/15
Let o(r) be the first derivative of r**8/2100 - r**7/350 + r**6/200 - 20*r**3/3 + 7. Let x(f) be the third derivative of o(f). Factor x(t).
t**2*(2*t - 3)**2/5
Let u = -8079/11 + 735. Solve -2/11*k**3 - 10/11*k**4 + 0 + u*k**5 + 10/11*k**2 - 4/11*k = 0 for k.
-1, 0, 2/3, 1
Let p = -2032 + 2034. Determine w, given that -w - 1/2*w**p + 3/2 = 0.
-3, 1
Let m = -146/77 + 24/11. Let r(g) be the first derivative of 1/7*g**2 + 2/21*g**3 - m*g - 2 - 1/14*g**4. Factor r(j).
-2*(j - 1)**2*(j + 1)/7
Factor -4/3*x**3 + 22/9*x + 14/9*x**2 - 4/9.
-2*(x - 2)*(x + 1)*(6*x - 1)/9
Let y(q) be the second derivative of 13/108*q**4 + 1/270*q**6 + 0 + 2/9*q**3 + 2/9*q**2 + 1/30*q**5 - 23*q. Solve y(o) = 0 for o.
-2, -1
Let g = -3902/51 + 1312/17. Find u, given that 5/9 - g*u + 1/9*u**2 = 0.
1, 5
Let t(f) = f**3 - 10*f**2 - 10*f - 8. Let v = 32 - 21. Let n be t(v). Factor 24*a**4 + 2*a**n + a**3 - 27*a**4.
-3*a**3*(a - 1)
Let -10*i**2 + 13*i**2 - 58*i - 50*i - 147*i = 0. Calculate i.
0, 85
Let g(d) be the first derivative of 4*d**3/3 - 80*d**2 + 1600*d + 95. Solve g(f) = 0.
20
Let c(d) be the first derivative of 0*d + 1/2*d**4 - 20 - 4*d**3 + 5*d**2. Determine h, given that c(h) = 0.
0, 1, 5
Find b, given that -4 + 1/3*b**4 + 4/3*b**3 - 16/3*b - 1/3*b**2 = 0.
-3, -2, -1, 2
Let s(d) = -18*d**2 + 3*d + 7. Let a(l) = 4*l**2 - 1. Let c(q) = 14*a(q) + 2*s(q). Let c(x) = 0. Calculate x.
-3/10, 0
Let y(v) = -9*v + 3. Let d be y(0). Let t(o) be the first derivative of -1/5*o + 1/15*o**d + 1/10*o**2 - 2 - 1/20*o**4. Factor t(r).
-(r - 1)**2*(r + 1)/5
Let j = -47 + 50. Find b, given that -5*b**4 - 6*b**5 + 20*b + 10*b**2 - 200*b**j - 5 + 26*b**5 + 160*b**3 = 0.
-1, 1/4, 1
Suppose 4*a + 3 = -s + 9, -5*a + s + 3 = 0. Suppose 0 = -i - a + 16. Factor -5 + 11*n**3 - 10*n**5 + 14*n**4 + 5 - i*n**3.
-2*n**3*(n - 1)*(5*n - 2)
Let d(h) = h**3 + h**2 - 5*h + 1. Let t be d(2). Let z(c) be the second derivative of 1/6*c**t - 1/48*c**4 + 0 - 5*c - 3/8*c**2. Factor z(m).
-(m - 3)*(m - 1)/4
Suppose 5*n - l - 15 = 10, 6 = -n - 2*l. Let j be 0 + n*6/8. Suppose -2*a**j - 5 + a**4 + 4 + 3 - 3 + 2*a = 0. What is a?
-1, 1
Let t be ((-57)/15 - -4) + (-4)/20. Let a(o) be the second derivative of -2/5*o**5 + t*o**4 - 2/21*o**7 + 0*o**3 + 0 - 2/5*o**6 + 2*o + 0*o**2. Factor a(w).
-4*w**3*(w + 1)*(w + 2)
Let l(k) be the third derivative of 1/24*k**3 - 7/240*k**5 + 0*k - 12*k**2 + 0 + 1/16*k**4. Determine o, given that l(o) = 0.
-1/7, 1
Let w(k) = k**2 + 2*k - 6. Let h be w(-5). Suppose -5*p + 41 = 4*r, 3*r - 2*r - h = -p. Factor -2 + 0*c - 5*c**2 + r*c**2 - 2*c + 1.
-(c + 1)**2
Suppose 2*o + 53 + 43 = 0. Let w be o/3*(195/50 + -4). What is v in 4/5*v**2 - 4/5*v**3 + w*v + 0 = 0?
-1, 0, 2
Let x(c) be the second derivative of c + 0 + 2*c**3 + 0*c**2 - 1/3*c**4. Factor x(p).
