 t(j) be the first derivative of -24*j + 21/2*j**2 - 51 + j**3. Factor t(m).
3*(m - 1)*(m + 8)
Let n(j) be the second derivative of 3*j**5/100 + 7*j**4/10 + 49*j**3/10 + 259*j. Suppose n(t) = 0. Calculate t.
-7, 0
Let d(y) be the second derivative of 0 + 10/3*y**3 + 7/9*y**4 + 6*y**2 - 39*y + 1/15*y**5. Suppose d(l) = 0. Calculate l.
-3, -1
Let m(r) be the third derivative of r**6/40 - 7*r**5/20 - r**4/8 + 7*r**3/2 - r**2 + 20*r. Factor m(n).
3*(n - 7)*(n - 1)*(n + 1)
Let f(l) be the third derivative of -l**8/112 - l**7/35 + 9*l**6/10 - 22*l**5/5 + 8*l**4 - 21*l**2 + 4. Factor f(b).
-3*b*(b - 2)**3*(b + 8)
Let v(h) be the first derivative of 3*h**4/4 - 8*h**3 + 18*h**2 + 562. Find b, given that v(b) = 0.
0, 2, 6
Let t be (-16)/(-48) - (-8)/120. Find n such that -12/5*n**2 - 16/5 - 24/5*n - t*n**3 = 0.
-2
Let o(p) = -5*p**5 + 16*p**4 - 2*p**3 - 13*p**2 + 11*p - 2. Let g(h) = -2*h**5 - 2*h**3 - h**2. Let l(a) = 2*g(a) + 2*o(a). Suppose l(m) = 0. Calculate m.
-1, 2/7, 1
Let o(d) = -d**3 - 1. Let v(i) = 4*i**2 + 4*i - 1. Let b = 90 - 94. Let c(r) = b*o(r) + 4*v(r). Factor c(y).
4*y*(y + 2)**2
Let x be -1 + 6 - ((-8)/(-20))/((-24)/(-60)). Solve 1/2*q + 3/2*q**3 + 0 + 1/2*q**x + 3/2*q**2 = 0.
-1, 0
Let m(f) = -f + 9. Let l be m(-11). Factor 16 + 15*g**4 + 64 + g**5 - l*g**3 + 4*g**5 - 80*g**2.
5*(g - 2)*(g - 1)*(g + 2)**3
Let i = -1023 + 28649/28. Let n = i - -13/84. Solve -n*u**2 + 1/3*u + 2/3 = 0.
-1, 2
Suppose -142*l - 10 = -140*l - 4*z, -2*l + 14 = 2*z. Let r = 11 - 7. Factor 0*k + 0*k**2 + 1/3*k**l - 1/3*k**r + 0.
-k**3*(k - 1)/3
Let u(a) be the first derivative of 3*a**5/40 + a**4/4 - 3*a**3/4 + 24*a - 3. Let d(g) be the first derivative of u(g). What is o in d(o) = 0?
-3, 0, 1
Let g(c) be the second derivative of -c**4/54 + 2*c**3/27 - c**2/9 - 104*c. Factor g(k).
-2*(k - 1)**2/9
Let m(n) be the second derivative of n**6/10 - 9*n**5/25 + 9*n**4/20 - n**3/5 + 230*n. Determine b so that m(b) = 0.
0, 2/5, 1
Let c(k) = 2*k**5 - k**4 + k**3 + k - 1. Let f(s) = 15*s**5 - 12*s**4 + 21*s**3 + 12*s**2 + 9*s - 9. Let t(x) = 9*c(x) - f(x). Factor t(p).
3*p**2*(p - 2)*(p + 1)*(p + 2)
Let z(g) be the second derivative of -g**7/63 + g**6/15 + g**5/6 - 5*g**4/6 - 4*g**3/9 + 4*g**2 - 59*g. Suppose z(p) = 0. Calculate p.
-2, -1, 1, 2, 3
Let n(r) = -r**3 + 15*r**2 - 12*r - 24. Let d be n(14). Factor -4*y**d - 12*y**5 + 11*y**5 + y**3 - 5*y**3 + 0*y**3.
-y**3*(y + 2)**2
Let l(k) be the third derivative of -4/3*k**3 + 2/21*k**7 + 23*k**2 + 0 + 7/6*k**4 + 0*k - 7/30*k**6 - 1/5*k**5. Factor l(o).
4*(o - 1)**2*(o + 1)*(5*o - 2)
Let t(f) be the third derivative of f**8/252 + 4*f**7/105 + 13*f**6/90 + 4*f**5/15 + 2*f**4/9 - 123*f**2 - 1. Suppose t(r) = 0. What is r?
-2, -1, 0
Let i(u) = u + 17. Let k be i(-7). Factor -k*v**3 + 26*v**3 - 10 - 15*v - 11*v**3.
