5*a. Let h = 23 - 22. Let v(l) = l**2 + l + 1. Let t(z) = h*k(z) + 10*v(z). Factor t(m).
5*(m - 2)*(m - 1)
Let m(b) = 8*b**4 - 60*b**3 - 81*b**2 + 75*b + 83. Let j(w) = -9*w**4 + 57*w**3 + 81*w**2 - 75*w - 84. Let a(p) = -5*j(p) - 6*m(p). Factor a(i).
-3*(i - 26)*(i - 1)*(i + 1)**2
Let w(m) be the third derivative of -m**8/448 + 13*m**7/280 + 9*m**6/32 + 47*m**5/80 + m**4/2 + 3*m**2 + 128*m. Let w(u) = 0. Calculate u.
-1, 0, 16
Let b be (-2 - 0 - -10)/(2/4). Let n be (1*b)/(-13 + 26). Solve 504/13*k**4 + 212/13*k**2 - 42*k**3 - n - 162/13*k**5 + 8/13*k = 0.
-2/9, 2/3, 1
Let q = -50664/5 + 10136. Find t such that -44/5*t - 2*t**2 - q = 0.
-4, -2/5
Let n(g) be the first derivative of g**5/40 + g**4/12 - g**3/4 - 9*g + 10. Let j(x) be the first derivative of n(x). Suppose j(w) = 0. What is w?
-3, 0, 1
Determine u so that -15*u - 10*u**4 + 8*u**2 + 17*u**2 - 5*u**5 - 15*u**2 + 20*u**3 = 0.
-3, -1, 0, 1
Let j be 3 - -11*(-2)/22. Factor 0*o + 0 - 2/3*o**j.
-2*o**2/3
Let k(n) be the first derivative of n**4/9 + 2*n**3/9 + 5*n - 11. Let f(r) be the first derivative of k(r). Factor f(v).
4*v*(v + 1)/3
Let g(h) be the first derivative of -h**4/7 + 8*h**3/7 + 481. Factor g(w).
-4*w**2*(w - 6)/7
Let h be (1561/70 + (-2)/(-10))*2. Factor h*x - 25*x + x**2 + 3 - 24*x.
(x - 3)*(x - 1)
Let q = 50 + -114. Let y be q/(-30) - 2/15. Factor -10/7*m**y + 6/7*m**3 + 4/7*m + 0.
2*m*(m - 1)*(3*m - 2)/7
Let c(n) = 21*n - 30. Let p(y) = -y**2 - 22*y + 31. Let d(o) = -4*c(o) - 3*p(o). Factor d(r).
3*(r - 3)**2
Suppose 0 = -31*c - 12*c. Let y(p) be the third derivative of 0*p**3 + 0*p + 10*p**2 + 0 + 0*p**5 - 1/360*p**6 + c*p**4. Solve y(v) = 0.
0
Let s = 20593 - 102963/5. Factor 1/5*k - 1/5*k**3 - 1/5*k**4 + 3/5*k**2 - s.
-(k - 1)**2*(k + 1)*(k + 2)/5
Let 1/5*f**5 + 0*f**3 + 0 + 53/5*f**4 + 0*f + 0*f**2 = 0. Calculate f.
-53, 0
Let p be 96/30 - 4/20. Let q(m) = 10*m**3 + 2*m**2 - 1. Let v be q(1). Factor 11 + 2*h**p - v.
2*h**3
Let f(z) be the second derivative of z**5/30 - z**4/3 + z**3 - 4*z**2/3 + 3*z + 9. Find g, given that f(g) = 0.
1, 4
Suppose 32/3*k + 2/3*k**2 + 10 = 0. Calculate k.
-15, -1
Let w(r) be the third derivative of 1/90*r**5 + 0*r**3 + 0*r - 1/36*r**4 + 0 - 8*r**2. Let w(f) = 0. Calculate f.
0, 1
Let c(v) be the third derivative of 4*v**2 + 125/72*v**4 + 0*v**3 - 5/18*v**5 + 0*v + 1/72*v**6 + 0. Let c(t) = 0. What is t?
0, 5
Suppose -5*a - 5*s + 29 = -26, -3*a - 4*s = -35. Factor 23 - 11 + 3*o**2 + a*o - 6.
3*(o + 1)*(o + 2)
Let q(n) = -3*n**2 + 456*n + 5. Let y(t) = -2*t**2 + 228*t + 2. Let c(z) = -2*q(z) + 5*y(z). Factor c(j).
-4*j*(j - 57)
Let m(i) = -i**2 + 5*i - 4. Let b be m(2). Find u, given that 4*u + 5 - b*u + 2*u + 3 - 4*u**2 = 0.
