the third derivative of x(s). Factor h(l).
-l**2*(l - 1)*(l + 2)/5
Let v(h) = 411*h - 2877. Let n be v(7). Suppose -3/5*a**4 + 9/5*a**3 + n - 4/5*a**5 - 2/5*a**2 + 0*a = 0. Calculate a.
-2, 0, 1/4, 1
Let l(r) be the third derivative of -r**5/120 + 17*r**4/16 + 53*r**3/6 + 535*r**2. Factor l(w).
-(w - 53)*(w + 2)/2
Suppose 3*b + 12 = 7*b. Let i(n) = -n + 0*n + b*n**2 - 2*n. Let t(f) = -3*f**2 + 3*f. Let r(v) = 5*i(v) + 6*t(v). Factor r(p).
-3*p*(p - 1)
Let p be (3 + -4)*5*-2. Let c(s) = s**2 - 9*s - 7. Let j be c(p). Suppose -2*z - 4*z**4 - 6*z**j + 0*z**3 - 13*z**2 + 7*z**2 + 2*z**4 = 0. Calculate z.
-1, 0
Let l(z) be the third derivative of -z**8/26880 - z**7/6720 + z**6/160 + 4*z**5/15 - 25*z**2. Let q(c) be the third derivative of l(c). Factor q(n).
-3*(n - 2)*(n + 3)/4
Let g be (1 - 1)/(16 + -14). Let d(t) be the first derivative of 27/35*t**5 + g*t - 5 + 12/7*t**2 - 4/7*t**3 - 27/14*t**4. Let d(y) = 0. What is y?
-2/3, 0, 2/3, 2
Let o(j) = j - 2. Let i be o(4). Suppose 3*t + 1 = -3*f + 4, 4*f + 5*t = -1. What is h in -8*h**2 - 3*h**5 + 4*h**3 + 0*h**3 - h**5 + f*h**4 + i = 0?
-1, -1/2, 1
Suppose 99*h - 3267 - 3/4*h**2 = 0. What is h?
66
Suppose -14*h + 17*h - 12 = 0. Let s(o) be the first derivative of 1/12*o**3 - 1/8*o**h + 3 + 0*o**2 + 0*o. Let s(r) = 0. Calculate r.
0, 1/2
What is q in 50/7*q - 8*q**2 + 2/7*q**3 + 108/7 = 0?
-1, 2, 27
Let m(p) be the first derivative of p**5/40 + p**4/4 + 3*p**3/4 - 9*p**2 + 20. Let s(k) be the second derivative of m(k). Find r such that s(r) = 0.
-3, -1
Suppose 4 = 2*d - 2. Suppose -4*h**2 + 123*h**3 - 126*h**d + h**2 = 0. What is h?
-1, 0
Let h(z) be the second derivative of z**7/168 + z**6/60 - 3*z**5/40 - 5*z**4/12 - 19*z**3/24 - 3*z**2/4 + 144*z. What is v in h(v) = 0?
-2, -1, 3
Let v(d) be the first derivative of -d**5 - 185*d**4/4 - 175*d**3/3 + 185*d**2/2 + 180*d + 382. Determine b so that v(b) = 0.
-36, -1, 1
Let z = 5/7 - -3/35. Let l be 4/(-15)*6 - -2. What is p in -2/5*p + l*p**2 - z = 0?
-1, 2
Let n be (-25104)/6272 - (-4 - 0). Let i = 2341/4312 - n. Determine r, given that -2/11*r**2 + i*r - 4/11 = 0.
1, 2
Let f(x) be the first derivative of x**3/15 + x**2/5 - 137. Let f(u) = 0. Calculate u.
-2, 0
Factor -441/4 - 21/2*n + 21/2*n**3 + 110*n**2 + 1/4*n**4.
(n - 1)*(n + 1)*(n + 21)**2/4
Let k(l) be the second derivative of l**7/84 - l**6/12 + l**5/8 + 5*l**4/24 - l**3/2 + 33*l + 1. Solve k(p) = 0.
-1, 0, 1, 2, 3
Let o = -1272/11 + 11470/99. Solve -2/9*g + o*g**2 + 2/9*g**3 - 2/9 = 0.
-1, 1
Let y(m) be the third derivative of m**7/105 - m**6/60 - m**5/15 - 63*m**2. Determine o so that y(o) = 0.
-1, 0, 2
Let w be (-34*(-3)/(-22))/1. Let n = w - -503/99. Factor 4/9*v**4 - 2/9*v**5 + 0*v**3 + 2/9*v - n*v**2 + 0.
-2*v*(v - 1)**3*(v + 1)/9
Let m be (8/(-140))/(144/(-4335)) - 1. Let j = m - 3/56. Factor 0*b - j + 2/3*b**2.