-4*p*(p - 3)
Let x(n) be the third derivative of -n**6/40 - n**5/20 + 5*n**4/8 - 3*n**3/2 + 26*n**2 + 6*n. Let x(s) = 0. Calculate s.
-3, 1
Let v(d) be the second derivative of -d**5/50 - d**4/10 + 5*d**3/3 - 21*d**2/5 - 188*d. Find k, given that v(k) = 0.
-7, 1, 3
Let j(p) be the second derivative of -p**7/42 - p**6/15 + 3*p**5/20 + 2*p**4/3 + 2*p**3/3 + 3*p + 16. Suppose j(q) = 0. What is q?
-2, -1, 0, 2
Let s(w) be the first derivative of -7*w**6/90 - 3*w**5/20 - w**4/18 + 20*w - 8. Let x(n) be the first derivative of s(n). Factor x(f).
-f**2*(f + 1)*(7*f + 2)/3
Let i(w) = -9*w**5 - 3*w**4 + 13*w**2 - w. Let r(l) = l**5 - l**4 - l**2 + l. Let k = 99 + -98. Let x(b) = k*i(b) + 5*r(b). Factor x(d).
-4*d*(d - 1)*(d + 1)**3
Let o(n) be the third derivative of 1/390*n**5 + 0*n + 2/13*n**3 + 0 - 7/156*n**4 + 26*n**2. Factor o(f).
2*(f - 6)*(f - 1)/13
Let c = -57/37 + 208/111. Let h(p) be the second derivative of 1/2*p**4 + c*p**3 + 7*p - 7/40*p**5 + 0*p**2 + 0. Solve h(o) = 0.
-2/7, 0, 2
Suppose -30/7*o**3 - 24*o + 80/7 + 116/7*o**2 + 2/7*o**4 = 0. What is o?
1, 2, 10
Determine m, given that 48 + 4*m**3 - 6*m**3 + 18*m - 27*m**2 + 5*m**3 = 0.
-1, 2, 8
Let o(y) be the second derivative of y**7/210 - y**6/24 - 7*y**5/60 + 5*y**4/24 + y**3 + 43*y**2/2 - 2*y. Let k(x) be the first derivative of o(x). Factor k(t).
(t - 6)*(t - 1)*(t + 1)**2
Suppose 54*z - 57*z = 0. Let j(f) be the second derivative of -1/12*f**4 + 0 - 1/10*f**6 + 1/42*f**7 + z*f**3 + 3/20*f**5 + 7*f + 0*f**2. Solve j(l) = 0 for l.
0, 1
Let q = -39 - -47. Let h(b) be the third derivative of 0 + 5/9*b**4 + 1/63*b**q - 1/18*b**6 - 5*b**2 + 0*b - 4/63*b**7 + 4/9*b**3 + 5/18*b**5. Factor h(k).
2*(k - 2)**2*(2*k + 1)**3/3
Let w(b) be the second derivative of -b**5/90 + 4*b**4/9 + b**3/27 - 8*b**2/3 - 912*b. Determine l so that w(l) = 0.
-1, 1, 24
Factor 315*r - 1372*r**2 + 230*r**2 + 579*r**2 + 5080*r**3 - 80*r**4 - 800*r**2 - 1162*r**2.
-5*r*(r - 63)*(4*r - 1)**2
Let l(g) be the first derivative of 1/12*g**4 - 1/60*g**5 + g**2 - 4 + 0*g**3 + 0*g. Let r(w) be the second derivative of l(w). Solve r(f) = 0.
0, 2
Let o be ((-1)/(-2))/(7/70). Let b = o + 0. Factor l**b + 7*l + 6*l**2 + 18*l**3 + 6*l**2 + 2*l**5 - 4*l + 12*l**4.
3*l*(l + 1)**4
Let x(d) be the second derivative of -d**5/30 - d**4/6 - d**3/3 - 10*d**2 - 7*d. Let a(r) be the first derivative of x(r). Suppose a(c) = 0. What is c?
-1
Determine h so that -36 + 9794*h**5 + 69*h**4 + 96*h - 7*h**2 - 9809*h**5 - 81*h**3 - 26*h**2 = 0.
-1, 3/5, 1, 2
Let i(u) = u**2 + u. Let a(n) = -16*n**2 - 82*n + 62. Let p(q) = -2*a(q) - 36*i(q). Factor p(c).
-4*(c - 31)*(c - 1)
Let o(n) = -1. Let h(a) = -a**3 - 16*a**2 + 19*a + 40. Let x(w) = -h(w) - 6*o(w). Let x(s) = 0. What is s?
-17, -1, 2
Let h be (-1)/(76/16 + -5). Let q be 0/(-2)*(-5 + 6). Solve 4*a**2 + 8*a + 23*a**h - 8*a**3 - 27*a**4 + q + 0 = 0.