5*(v - 2)*(v + 1)**2
Let j = 1687/3382 - -2/1691. Let 1/8*w**2 - 1/2*w + j = 0. What is w?
2
Factor 0*r - 2/7*r**5 - 10/7*r**3 + 0 + 4/7*r**2 + 8/7*r**4.
-2*r**2*(r - 2)*(r - 1)**2/7
Let v(c) be the third derivative of c**10/10080 - c**9/2520 + c**8/2240 + 17*c**4/24 + 13*c**2. Let o(l) be the second derivative of v(l). Factor o(g).
3*g**3*(g - 1)**2
Suppose -6*h + 4 + 8 = 0. Suppose 3*b + h*b - 15 = -3*i, 4*b + 4*i - 12 = 0. Solve 5/2*f**b - 5/2*f - 1/2*f**2 - 1 + 3/2*f**4 = 0 for f.
-1, -2/3, 1
Let b(h) be the first derivative of -h**5 - 35*h**4/4 - 10*h**3 + 80*h**2 + 160*h - 70. Factor b(w).
-5*(w - 2)*(w + 1)*(w + 4)**2
Let p(u) be the second derivative of -u**5/150 - 7*u**4/90 - u**3/3 - 3*u**2/5 + 50*u. Factor p(c).
-2*(c + 1)*(c + 3)**2/15
Let r(a) be the first derivative of -6 + 5/21*a**2 + 4/63*a**3 - 2/7*a. Factor r(j).
2*(j + 3)*(2*j - 1)/21
Let b(l) be the third derivative of l**7/70 + 13*l**6/40 + 12*l**5/5 + 17*l**4/2 + 16*l**3 - 35*l**2 - 2*l. Factor b(u).
3*(u + 1)*(u + 2)**2*(u + 8)
Factor -1/2*g**3 + 121/2*g + 41 + 19*g**2.
-(g - 41)*(g + 1)*(g + 2)/2
Let a be -2*(1 + -3)/1. Let z be (2 - a)/((-2)/2). Factor -4*h**z - 3*h - h + 4 + 4*h**3 + 0*h.
4*(h - 1)**2*(h + 1)
Let m = 5/2249 - -6737/4498. Determine i so that i + 0 + 3/2*i**4 - m*i**2 - 1/2*i**3 - 1/2*i**5 = 0.
-1, 0, 1, 2
Let n(c) = -c**2 - 10*c + 4. Let d be n(-10). Factor -d*s - 6*s - 9*s**2 - 5*s**3 - 7*s**2 + s**2.
-5*s*(s + 1)*(s + 2)
Suppose -4 = -2*o - 0. Let w(c) be the third derivative of -2/45*c**3 - 11*c**o + 0 + 0*c + 1/60*c**4 + 1/225*c**5. Factor w(l).
2*(l + 2)*(2*l - 1)/15
Solve 2/15*r + 4/15 + 4/15*r**4 + 2/15*r**5 - 8/15*r**2 - 4/15*r**3 = 0 for r.
-2, -1, 1
Suppose -6 = 4*j + 6. Let v be (2 - 3 - j)*1. Suppose 2*f**3 + 8*f + 5*f**2 + f**2 + v*f**2 = 0. What is f?
-2, 0
Let b(q) = -2*q**5 + q**4 - q**3 - q**2 - q + 2. Let u(k) = 5*k**5 - 4*k**4 - 7*k**3 + 24*k**2 + 6*k - 28. Let x(m) = -6*b(m) - 3*u(m). Solve x(f) = 0.
-3, -1, 2
Factor -a**2 - 18 + a**2 - a**2 - 24*a - 3*a**2 - 14.
-4*(a + 2)*(a + 4)
Let t(g) be the second derivative of g**4/21 - 263*g**3/42 - 33*g**2/7 - 230*g. Factor t(y).
(y - 66)*(4*y + 1)/7
Let 291/7*z - 90/7*z**2 - 198/7 - 3/7*z**3 = 0. Calculate z.
-33, 1, 2
Let u(f) be the third derivative of -f**7/5670 - f**6/405 + f**4/24 + f**2. Let s(c) be the second derivative of u(c). Find l, given that s(l) = 0.
-4, 0
Let m = 189975/66479 - 5/9497. Factor r**3 - 18/7*r**2 - 8/7 - 1/7*r**4 + m*r.
-(r - 2)**3*(r - 1)/7
Let c(h) = 3*h**4 + 6. Suppose i = -13 + 5. Let o be -6 - 4/(i/2). Let t(f) = -3*f**4 + f**3 - 5. Let n(y) = o*c(y) - 6*t(y). Determine k, given that n(k) = 0.
0, 2
Factor 0*t + 15/7*t**4 + 0 + 12/7*t**2 - 3/7*t**5 - 24/7*t**3.
