 = -15*d**4 + 129*d**3 - 249*d**2 + 99*d. Let x(n) = n**4 - n**2 + 2*n. Let s(p) = m(p) + 18*x(p). Let s(h) = 0. Calculate h.
-45, 0, 1
Suppose -3*c = -3*j - 51, -3*j - c - c = 71. Let y be (24/j)/((-48)/56). Find m, given that 4/3*m**3 - 1/3*m**4 + y*m - 1/3 - 2*m**2 = 0.
1
Let t(w) be the first derivative of 0*w + 39 + 11/5*w**3 + 9/10*w**2 - 3/5*w**4. Let t(x) = 0. What is x?
-1/4, 0, 3
Let r = -277 - -1125/4. Let a = r + -4. What is q in 3/4 + 1/2*q - a*q**2 = 0?
-1, 3
Let n(c) be the third derivative of 0*c**3 - 4/105*c**5 - 14*c**2 + 0*c + 0 - 2/21*c**4 - 1/210*c**6. Factor n(t).
-4*t*(t + 2)**2/7
Determine c, given that 238/5*c**3 + 3370318/5*c + 200533921/10 + 42483/5*c**2 + 1/10*c**4 = 0.
-119
Solve 0 - 1/2*n**2 + 45/2*n = 0 for n.
0, 45
Let j(r) be the second derivative of -r**6/30 - r**5/5 + r**4/6 + 2*r**3 - 9*r**2/2 - 234*r. Factor j(k).
-(k - 1)**2*(k + 3)**2
Suppose 4*f - 11 = 2*t - f, t + 3*f = 22. Let b = t + -3. Find j such that b*j - 2 - 5*j**2 + j**2 + 2*j**2 = 0.
1
Let g(p) be the first derivative of 1/45*p**5 - 3 + 0*p**4 + 0*p + 3*p**2 - 8/9*p**3. Let d(h) be the second derivative of g(h). Factor d(j).
4*(j - 2)*(j + 2)/3
Let j be (-4)/10 - 578/(-20). Let m = 29 - j. Solve m*c**4 - 5/4*c**3 + 0 - 1/4*c + c**2 = 0.
0, 1/2, 1
Let r(f) = -10*f**3 - 450*f**2 - 1180*f - 670. Let a(b) = -b**3 - 50*b**2 - 131*b - 74. Let z(t) = -35*a(t) + 4*r(t). Factor z(o).
-5*(o + 1)*(o + 3)*(o + 6)
Let j(u) be the third derivative of 1/30*u**6 - 3*u**2 - 1/735*u**7 - 61/210*u**5 - 12/7*u**3 + u**4 + 0 + 0*u. Factor j(w).
-2*(w - 6)**2*(w - 1)**2/7
Let b be 5/(-3) + 3 - 85/(-51). Let j(a) be the third derivative of -2/15*a**3 + b*a**2 - 1/150*a**5 + 1/20*a**4 + 0 + 0*a. Factor j(m).
-2*(m - 2)*(m - 1)/5
Let z(a) be the third derivative of a**10/604800 - a**8/40320 + a**6/2880 + a**5/3 - a**2 + 5*a. Let m(l) be the third derivative of z(l). Factor m(g).
(g - 1)**2*(g + 1)**2/4
Factor 99/7*w**2 + 51*w + 3/7*w**3 + 261/7.
3*(w + 1)*(w + 3)*(w + 29)/7
Let m be (-12)/60*((-10)/(-12))/(-1). Let h(y) be the first derivative of 7/8*y**2 - 7/16*y**4 + 6 + m*y**3 - 1/2*y. Factor h(u).
-(u - 1)*(u + 1)*(7*u - 2)/4
Let v be 1/4 - (-35)/20. Let f(i) = 6*i - 4. Let g be f(v). Factor 4*d**4 + g*d**2 + 9*d**3 - 4*d**2 - d**3.
4*d**2*(d + 1)**2
Factor -8731 - 8693 - 542*i + 14*i - 10*i**2 + 6*i**2.
-4*(i + 66)**2
Let y(t) = -t**2 + 5*t - 7. Let x(d) = -1. Let k(z) = 3*x(z) - y(z). Let i(o) = o**2 - 6*o + 5. Let v(r) = 4*i(r) - 5*k(r). Factor v(n).
-n*(n - 1)
Let h be 1/(-4) - 7/((-140)/(-135)). Let x(s) = 3*s**2 + 23*s + 17. Let t be x(h). Factor 0*l**4 - 6/7*l**t + 0*l + 2/7*l**5 + 0 - 4/7*l**2.
2*l**2*(l - 2)*(l + 1)**2/7
Let p(y) = y**2 + 293. Let n be p(0). Let a = -573/2 + n. Find z such that -a*z**4 + 17/2*z**3 - 1/4*z + 7/4*z**5 - 4*z**2 + 1/2 = 0.