2*(b - 1)*(b + 1)/3
Suppose -j - 54 = -28*j. Suppose 6/11*p**3 + 0*p + 2/11*p**j + 0 + 6/11*p**4 + 2/11*p**5 = 0. Calculate p.
-1, 0
What is q in 2/3*q**4 + 8/3*q**3 - 20/3*q + 16/3 - 2*q**2 = 0?
-4, -2, 1
Suppose b + 5 = 2*b, 5*b = -j + 28. Find a, given that -38*a**2 + 10*a + 39*a**3 + 25*a**4 - 15*a**5 - 34*a**j + 13*a**2 = 0.
-1, 0, 2/3, 1
Let r be (-3)/(-15)*60/45. Let o(g) = -g**3 + 6*g**2 - 7*g + 10. Let j be o(5). Factor 2/15*h**2 + 0*h + j + r*h**3 + 2/15*h**4.
2*h**2*(h + 1)**2/15
Factor -2/7*y**3 - 38/7*y**2 - 6 + 82/7*y.
-2*(y - 1)**2*(y + 21)/7
Let z be (15/(-6))/(-5) - (-3)/2. Let c(q) be the first derivative of 15/4*q**4 - 3 - 3/5*q**5 - 6*q - 9*q**3 + 21/2*q**z. Find a, given that c(a) = 0.
1, 2
Let t(r) = -5 + 2*r + 0*r**4 - r**2 - 3*r + r**4 + 6. Let m(s) = -8*s**4 - 10*s**3 - 2*s**2 + 3*s - 3. Let f(i) = -m(i) - 3*t(i). Find j, given that f(j) = 0.
-1, 0
Let m(f) be the first derivative of 2*f**3/21 + 50*f**2/7 + 14*f + 32. Factor m(b).
2*(b + 1)*(b + 49)/7
Let p(b) = b**4 - b**3 + b**2 - 1. Let q(u) = -5*u**5 + 10*u**4 - 30*u**2 + 15*u + 10. Let s(t) = -10*p(t) - q(t). Solve s(c) = 0.
-1, 0, 1, 3
Let i(y) be the third derivative of 0 - 1/8*y**3 + 9/560*y**7 + 0*y + 21/160*y**5 - 3/64*y**4 - 5/64*y**6 + 8*y**2. Factor i(f).
3*(f - 1)**3*(9*f + 2)/8
Let g(f) be the third derivative of 1/9*f**4 - 1/3*f**3 + 5*f**2 + 0 + 0*f - 1/90*f**5. Factor g(t).
-2*(t - 3)*(t - 1)/3
Let y(d) = -15*d**2 + 1270*d + 1710. Let g(s) = s**2 - 91*s - 122. Let l(o) = 85*g(o) + 6*y(o). Factor l(m).
-5*(m + 1)*(m + 22)
Let u(f) be the second derivative of -f**7/525 - f**6/60 - f**5/50 + 3*f**4/20 - 5*f**2 - 22*f. Let w(n) be the first derivative of u(n). Solve w(l) = 0 for l.
-3, 0, 1
Let q be 1*12/99*12/8. Let i(w) be the first derivative of -3/11*w**2 + 7 + 3/22*w**4 + 2/33*w**3 - q*w. Determine o so that i(o) = 0.
-1, -1/3, 1
Determine k, given that 16 + 8*k - 4*k**3 + k**4 - 8*k**2 + 1/2*k**5 = 0.
-2, 2
Let z(i) = -i**2 + 8*i - 7. Let f be z(6). Let l(m) be the second derivative of 3/5*m**3 + 2/5*m**2 - 6*m + 0 + 2/5*m**4 + 1/10*m**f. Factor l(j).
2*(j + 1)**2*(5*j + 2)/5
Determine y so that 9/4*y**2 + 0 - 3/2*y - 3/4*y**3 = 0.
0, 1, 2
Let r(u) be the second derivative of -u**6/1080 + u**4/18 + u**3 - 4*u. Let h(y) be the second derivative of r(y). Factor h(j).
-(j - 2)*(j + 2)/3
Determine t so that 6/17*t**3 + 2/17*t**5 + 8/17*t**4 + 0*t + 0 + 0*t**2 = 0.
-3, -1, 0
Let v(f) be the second derivative of 0 - 9/80*f**5 + 0*f**4 - 1/40*f**6 + 0*f**3 + 3*f + 0*f**2. Let v(x) = 0. What is x?
-3, 0
Let h(y) = 3*y - 12. Let n be 3 - -4*(0 + 1). Let i be h(n). Factor -3 + 0*c**2 + i + 0 + 9*c + 3*c**2.