-1, 2
Suppose -5*d + x = -45, 3*d + 4*x = 6*d - 10. Let c be (-4)/((-18)/d - (-1)/(-5)). Determine h so that 1/5*h - 1/5*h**3 + 1/5 - 1/5*h**c = 0.
-1, 1
Let x(b) be the third derivative of -b**6/120 + b**5/12 - b**4/6 + 276*b**2. Solve x(r) = 0.
0, 1, 4
Let c(j) = -146*j + 295. Let k be c(2). Solve -1/10*u**5 + 9/10*u + 1/5*u**2 - 4/5*u**k - 3/5*u**4 + 2/5 = 0.
-4, -1, 1
Let t be ((-3)/10)/((-30)/25). Solve -t*b + 0 + 1/4*b**2 = 0.
0, 1
Let l(g) = -3*g + 12. Let q(j) = -j**2 - 14*j - 20. Let i be q(-12). Let s be l(i). Factor s + 1/2*t**3 + 0*t + 0*t**2.
t**3/2
Let u(w) = w**4 + w**2. Let n(d) = -d**5 + 2*d**4 + 9*d**2 - 40 + 86 - 46. Let h(p) = -2*n(p) + 10*u(p). Let h(r) = 0. What is r?
-2, 0, 1
Let n = -59 - -62. Find r, given that 7*r**n - 12*r**5 + 8*r**5 - 7*r**3 = 0.
0
Factor 125*m - 2*m**2 - 38*m + 132*m - 8442 - 270 + 45*m.
-2*(m - 66)**2
Suppose 175*x - 159*x = 32. What is g in -4/9 + 2/3*g**3 - 20/9*g**x + 2*g = 0?
1/3, 1, 2
Let t(d) be the first derivative of -7 - 4/3*d + 4/9*d**3 + 1/3*d**2 - 1/6*d**4. Suppose t(s) = 0. What is s?
-1, 1, 2
Let o(s) = s**2 - 7*s - 18. Let t be o(10). Factor 11 + 28*m**2 + 92*m + t + 6 - 5.
4*(m + 3)*(7*m + 2)
Let z be 9 - -5 - 4 - 0. Let m(n) be the second derivative of 0 + 2/15*n**3 + z*n - 1/90*n**4 - 3/5*n**2. Factor m(d).
-2*(d - 3)**2/15
Let g be 5375/40 - 5 - (-3)/(-8). Suppose -g = 5*k - 134. Let -5/4*h**3 - 17/4*h**2 - 4*h - k = 0. What is h?
-2, -1, -2/5
Suppose -4*s = -973 - 819. Factor 8*q**2 + 52*q**2 - 8*q + 0*q**2 + s*q**4 + 32*q**2 - 352*q**3.
4*q*(4*q - 1)**2*(7*q - 2)
Let u(d) be the first derivative of 84*d**2 - 93/20*d**5 - 32*d - 226/3*d**3 - 21 + 223/8*d**4 + 7/24*d**6. Let u(b) = 0. Calculate b.
2/7, 1, 4
Let b(l) be the second derivative of l**5/100 - l**4/12 - 7*l**3/15 - 123*l - 2. Determine t, given that b(t) = 0.
-2, 0, 7
Let k(m) be the third derivative of m**6/280 + 23*m**5/140 + 43*m**4/56 + 3*m**3/2 - 11*m**2. Determine u, given that k(u) = 0.
-21, -1
Solve -192/7*p + 4/7*p**2 + 2304/7 = 0 for p.
24
Let r(g) be the first derivative of 1/8*g**4 + 1/9*g**3 - 1/30*g**5 - g**2 - 10 + 4/3*g. Factor r(l).
-(l - 2)**2*(l - 1)*(l + 2)/6
Suppose -4*a - 5*b + 3*b = -8, 4 = -b. Suppose z + 2*t = 2*z - 2, 4*t = 4*z - a. Solve 0 + z*k + 2/7*k**3 + 4/7*k**2 = 0 for k.
-2, 0
Suppose -4*v - 2*c = -14, -3*v = 2*v + 2*c - 16. Let s(d) be the first derivative of 0*d**v + 2/27*d**3 + 0*d + 2. Factor s(l).
2*l**2/9
Factor 72*q + 1/2*q**2 + 143/2.
(q + 1)*(q + 143)/2
Determine i so that 3*i**3 + 34 - 32*i - 102*i + i**3 - 24*i**2 - 106 + 34*i = 0.
-2, -1, 9
Let h(g) be the second derivative of 0 + 4*g - 5/6*g**3 + 5/12*g**4 - 5*g**2. Factor h(s).
5*(s - 2)*(s + 1)
Let r(q) be the second derivative of 0 + 1/15*q**6 - 1/5*q**5 - 2/3*q**4 - 13*q + 2/3*q**3 + 3*q**2. Suppose r(h) = 0. Calculate h.
