m) be the first derivative of 3*m + 41 + 1/4*m**3 - 3/2*m**2. Factor n(a).
3*(a - 2)**2/4
Let k(z) be the second derivative of -z**4/54 - 28*z**3/27 - 44*z**2/3 + 680*z. Factor k(x).
-2*(x + 6)*(x + 22)/9
What is j in 25/4*j**2 + 1 + 3/2*j**3 + 7*j = 0?
-2, -1/6
Find n, given that 78*n**2 - 16*n**4 - 27*n**4 + 22*n**3 + 168 + 3*n**5 - 276*n + 37*n**3 - 2*n**3 + 13*n**4 = 0.
-2, 1, 2, 7
Suppose y - 2 = -3*q - 0*y, -y = -2. Factor -l**4 + 3*l**3 + 11*l**2 - 24*l**2 + 2 - 3*l + 12*l**2 + q*l.
-(l - 2)*(l - 1)**2*(l + 1)
Let a(y) be the first derivative of -5*y - 11*y**3 - 8 - 5*y**4 - y**5 - 10*y**2 - 12*y**3 + 13*y**3. Factor a(i).
-5*(i + 1)**4
Let v(f) = -7*f - 39. Let k be v(-6). Let x(o) be the first derivative of 4 - 6/25*o**5 + 0*o**2 + 1/10*o**4 + 0*o**k - 4/15*o**6 + 0*o. Factor x(y).
-2*y**3*(y + 1)*(4*y - 1)/5
Let i(o) = -o**3 - 12*o**2 + o + 14. Let d be i(-12). Let -8*m - d*m**2 + 4*m + 0*m**2 = 0. What is m?
-2, 0
Let y(n) be the third derivative of 0 + 0*n**4 + 0*n - 11/80*n**6 - 1/32*n**8 - 4/35*n**7 + 7*n**2 + 0*n**3 - 1/20*n**5. Factor y(t).
-3*t**2*(t + 1)**2*(7*t + 2)/2
Let i(x) be the first derivative of x**8/336 - x**6/30 - 7*x**2/2 - 28. Let d(k) be the second derivative of i(k). Let d(b) = 0. Calculate b.
-2, 0, 2
Suppose 35/3*p**4 - 5/3*p**5 + 10/3*p**2 + 25*p - 70/3*p**3 - 15 = 0. What is p?
-1, 1, 3
Suppose -54*n**3 - 14*n**2 - 51*n**3 + 154*n**3 - 51*n**3 = 0. What is n?
-7, 0
Let j(y) be the second derivative of -24*y - 1/39*y**3 + 5/26*y**4 + 0 - 19/130*y**5 - 2/13*y**2 + 7/195*y**6. Solve j(c) = 0 for c.
-2/7, 1
Let x(r) = -r**4 + 156*r**3 - 4084*r**2 - 17952*r - 18490. Let q(u) = u**4 - 160*u**3 + 4084*u**2 + 17952*u + 18489. Let a(o) = 6*q(o) + 7*x(o). Factor a(y).
-(y - 68)**2*(y + 2)**2
Let o(b) be the second derivative of 1/45*b**7 + 2/225*b**6 + 0*b**2 + 0 + 10*b + 4/45*b**4 + 4/45*b**3 - 7/50*b**5. Let o(h) = 0. What is h?
-2, -2/7, 0, 1
Let i(d) = 21*d**4 - 87*d**3 + 36*d**2 + 6*d + 6. Let k(z) = 22*z**4 - 88*z**3 + 37*z**2 + 7*z + 7. Let f(p) = 7*i(p) - 6*k(p). Factor f(c).
3*c**2*(c - 5)*(5*c - 2)
Let h = -1124 - -2249/2. Factor -h*r**2 + 0 + 1/2*r.
-r*(r - 1)/2
Let v(m) be the third derivative of m**5/150 - m**4/30 + m**3/15 - 7*m**2 + 7*m. Factor v(x).
2*(x - 1)**2/5
Suppose -2*n + p = 5*p - 12, 15 = -3*n + 5*p. Suppose 5*t + 3*y + 12 = 0, -4*t = -0*y + y + 4. Let t*z**2 + 4*z**3 + n*z**2 - 2*z**3 = 0. What is z?
0
Determine l, given that 2/9*l**2 + 0 + 1/9*l**3 - 2/9*l**4 - 1/9*l**5 + 0*l = 0.
