. Let y(l) = 2*a(l) - 2*b(l). Solve y(m) = 0.
0, 3
Let f(a) be the first derivative of -a**3/18 - a**2/3 + 2*a - 203. Determine h so that f(h) = 0.
-6, 2
Let s(b) be the first derivative of -b**4/60 + b**3/15 - b**2/10 - 13*b + 21. Let w(r) be the first derivative of s(r). Find x, given that w(x) = 0.
1
Suppose 2*t + 21*v - 15 = 18*v, -t - 3 = -2*v. Solve 3/2*p + 3*p**t - 15/4*p**2 + 0 - 3/4*p**4 = 0.
0, 1, 2
Let v(b) be the first derivative of -2*b**3/21 - 4*b**2/7 + 22. Factor v(y).
-2*y*(y + 4)/7
Factor 1471*z**2 + 60*z - 699*z**2 + 9 - 672*z**2.
(10*z + 3)**2
Let i = -205 + 210. Let m(l) be the third derivative of 0*l**3 - 3*l**2 - 1/48*l**4 + 0*l + 0 - 1/60*l**i - 1/240*l**6. Determine c so that m(c) = 0.
-1, 0
Let g = -183 - -174. Let l be (1/g*-6)/(16/6). Suppose -1 + 5/4*p - l*p**2 = 0. What is p?
1, 4
Let u(q) be the second derivative of 6*q**6/5 + 13*q**5 + 140*q**4/3 + 200*q**3/3 + 32*q**2 + 4*q - 8. Suppose u(a) = 0. What is a?
-4, -2, -1, -2/9
Suppose q + v = -2*v, 3*v = 5*q + 36. Let b be q*(-1)/2 + (-203)/77. Factor 2/11*h + 2/11*h**2 - b.
2*(h - 1)*(h + 2)/11
Suppose 1277 - 1261 = 8*k. Factor 2/17*l**3 + 10/17*l - 12/17*l**k + 0.
2*l*(l - 5)*(l - 1)/17
Factor -k**2 + 32*k - 71*k - 85*k - 1 + 1.
-k*(k + 124)
Let r(p) be the second derivative of p**6/255 - p**5/170 + 8*p. Factor r(u).
2*u**3*(u - 1)/17
Let m(p) = 16*p**3 + 62*p**2 + 87*p + 63. Let w(q) = 3*q**3 + 12*q**2 + 17*q + 12. Let o(g) = -2*m(g) + 11*w(g). Factor o(y).
(y + 1)**2*(y + 6)
Let z(f) be the third derivative of f**6/40 + 111*f**5/20 + 4107*f**4/8 + 50653*f**3/2 + 347*f**2. Factor z(t).
3*(t + 37)**3
Let i(a) be the third derivative of -7*a**5/120 + 3*a**4/8 + 3*a**3/4 + 528*a**2. Let i(d) = 0. Calculate d.
-3/7, 3
Let t(w) = -2*w**3 + 2*w**2 + 10*w. Let r be t(-2). Factor -3/7 + 6/7*g**3 + 6/7*g**2 - 3/7*g**r - 3/7*g**5 - 3/7*g.
-3*(g - 1)**2*(g + 1)**3/7
Suppose 24 = 6*w - 12. Let o(q) = -26*q + 158. Let t be o(w). Solve 6/11*p**t - 2/11*p + 0 + 2/11*p**4 - 6/11*p**3 = 0 for p.
0, 1
Let q be (-16)/(-360)*20/((-16)/(-4)). Factor -q - 2/9*f**2 + 4/9*f.
-2*(f - 1)**2/9
Let s = -457 - -460. Let u = 8 - 3. Factor -2*g**4 + 1/2*g + s*g**3 + 0 + 1/2*g**u - 2*g**2.
g*(g - 1)**4/2
Let f(i) = -i**3 + 8*i**2 - 6*i - 5. Let t be f(7). Let v(y) = 19*y + 217. Let h be v(-11). Factor h*d**t + 18/5*d**3 + 26/5*d + 4/5.
2*(d + 1)**2*(9*d + 2)/5
Let y be (-96)/18*(-6)/8. Determine k, given that k + y - 4*k + 9*k - 2*k**3 = 0.
-1, 2
Let q be 6/(-3 + (-18)/(-4)). Let o be (-5 - -11)*2/q. Determine d so that 2/3*d + 0 + 2/3*d**o - 4/3*d**2 = 0.
0, 1
Factor -3/7*j**3 - 15/7 + 3/7*j + 15/7*j**2.
-3*(j - 5)*(j - 1)*(j + 1)/7
Let g be -6 - -4 - -3 - 174/172. Let v = g + 175/258. Factor -v + 2/3*n**2 + 0*n.
2*(n - 1)*(n + 1)/3
Let -4/7*r**2 - 2/7*r - 2/7*r**3 + 0 = 0. Calculate r.