-1, 1, 3
Let o(a) = 5. Let f(j) = -6. Let b(c) = -4*f(c) - 5*o(c). Let q(r) = r**2 - 4*r + 2. Let g(h) = -21*b(h) - 3*q(h). Factor g(y).
-3*(y - 5)*(y + 1)
Let y(s) = -15*s**4 + 3*s**3 + 16*s**4 - 4*s**3. Let g(o) = o**4 + o**3 + 2*o**2 - 4*o. Let l(p) = 2*g(p) - 6*y(p). Factor l(f).
-4*f*(f - 2)*(f - 1)*(f + 1)
Suppose 0*q + 2*q**5 + 4 - 64*q**2 - 14*q + 80*q**2 - 4*q**4 - 4*q**3 = 0. Calculate q.
-2, 1
Factor -12*d + 2*d**4 - 2*d**2 + 4*d**2 - 6*d**2 + 10 + 12*d**3 - 4*d**2 - 4*d**4.
-2*(d - 5)*(d - 1)**2*(d + 1)
Let q(k) = -k**3 - 63*k - 214. Let s be q(-3). Factor 0 - 1/7*p**4 - 4/7*p**s + 0*p - 5/7*p**3.
-p**2*(p + 1)*(p + 4)/7
Let a be (-2972)/(-60) - 2 - (-1)/(-3). Let p = a + -47. Find j, given that 0 - 3/5*j**3 - p*j**2 + j**4 + 1/5*j - 2/5*j**5 = 0.
-1/2, 0, 1
Let r(g) be the second derivative of -11*g**4/3 - 28*g**3/3 - 6*g**2 + 87*g. Suppose r(w) = 0. Calculate w.
-1, -3/11
Let -135/2*m**5 - 72*m + 1032*m**3 - 216 + 1164*m**2 - 531/2*m**4 = 0. What is m?
-6, -2/3, 2/5, 3
Let t(m) be the first derivative of 0*m**4 + 0*m + 1/90*m**5 + 0*m**3 - 2*m**2 - 2. Let c(r) be the second derivative of t(r). Find g, given that c(g) = 0.
0
Let k(z) be the third derivative of z**8/336 + z**7/210 - z**6/120 - z**5/60 + 220*z**2. Factor k(r).
r**2*(r - 1)*(r + 1)**2
Let t = -31487/2 - -15745. Factor -1/4*b**2 - t*b - 9/4.
-(b + 3)**2/4
Let o(u) be the second derivative of u**6/2 + u**5/4 - 185*u**4/6 + 130*u**3 - 180*u**2 - 3*u + 8. Determine p, given that o(p) = 0.
-6, 2/3, 2, 3
Let l(a) be the first derivative of a**4/12 + 755. Factor l(z).
z**3/3
Determine m so that -m + 5*m**2 + 10*m + 0*m - 4*m = 0.
-1, 0
Let a(s) be the second derivative of -s**6/10 + 3*s**5/5 - 3*s**4/4 - 2*s**3 + 6*s**2 + 3*s + 2. Find i such that a(i) = 0.
-1, 1, 2
Let g be ((-3)/12)/(78/40 - 2). Suppose 6*t**3 - g*t**5 + 4*t**4 + 4*t - 10*t**2 + 3*t**5 - 2*t**4 = 0. What is t?
-2, 0, 1
Let l be -20*(-962)/1300 + 2/2 + -7. Suppose -l*a**2 - 34/5*a**4 - 2/5 - 8/5*a**5 - 56/5*a**3 - 16/5*a = 0. What is a?
-1, -1/4
Let i(r) = r**3 - 20*r**2 + 16*r. Suppose -n + 10 = j, 5*n + 2*j - 25 - 19 = 0. Let a(q) = -4*q**3 + 60*q**2 - 48*q. Let s(o) = n*i(o) + 3*a(o). Solve s(z) = 0.
0, 1, 4
Let j(p) = 535*p**2 + 94*p + 2. Let q(h) = 1073*h**2 + 189*h + 3. Let g(y) = 10*j(y) - 4*q(y). Suppose g(s) = 0. Calculate s.
-2/23
Suppose 10*v**2 + 4*v - 16/3 + 2*v**4 - 32/3*v**3 = 0. Calculate v.
-2/3, 1, 4
Let m = 18 + -14. Suppose 0*k - k = -2*u + 8, -k + 22 = m*u. What is b in 10*b - 34*b - 48*b**4 + 142*b**3 - 21*b + 7*b - 18*b**2 - 32*b**u - 6 = 0?
-3, -1/4, 1
Let l be (-182)/52*((-24)/21)/2. Factor 5/4*h**l - 1/2 + 3/4*h.
(h + 1)*(5*h - 2)/4
Suppose 80 = -95*c + 99*c. Factor 0*g**5 + 4*g**5 - 16*g**4 + 82*g**2 - 