-3*t**2*(t - 2)**2*(t - 1)/7
Let 2*r**4 - 52*r - 17*r**2 - 10*r**4 + 0*r**5 + 24*r**3 - 3*r**5 + 33*r**2 - r**5 + 24 = 0. Calculate r.
-3, -2, 1
Let x = -1469/1830 + 51/61. Let n(m) be the second derivative of 5/12*m**4 + x*m**6 + 0 + 1/5*m**5 - 10*m + 1/3*m**3 + 0*m**2. Factor n(o).
o*(o + 1)**2*(o + 2)
Suppose 5*g - 5*m = 2*g + 25, 3*m + 15 = 0. Let t(n) be the third derivative of g + 0*n**3 + 7*n**2 + 1/8*n**4 + 0*n + 1/20*n**5. Factor t(y).
3*y*(y + 1)
Let h(a) = 19*a + 536. Let o be h(-28). Let p(l) be the second derivative of 1/5*l**5 + 0*l**2 - 9*l + 0 + 0*l**3 - 1/3*l**o. Determine x, given that p(x) = 0.
0, 1
Let z be 4*3/30 - 516/1440. Let p(i) be the second derivative of 8*i + 1/48*i**4 + 0*i**2 + z*i**3 + 0. Solve p(o) = 0 for o.
-1, 0
Let d = 3754261/17 + -220567. Let i = 272 - d. Determine z, given that -2/17 + i*z**2 + 0*z = 0.
-1, 1
Factor 63/11*w**2 + 56/11*w + 9/11*w**3 + 12/11.
(w + 6)*(3*w + 1)*(3*w + 2)/11
Let z be 2/7 - 1/((-21)/204). Let w be ((3 + 21)/2)/(75/z). Factor 16/5*h**2 + w*h + 0 - 2*h**3.
-2*h*(h - 2)*(5*h + 2)/5
Let t be ((-48)/(-15))/(3/(-15)). Let k = 0 - t. Determine p, given that -3*p**3 - 3*p**4 - p**2 + 16*p - p**5 - k*p = 0.
-1, 0
Let s(y) be the third derivative of 0*y - 13/6*y**5 + 0 - 9*y**2 + 25/24*y**4 + 1/3*y**6 + 5/2*y**3. Find t, given that s(t) = 0.
-1/4, 1/2, 3
Suppose -143 - 193 = -21*o. What is h in o*h**2 - 9*h**2 + 39 - 5*h**2 + 89 + 32*h = 0?
-8
Let y be ((-48)/42)/(-5 - (-8)/2). Let f(s) be the second derivative of 0 + 7*s - 4/21*s**3 - y*s**2 - 1/84*s**4. Solve f(v) = 0 for v.
-4
Let p = 7 - 7. Suppose -4*y + 1 = -3*v - 2, 30 = 5*y + 5*v. Determine h so that -h**y + 2 - 2*h**2 + p*h + 4*h - 3*h = 0.
-2, -1, 1
Suppose 98 - 106 = 4*a - 2*w, 2*a = -w + 4. Factor -1/5*m**2 + a + 1/5*m.
-m*(m - 1)/5
Let c(x) = 8*x**2 - 54*x. Let o(u) = -u**2 + 2*u. Let w(h) = c(h) + 6*o(h). Factor w(m).
2*m*(m - 21)
Let g = -234 + 236. Let v(d) be the first derivative of 2/9*d**6 + 4*d**4 + 0*d + 32/9*d**3 + 7 + 8/5*d**5 + 0*d**g. Factor v(m).
4*m**2*(m + 2)**3/3
Factor 5*x**2 + 450*x + 3438 + 3609 + 3078.
5*(x + 45)**2
Let h(r) be the third derivative of -r**5/150 + r**4/20 + 2*r**3/3 - 67*r**2. Factor h(o).
-2*(o - 5)*(o + 2)/5
Let y = 1739/772 + -1/386. What is d in -3/4*d**2 - y*d - 3/2 = 0?
-2, -1
Let v be 120/72*(-5)/(10/(-12)). Suppose 0 = -b + v*b. Solve -2/9*u**3 + b + 2/9*u + 2/9*u**2 - 2/9*u**4 = 0.
-1, 0, 1
Solve -10*r + 19/2 + 1/2*r**2 = 0.
1, 19
Let n(o) = -2*o + 100. Let w be n(49). Let i(p) be the first derivative of -4*p**w - 5/22*p**4 - 4*p**3 - 4 + 10/11*p**5 - 16/11*p. Solve i(l) = 0.
-1, -2/5, 2
Let p be (-9)/(-21) + (-4128)/126. Let u = 799/21 + p. Factor u*f - 8/7 - 50/7*f**2.
-2*(5*f - 2)**2/7
Let u = -888