-1, 0
Factor w**2 + 762 + 42*w - 278 + 46*w + 3*w**2.
4*(w + 11)**2
Let q be (-4)/(-6)*(-9 - -15). Factor 0*a**q + 8*a**3 - 11*a**3 + a + 2*a**4.
a*(a - 1)**2*(2*a + 1)
Suppose -20*u + 2*u**2 - 40 + 2*u + 3*u**2 + u**2 - 8*u**2 = 0. What is u?
-5, -4
Suppose 12 = -22*r + 56. Let c(s) be the third derivative of 1/180*s**5 + 0*s**4 + 0*s**3 - 1/360*s**6 + 0*s + 0 + 7*s**r. Factor c(j).
-j**2*(j - 1)/3
Let h(a) be the first derivative of -a**6/10 - 3*a**5/20 + 3*a**4 + 14*a**3 + 24*a**2 + 30*a - 8. Let k(o) be the first derivative of h(o). Factor k(w).
-3*(w - 4)*(w + 1)*(w + 2)**2
Let o(h) be the first derivative of -2*h**3 + 12*h - 3 - 11*h**2 - 5*h**3 + 9*h**3. Factor o(k).
2*(k - 3)*(3*k - 2)
Let o(a) = -a + 1. Let d be o(-6). Suppose -5*w = -d - 38. Suppose 7*r**2 - 8*r**2 + 12*r - 2*r**2 - w = 0. What is r?
1, 3
Let a be (-894)/(-1080) - 44/55. Let t(o) be the third derivative of 4*o**2 + 1/36*o**4 + 1/180*o**6 - a*o**5 + 0*o + 0*o**3 + 0. Determine w so that t(w) = 0.
0, 1/2, 2
Suppose 0*o = 2*o + 8, -3*s - 14 = 5*o. Suppose -4*y - 4*i - 4 = 0, 2*y + 6*i - 5 + 23 = 0. Determine k so that 0*k - 1/6*k**s + 2/3*k**y + 0 = 0.
0, 1/4
Let y = 12285 + -12282. Determine b so that -2/7*b**y - 432/7 - 36/7*b**2 - 216/7*b = 0.
-6
Let l = -50 + 50. Suppose 4*m - 1 - 11 = l. Determine y so that 0 + 3/7*y - 3/7*y**2 + 3/7*y**4 - 3/7*y**m = 0.
-1, 0, 1
Let d(n) be the second derivative of -5*n**7/56 + 11*n**6/24 + 13*n**5/16 - 65*n**4/16 + 25*n**3/12 + 5*n**2 + 130*n. Determine g, given that d(g) = 0.
-2, -1/3, 1, 4
Factor -2/3 - 1/3*g**2 - g.
-(g + 1)*(g + 2)/3
Let v be -3 - (-4)/((-280)/(-235)). Let r(i) be the first derivative of v*i**4 - 4/21*i**6 - 3 + 6/35*i**5 - 2/7*i**3 - 1/7*i**2 + 0*i. Solve r(m) = 0 for m.
-1, -1/4, 0, 1
Factor 57 + 51/2*h - 3/2*h**2.
-3*(h - 19)*(h + 2)/2
Let p(c) be the first derivative of -c**4/2 - 2*c**3/3 + 5*c**2 - 6*c - 744. Factor p(o).
-2*(o - 1)**2*(o + 3)
Let v(u) be the first derivative of 5*u**3/3 + 35*u**2/2 + 30*u - 83. Factor v(t).
5*(t + 1)*(t + 6)
Let q be 174/(-1276)*66/(-18). Factor 1/2*o + 1/2 - q*o**3 - 1/2*o**2.
-(o - 1)*(o + 1)**2/2
Let i be (1033/27*1)/((-12)/36). Let s = i - -115. Factor 2/3*m - 4/9*m**2 - s + 2/3*m**4 - 2/9*m**5 - 4/9*m**3.
-2*(m - 1)**4*(m + 1)/9
Let b(y) = 50*y**3 + 20*y**2 - 490*y - 810. Let v(h) = -7*h**3 - 3*h**2 + 70*h + 116. Let r(k) = 2*b(k) + 15*v(k). Factor r(p).
-5*(p - 4)*(p + 2)*(p + 3)
Let k(m) = 7*m**2 - 11*m - 3. Let n(f) = 3*f**2 - 5*f - 2. Let j(y) = -2*k(y) + 5*n(y). Factor j(l).
(l - 4)*(l + 1)
Let o = 1209/5 - 241. Let m(k) be the first derivative of -3/2*k**4 + 4/3*k**3 - 1/2*k**2 - 8 + 0*k - 1/6*k**6 + o*k**5. Solve m(u) = 0 for u.