-2, -1, 0, 1
Find b such that 11*b**2 + 14*b**2 + 23*b**2 - 5*b**3 - 80*b - 8*b**2 + 0*b**2 = 0.
0, 4
Let n be (1/2 + 4/(-8))*-1. Let g(v) be the second derivative of -1/8*v**4 + 0 + 3/4*v**2 + n*v**3 + v. Solve g(a) = 0 for a.
-1, 1
Suppose 0 = -17*m + 22*m - 15. Solve -3/2*f**m + 2*f - 1/2*f**4 + 0*f**2 + 0 = 0 for f.
-2, 0, 1
Let d(o) = o**3 - 3*o**2 - 4*o + 3. Let x = 4 + 0. Let a be d(x). Suppose 26*m**2 + 6*m**2 + 16*m + 5 - a = 0. Calculate m.
-1/4
Let w(n) be the first derivative of 1/6*n**3 - 22 + 3/2*n - n**2. Factor w(f).
(f - 3)*(f - 1)/2
Factor 0*b + 260*b**3 + 4/3*b**5 - 300*b**2 + 116/3*b**4 + 0.
4*b**2*(b - 1)*(b + 15)**2/3
Let q(g) = -g + 10. Let p be q(6). Solve -x**4 + 6*x**4 - 4*x**3 - 9*x**p = 0.
-1, 0
Let u be (-550)/(-2541) - (-4)/(-42). Let h(l) be the first derivative of 3 + 0*l - u*l**3 - 1/11*l**2 - 1/22*l**4. Let h(s) = 0. What is s?
-1, 0
Determine j, given that 188*j**3 + 3*j**5 - 24*j**4 + 5*j**4 + 69*j - 102*j**2 - 7*j**4 - 18 - 116*j**3 + 2*j**4 = 0.
1, 2, 3
Factor -4/5*u**3 - 2/5*u**2 - 2/5 + 4/5*u**4 - 1/5*u**5 + u.
-(u - 2)*(u - 1)**3*(u + 1)/5
Factor 0*t + 0*t**2 + 0 - 2/3*t**5 - 2/3*t**3 - 4/3*t**4.
-2*t**3*(t + 1)**2/3
Let t(l) = 7*l**2 - 32*l + 34. Let a(o) = -2*o**2 - o. Let y(v) = 3*a(v) + t(v). Solve y(b) = 0.
1, 34
Let s be (-5 - -1)*1/(-152)*4. Let m be 2*(-1)/(-2)*56/133. Find d such that -s - 4/19*d**2 + 6/19*d**4 - 8/19*d**3 + m*d = 0.
-1, 1/3, 1
Let z(a) be the third derivative of -a**6/60 - 2*a**5/5 - 29*a**4/12 - 6*a**3 - 12*a**2 - 1. Factor z(p).
-2*(p + 1)*(p + 2)*(p + 9)
Factor -24 + 0*f**2 - 124/5*f + 4/5*f**3.
4*(f - 6)*(f + 1)*(f + 5)/5
Find g, given that -104 + 560*g + 138 - 290*g**2 + 65 + 183 - 336*g**3 + 8*g**4 - 224*g**3 = 0.
-1, -1/2, 1, 141/2
Let m(d) be the third derivative of d**5/15 + 3*d**4/2 + 12*d**3 + 17*d**2 - 4*d. Factor m(w).
4*(w + 3)*(w + 6)
Suppose 0*c + 170 = -5*c. Let m be (3 - c/(-8))*-4. Factor 0*k**2 + 9*k**3 - 2*k**4 + 3*k + m*k**4 + 9*k**2.
3*k*(k + 1)**3
Let x(g) = -2*g**5 + 6*g**4 - 4*g**3 + 4*g**2 - 2. Let y = -57 - -61. Let h(r) = -r**3 - r**2 + 1. Let p(n) = y*h(n) + 2*x(n). Determine f so that p(f) = 0.
0, 1
Let x be -4 - (-4 + (-7446)/(-12)). Let p = 634 + x. Suppose -9*r + 3/2*r**2 + p = 0. Calculate r.
3
Suppose 5*t + 17 = -g + 7, 8*t + 16 = 0. Factor 0*s**2 - 8/19*s**3 - 2/19*s**5 + g + 8/19*s**4 + 0*s.