-2/7, 1
Let m(k) be the first derivative of k**7/70 - k**6/8 + 2*k**5/5 - k**4/2 + 3*k**2/2 + 22. Let t(u) be the second derivative of m(u). Factor t(c).
3*c*(c - 2)**2*(c - 1)
Suppose 2*a**5 - 8 + 28 + 14*a + 8*a**4 - 16*a**3 + 822*a**2 - 850*a**2 = 0. Calculate a.
-5, -1, 1, 2
Let h(p) = -p**4 - p**3 + p**2 - 6*p + 1. Let f(y) = -8*y**4 - 76*y**3 - 480*y**2 - 1464*y - 1596. Let x(c) = f(c) - 4*h(c). Let x(u) = 0. What is u?
-5, -4
Suppose 6*u - 504 = 3*o + 7*u, 2*o = -3*u - 336. Let i be ((-240)/o)/((-18)/(-21)). Suppose -10/3 - 5/3*s + i*s**2 = 0. Calculate s.
-1, 2
Factor -25*w**2 + 310410 - 310410 + 10*w + 20*w**3 - 5*w**4.
-5*w*(w - 2)*(w - 1)**2
Let z(r) be the second derivative of -r**6/105 - 13*r**5/35 - 12*r**4/7 - 10*r**3/3 - 23*r**2/7 - r - 5. Factor z(y).
-2*(y + 1)**3*(y + 23)/7
Let v(x) be the second derivative of -3*x**5/140 - 2*x**4/7 - 8*x**3/7 + 63*x. Solve v(f) = 0 for f.
-4, 0
Suppose -t = 5*s + 14, -3*s = -3*t + 4*t + 18. Let c = 25 + t. Factor -16*h - c + 6*h + 6*h**2 + 5 + 0*h**4 - 2*h**4 + 2*h**3.
-2*(h - 1)**3*(h + 2)
Let i = -525 - -528. Let j(w) be the third derivative of 0*w - 4/21*w**7 - 2/3*w**4 + w**2 + 8/3*w**i + 0 + 31/30*w**6 - 7/5*w**5. What is g in j(g) = 0?
-2/5, 1/2, 1, 2
Let u = 22738 + -22735. Find i, given that -4/7*i**2 - 4/7*i**u - 1/7*i**4 + 0 + 0*i = 0.
-2, 0
Let j = -61/210 + -1/105. Let i = 7/10 + j. Let -2/5*q**4 + 0*q**3 + 4/5*q**2 - i + 0*q = 0. What is q?
-1, 1
Determine l, given that 54872/5 - 3876/5*l**2 - 18772/5*l - 44*l**3 - 4/5*l**4 = 0.
-19, 2
Let s(n) be the first derivative of -3*n**5/20 + n**4/4 + n**3 - 17*n - 19. Let q(x) be the first derivative of s(x). Factor q(r).
-3*r*(r - 2)*(r + 1)
Let a be (0 - -6)*1/8. Let b be (((-507)/(-52))/(-13))/((-3)/(3/3)). Factor -a*x**2 + b*x**4 - 1 - 1/2*x**3 + 2*x.
(x - 2)*(x - 1)**2*(x + 2)/4
Let z(o) = -o**2 + o + 1. Let p(g) = 10*g**2 - 24*g + 3. Let a(c) = -2*p(c) - 22*z(c). Suppose a(j) = 0. What is j?
-14, 1
Let b = -93 - -132. Suppose 9 = 4*q - b. Determine x so that -q - 10*x + 3*x**2 - 4*x + 39 - 4*x = 0.
3
Factor 1/4*c**4 + 29/4*c**2 - 39/4*c + 9/2 - 9/4*c**3.
(c - 3)**2*(c - 2)*(c - 1)/4
Let h(l) be the second derivative of l**6/6 - 45*l**4/4 - 45*l**3 + 74*l - 1. Factor h(d).
5*d*(d - 6)*(d + 3)**2
Factor 4096/3*q + 108*q**3 + 896/3 + 1608*q**2.
4*(q + 14)*(9*q + 4)**2/3
Let t(c) = -100*c**4 - 125*c**3 + 44*c**2 + 53*c - 26. Let h(q) = -300*q**4 - 376*q**3 + 132*q**2 + 160*q - 80. Let w(a) = 5*h(a) - 16*t(a). Factor w(j).
4*(j + 1)**2*(5*j - 2)**2
Factor -1/5*f**2 + 11/5*f - 28/5.
-(f - 7)*(f - 4)/5
Let q be (-4)/((-72)/23) - (-148)/(-333). Factor -5/6*u + 1/2*u**2 + q*u**3 - 2/3 + 1/6*u**4.