3*(c + 1)*(c + 2)
Let w(l) be the third derivative of l**5/72 + 845*l**4/72 + 142805*l**3/36 - 221*l**2. Let w(d) = 0. What is d?
-169
Let c be (-24)/(-10) + 39/65. Let -7*x**3 + 6*x**c + x**4 + 2*x**3 = 0. Calculate x.
-1, 0
Let j(h) be the second derivative of -h**7/462 + h**6/110 - h**5/110 - 3*h - 3. Factor j(u).
-u**3*(u - 2)*(u - 1)/11
Let y be (-12)/(-27)*(-72)/(-384). Let t(r) be the second derivative of 0 + 1/3*r**3 - 5*r + 3/2*r**2 - y*r**4. Suppose t(z) = 0. Calculate z.
-1, 3
Suppose 0 = 35*c - 30*c - 10. Let k be (c - (-11)/(-4)) + (-290)/(-120). Factor -k*r**2 - r - 1/3*r**3 + 3.
-(r - 1)*(r + 3)**2/3
Let -7 - 2020*n + 17033*n**2 + 18 + 33972*n**2 + 9 = 0. What is n?
2/101
Factor -6*s**3 + 15 + 180*s**2 - 320*s**2 + 161*s**2 + 42*s.
-3*(s - 5)*(s + 1)*(2*s + 1)
Let l(j) be the first derivative of 12 + 2/3*j**2 - 2/3*j**3 - 5/6*j**4 + 0*j. Find o, given that l(o) = 0.
-1, 0, 2/5
Factor 114/5*g - 63/5 - 36/5*g**2 - 18/5*g**3 + 3/5*g**4.
3*(g - 7)*(g - 1)**2*(g + 3)/5
Let w(p) be the third derivative of p**9/5040 - p**8/2240 - p**7/840 + p**6/240 + p**4/24 + 42*p**2. Let c(n) be the second derivative of w(n). Factor c(k).
3*k*(k - 1)**2*(k + 1)
Factor 40 + 49*r + 36*r**2 + 29*r - 187*r**3 + 185*r**3.
-2*(r - 20)*(r + 1)**2
Factor -3*b**2 - 12 + 8 + 0 + 7.
-3*(b - 1)*(b + 1)
Let f = -317 - -514. Determine n, given that 4*n**2 + 3*n**3 - 198*n**5 - 4*n - n**4 + f*n**5 - n**4 = 0.
-2, 0, 1
Factor 1/6*m**2 - 4 - 1/3*m.
(m - 6)*(m + 4)/6
Let u(j) be the second derivative of 5/6*j**4 + 4*j**2 + 0 + 1/10*j**5 - 13*j + 8/3*j**3. Suppose u(l) = 0. What is l?
-2, -1
Let u(d) be the third derivative of 7*d**8/24 + d**7/3 - 4*d**6/5 - 6*d**5/5 - 289*d**2. Factor u(i).
2*i**2*(i - 1)*(7*i + 6)**2
Let -3360*a - 2/3*a**3 - 286/3*a**2 + 3456 = 0. Calculate a.
-72, 1
Determine w, given that 1/8*w**3 + 1/4*w**2 - 9/4 - 9/8*w = 0.
-3, -2, 3
Let n(h) be the second derivative of -5/6*h**3 + 1/4*h**2 + 25/24*h**4 + 9*h + 0. Find z such that n(z) = 0.
1/5
Let p be 2*-8 - 16/(-8). Let c = p + 18. Factor -4*g**4 + c*g**3 + 2*g**2 - g**2 - g**3.
-g**2*(g - 1)*(4*g + 1)
Let w be (-10)/(-15)*((-24)/(-4))/1. Let y(z) be the second derivative of -1/3*z**w - 1/10*z**5 - 5*z + 0 + 0*z**3 + 0*z**2. Factor y(q).
-2*q**2*(q + 2)
Suppose 2*m = 0, -3*l + 2*m = -0*m - 18. Determine o, given that 10*o**3 - 10*o**2 - 5*o**2 - 19*o**3 + l*o = 0.
-2, 0, 1/3
Suppose 57 = -14*f + 127. Let h(y) be the second derivative of -1/10*y**f - 1/18*y**4 - 1/15*y**6 - 7*y + 0 - 1/63*y**7 + 0*y**2 + 0*y**3. Factor h(q).
-2*q**2*(q + 1)**3/3
Let b(c) be the third derivative of c**7/735 - 19*c**6/30 + 3916*c**5/35 - 340603*c**4/42 - 704969*c**3/21 + 254*c**2. Factor b(j).
2*(j - 89)**3*(j + 1)/7
Let o(u) = u**3 - 10*u**2 + 10*u + 51.