-2*s**3*(s - 2)**2/19
Let m(o) be the third derivative of 0 + 1/120*o**5 - 1/720*o**6 + 0*o + 13*o**2 + 0*o**4 + 0*o**3. Let m(a) = 0. What is a?
0, 3
Let j(l) be the first derivative of -1/14*l**4 + 17 + 32/7*l - 24/7*l**2 + 6/7*l**3. Factor j(r).
-2*(r - 4)**2*(r - 1)/7
Let p = 16/1057 - -18818/13741. Factor -2/13 - 16/13*b + p*b**2.
2*(b - 1)*(9*b + 1)/13
Factor -207*j**2 - 25*j + 2 + 211*j**2 + 5*j + 22.
4*(j - 3)*(j - 2)
Let u(h) be the second derivative of -h**7/5460 - h**6/2340 + h**3/2 - 14*h. Let a(r) be the second derivative of u(r). Factor a(b).
-2*b**2*(b + 1)/13
Let d(u) = -11*u**3 + 18*u**2 - u - 38. Let a(w) = -6*w**2 + 22*w**3 - 18*w**3 - 4 + 17. Let s(c) = 8*a(c) + 3*d(c). Factor s(k).
-(k - 5)*(k - 2)*(k + 1)
Let h(m) be the third derivative of -m**6/660 - m**5/55 - 5*m**4/132 - 2*m**2 - 2*m. Let h(k) = 0. What is k?
-5, -1, 0
Let t(n) be the third derivative of -n**7/1050 + n**5/150 - n**3/30 + 2*n**2 - 119*n. Factor t(a).
-(a - 1)**2*(a + 1)**2/5
Let w be 4/3*21/126. Let p(i) be the first derivative of 0*i - 1/3*i**2 + 4 + w*i**3. Find n such that p(n) = 0.
0, 1
Let u(x) be the third derivative of -x**2 + 1/6*x**5 + 1/24*x**6 + 0*x + 5/24*x**4 + 0 + 0*x**3. Factor u(y).
5*y*(y + 1)**2
Let j(c) be the second derivative of 13*c**7/56 - c**6/8 - 39*c**5/80 + 5*c**4/16 - c + 49. Suppose j(t) = 0. Calculate t.
-1, 0, 5/13, 1
Let l(t) be the second derivative of -t**7/12600 - t**6/3600 + t**5/300 + 7*t**4/12 - t. Let p(g) be the third derivative of l(g). Suppose p(f) = 0. What is f?
-2, 1
Suppose 0 = 4*v + 4*n + 16, 3*n = 3*v + n + 12. Let c be 8 + -4 - (0 - v). Factor 0*s + 2/5*s**3 + 4/5*s**4 + 0 + c*s**2.
2*s**3*(2*s + 1)/5
Let m(w) be the first derivative of -w**5/150 - w**4/10 - 8*w**3/15 - 23*w**2/2 + 19. Let x(g) be the second derivative of m(g). Factor x(h).
-2*(h + 2)*(h + 4)/5
Suppose 2*s = 4*y, -2*s - 3*s = -y + 18. Let l = s + 7. Factor 14*u + 3*u**l - 4*u - u - 15*u**2 - 12 + 39.
3*(u - 3)**2*(u + 1)
Find x, given that -4 - 50/9*x - 2/9*x**4 + 2*x**3 + 2/3*x**2 = 0.
-1, 2, 9
Let u(w) be the first derivative of w**5/270 + 5*w**4/54 + 25*w**3/27 - 9*w**2/2 - 10. Let f(a) be the second derivative of u(a). Factor f(i).
2*(i + 5)**2/9
Let x(f) = -72*f + 2090. Let b be x(29). Let w = 23/5 - 3. Factor 8/5 + w*t + 2/5*t**b.
2*(t + 2)**2/5
Let m(r) be the third derivative of r**8/1176 - 8*r**7/735 + r**6/70 + 4*r**5/21 + 25*r**4/84 + 41*r**2 + 1. Let m(v) = 0. Calculate v.
-1, 0, 5
Let w(h) = 19*h - 89. Let l be w(5). Let a(f) be the first derivative of -l + 8*f + 4/3*f**3 + 6*f**2. Find o, given that a(o) = 0.
-2, -1
Let v = 25 - 35. Let a be 0/((-5)/(-2)*8/v). Let a + 1/3*h**3 - 1/3*