(u - 1)*(u + 1)**2*(u + 4)/6
Let f(g) be the third derivative of 0*g**4 + 4*g**2 + 0*g**3 + 0 + 1/20*g**5 + 0*g. Factor f(x).
3*x**2
Suppose -3*c + 16 = 2*f - 7*c, 9*c + 36 = f. Determine k, given that 1/2*k**2 + f + 1/2*k = 0.
-1, 0
Suppose 2*t + 2*b - 64 = 0, -156 = -3*t - 2*t - b. Suppose -t*u + 28*u + 12 = 0. Find q such that 1/6*q**u + 1/6 - 2/3*q + q**2 - 2/3*q**3 = 0.
1
Let s(p) be the first derivative of -p**6/36 + 23*p**5/30 - 211*p**4/24 + 965*p**3/18 - 550*p**2/3 + 1000*p/3 + 23. Determine q so that s(q) = 0.
4, 5
Factor -2/7*i**2 + 1/7*i**4 + 1/7 + 0*i + 0*i**3.
(i - 1)**2*(i + 1)**2/7
Let y be (-1)/(-2)*(10 - (1 + 1)). Let z(q) be the first derivative of -5/2*q**4 + 3 + 0*q + 16/3*q**3 - y*q**2 + 2/5*q**5. Suppose z(w) = 0. What is w?
0, 1, 2
Let x(r) be the first derivative of 3*r**4/8 - 3*r**3 + 33*r**2/4 - 9*r + 267. Suppose x(f) = 0. What is f?
1, 2, 3
Let p(a) be the first derivative of -a**5/30 + 7*a**4/12 - 2*a**3 + 17*a**2/6 - 11*a/6 - 312. Factor p(q).
-(q - 11)*(q - 1)**3/6
Determine f, given that 224*f**4 + 223*f**4 - 444*f**4 - 3*f**2 = 0.
-1, 0, 1
Factor 1/6*t**4 + 5/3*t + 1/2*t**2 - t**3 + 0.
t*(t - 5)*(t - 2)*(t + 1)/6
Let a = 26 - 13. Let f be 713/a + (-6)/(-39). Factor 4*v**3 - 2*v**2 - 55 + f - 2*v**4.
-2*v**2*(v - 1)**2
Solve 18 - 1/5*o**3 + 16/5*o**2 - 69/5*o = 0.
3, 10
Let p(i) = -2*i**4 - 4*i**3 - i**2 + i + 1. Let d = 17 + -10. Let y(j) = j - 2 + d - 4 - j**2. Let w(v) = -p(v) + y(v). Factor w(c).
2*c**3*(c + 2)
Factor 0 + 0*k + 8/13*k**4 + 66/13*k**3 + 16/13*k**2.
2*k**2*(k + 8)*(4*k + 1)/13
Let r be (3/(-6))/(((-1)/(-48))/1). Let u be (9/(-6))/(-3) + r/112. Factor 0 + 2/7*i - u*i**2.
-2*i*(i - 1)/7
Let t(c) = 5*c**2 - 1. Suppose -8*h - 44 - 28 = 0. Let w(k) = 11*k**2 - 2. Let l(i) = h*t(i) + 4*w(i). Solve l(f) = 0 for f.
-1, 1
Let b(j) = 11*j**2 - 9*j. Let m be 1/2*6 + 4. Let k = 16 - m. Let f(q) = -5*q**2 + 4*q. Let y(l) = k*f(l) + 4*b(l). Let y(d) = 0. Calculate d.
0
Let r(w) be the third derivative of -5*w**7/42 + 47*w**6/24 - 59*w**5/6 + 125*w**4/6 - 20*w**3 - 109*w**2. Let r(j) = 0. Calculate j.
2/5, 1, 2, 6
Let j(s) = 3*s**4 + 33*s**3 - 4*s**2 - 105*s - 76. Let t(g) = -6*g**4 - 66*g**3 + 9*g**2 + 210*g + 150. Let r(z) = 9*j(z) + 5*t(z). Factor r(d).
-3*(d - 2)*(d + 1)**2*(d + 11)
Suppose 8*y - 6*y - 10 = 0. Suppose -7*c = -y*c + 5*j - 9, -2*j = -c. Solve -c*k - 4/9 - 14/9*k**2 = 0.
-1, -2/7
Find t such that -4 - 56*t - 51*t + 156*t - 43*t - 2*t**3 = 0.
-2, 1
Let p(q) be the third derivative of -q**5/140 - 55*q**4/28 + 111*q**3/14 + 435*q**2. Determine x, given that p(x) = 0.
-111, 1
Let d be 4*3/(-12)*-2. Let q = 0 + d. Factor -q*b**3 - 8*b - 4*b**2 + 10*b**3 - 16*b**2 + 20*b**4.
4*b*(b - 1)*(b + 1)*(5*b + 2)
Let p(t) be the first derivative of -t**7/98 + 3*t**6