-2, -1, 0, 1
Let z(t) = -3*t**2 + 24*t - 12. Let p(y) = -3*y**2 + 23*y - 14. Let m(s) = -6*p(s) + 5*z(s). Factor m(j).
3*(j - 4)*(j - 2)
Let s(f) = 4*f**4 - 37*f**3 - 75*f**2 + 7*f + 7. Let o(p) = -3*p**4 + 25*p**3 + 50*p**2 - 5*p - 5. Let w(h) = 7*o(h) + 5*s(h). Let w(j) = 0. What is j?
-5, 0
Factor 75/7*v**2 - 264/7*v - 3/7*v**3 + 36.
-3*(v - 21)*(v - 2)**2/7
Let o = 35576/12321 + 2/1369. Determine x so that 2*x**2 + 10/9*x**4 - 2/9*x - 4/9 + o*x**3 = 0.
-1, 2/5
Let u be (-64)/80 - 132/(-140). Let -1/7*d**2 + u*d + 2/7 = 0. Calculate d.
-1, 2
Factor -24*p - 8/3*p**5 + 46/3*p**3 + 8/3*p**4 + 0 - 8*p**2.
-2*p*(p - 2)**2*(2*p + 3)**2/3
Factor 85/6*k - 1/6*k**2 + 0.
-k*(k - 85)/6
Let i(l) be the third derivative of -3*l**6/10 - 17*l**5/15 - 4*l**4/3 - l**2 - 209. Find n, given that i(n) = 0.
-1, -8/9, 0
Let f(v) = v**3 - 27*v**2 + 25*v + 29. Let k be f(26). Suppose -k*d = 4*o + 2, 5 = 4*d - 2*o - 7. Factor 9/5*h**3 - 3/5*h**d - 9/5*h**4 + 0 + 0*h + 3/5*h**5.
3*h**2*(h - 1)**3/5
Factor -2/7*c**4 + 0 + 2/7*c - 2/7*c**3 + 2/7*c**2.
-2*c*(c - 1)*(c + 1)**2/7
Let p = -1347 - -2709/2. Factor -p - 5/4*g**2 + 25/4*g.
-5*(g - 3)*(g - 2)/4
Let h(a) be the second derivative of -16/7*a**2 + 5*a + 8/21*a**3 + 0 + 2/21*a**4 - 1/35*a**5. Factor h(w).
-4*(w - 2)**2*(w + 2)/7
Factor -3*f**3 - 2*f**3 - 39*f**2 - 110*f - f + 30 + 17*f**3.
3*(f - 5)*(f + 2)*(4*f - 1)
Let r be 70/22 + 10/((-30)/(-9)). Let n = r - 6. Solve -2/11*y - 2/11 + 2/11*y**3 + n*y**2 = 0.
-1, 1
Let s(t) be the third derivative of -t**7/210 - t**6/24 + t**5/60 + 5*t**4/24 - 103*t**2. Factor s(x).
-x*(x - 1)*(x + 1)*(x + 5)
Let x be -5 - (-32 - -29)*(-43)/(-21). Solve -4/7*j - 4/7*j**3 + x*j**2 + 0 = 0 for j.
0, 1
Suppose -10*t**3 + 0*t - 46*t**2 + 25*t**2 + 19*t**2 + 0*t = 0. What is t?
-1/5, 0
Suppose 0 = 5*u + 2*j + j - 72, -4*j - 4 = 0. Let q be u/28 + (0 - 2/7). Find k such that -64*k - 4*k**3 - 64 - q*k**4 - 24*k**2 = 0.
-4
Suppose 8*j - 43 = -83. Let g be ((-32)/20 - 0)/(6/j). Let -3*z + z**2 + 2/3 + g*z**3 = 0. What is z?
-2, 1/4, 1
Let x be 4 - (-5 - -1 - -2). Solve 11*p**2 - 3*p**4 - 6*p**3 - 9*p**2 + x*p - 4 + 5*p**4 = 0 for p.
-1, 1, 2
Let t(n) = -n**3 - 6*n**2 + 6*n - 5. Let m be t(-7). Let i be (m + -1)*3 - -1. Factor -d**2 - 8*d**i - d**3 + 5*d**4 - d**5 - 2*d**3.
-d**2*(d + 1)**3
Let y = 158835/7 - 22689. Find n, given that 2/7*n**2 - y + 2/7*n = 0.
-3, 2
Let c = 27/14 - 53/42. Let d be (-2)/8 - (-16)/64. Factor -4/3*p**2 + 0*p + d + c*p**5 - 8/3*p**4 + 10/3*p**3.
2*p**2*(p - 2)*(p - 1)**2/3
Let j = 1298 + -1292. Let h(z) be the first derivative of -2/3*z**3 - 3 + j*z