0, 1
Let t be (-1)/(-3)*24/(-9 + 13). Solve -40/3*n - 10/3*n**3 - 16/3 - 11*n**t - 1/3*n**4 = 0.
-4, -1
Let m = -251 + 251. Let s(i) be the third derivative of 1/30*i**5 + 0 + 0*i**4 - 4*i**2 + 0*i**6 + 0*i**3 - 1/105*i**7 + m*i. Factor s(v).
-2*v**2*(v - 1)*(v + 1)
What is a in -1053 + 33*a**3 - 125*a**2 + 22*a**3 + 1193 + 45*a**4 - 120*a + 5*a**5 = 0?
-7, -2, 1
Suppose 0 = 4*p - 4, -y = 2*y - 2*p - 1. Let b(q) = q**3 - q**2 + 1. Let t(m) = -2*m**2 - 8*m + 14. Let c(k) = y*t(k) + 2*b(k). Let c(s) = 0. What is s?
-2, 2
Let y(p) be the second derivative of 3*p**5/140 + 3*p**4/28 + 11*p - 5. Factor y(z).
3*z**2*(z + 3)/7
Let t(h) be the second derivative of 0 - 1/5*h**5 + 1/3*h**4 + 0*h**3 + 1/30*h**6 + 10*h + 0*h**2. Factor t(q).
q**2*(q - 2)**2
Let n be -11 - -68*(-55)/(-308). Let 0 + 0*t - n*t**2 - 4*t**3 = 0. Calculate t.
-2/7, 0
Let s(k) be the first derivative of 2*k**3 + k**2/2 - 2. Let a be s(-5). Factor -81*q**5 + 145*q - a*q - 4*q**2 - 40*q**3 - 117*q**4.
-q**2*(q + 1)*(9*q + 2)**2
Let i be -2 + 5/1 - 36/(-18). Suppose -4*q + 2*s - 2 = 0, -3*q + 5*q + 5 = i*s. Determine p, given that 2/7*p**2 + 2/7*p + q = 0.
-1, 0
Let b = 613 - 613. Let -3/4*t**4 + 0 + b*t + 1/4*t**5 + 3/4*t**3 - 1/4*t**2 = 0. What is t?
0, 1
Let z(x) be the second derivative of -x**6/10 - 3*x**5/5 + x**4/4 + 2*x**3 + 13*x - 1. Factor z(l).
-3*l*(l - 1)*(l + 1)*(l + 4)
Let v be 1*2 - (3 - 0 - 3). Factor -65*r**v + 40*r**2 - 35*r + 1 - 5*r**3 - 16.
-5*(r + 1)**2*(r + 3)
Factor 10*l + 256*l**2 - 12 - 123*l**2 - 135*l**2.
-2*(l - 3)*(l - 2)
Factor -7/4*x**3 - 1/4*x**5 + 0*x - 5/4*x**4 + 0 - 3/4*x**2.
-x**2*(x + 1)**2*(x + 3)/4
Suppose 4*r = 3*p - 1, -r + 4*r = p - 2. Let d be -2*(-4)/(3 - p). Factor 4*t**2 - 2*t - 5*t**d - t**2.
-2*t*(t + 1)
Let n be ((-396)/80 + 5)/6. Let m(s) be the second derivative of 0*s**2 - 8*s + 1/80*s**5 - 1/48*s**4 - 1/24*s**3 + n*s**6 + 0. Factor m(h).
h*(h - 1)*(h + 1)**2/4
Let k(c) = -c**2 + 99*c - 1746. Let q be k(76). Solve -18*a - q - 36*a**3 - 97/2*a**2 - 8*a**4 = 0 for a.
-2, -1/4
Let s = -17/25 + 93/100. Suppose s*o**3 + 1/4*o**4 + 0 + 0*o**2 + 0*o = 0. Calculate o.
-1, 0
Suppose 6*j + 138 = -z + 3*j, z + 142 = -4*j. Let a = z + 131. Determine g so that -72/5*g**4 - 9*g**3 - 33/5*g**a + 0*g + 0 - 6/5*g**2 = 0.
-1, -2/11, 0
Let m(h) be the first derivative of 2*h**5/5 - 23*h**4/2 - 397. Factor m(n).
2*n**3*(n - 23)
Suppose -6*h**2 - 40*h + 120 - 15*h + 11*h**2 = 0. What is h?
3, 8
Suppose -7*p = -6*p + 2. Let y(a) = -4*a**2 - 5*a. Let o(n) = n**2 + 2*n. Let q(x) = p*y(x) - 7*o(x). Determine u so that q(u) = 0.
0, 4
Solve 38/3*q**2 - 4/3*q**3 - 24 + 42*q = 0.
-3, 1/2, 12
Let l(u) be the second derivative of u**8/2688 - u**7/840 - 3*u**2 + 4*u. Let d(f) be the first derivative of l(f). Sup