- -1). Suppose -16*p**5 + 21*p**k + 20*p**4 + 23/4*p**2 + 1/2*p + 0 = 0. Calculate p.
-1/4, 0, 2
Suppose -3*q + 4*q = 2*p + 1, 4*q - 4 = 3*p. Let h be ((16 - p)/4)/10 - 0. Factor h*u**3 + 0 + 4/5*u + 6/5*u**2.
2*u*(u + 1)*(u + 2)/5
Let f(s) be the second derivative of s**6/540 - s**5/180 + 8*s**3/3 - 7*s. Let h(v) be the second derivative of f(v). Determine j, given that h(j) = 0.
0, 1
Factor 1/2*h**2 - h**3 - 3/4 + h + 1/4*h**4.
(h - 3)*(h - 1)**2*(h + 1)/4
Suppose -1372*k = -1453*k + 243. What is w in -9*w**2 + 5/2*w**5 + 9*w**4 - 13/2*w**k + 4*w + 0 = 0?
-4, -1, 0, 2/5, 1
What is a in -336 + 27*a**3 + 36*a + 24*a**2 + 26*a**2 + 5*a**4 + 344 = 0?
-2, -1, -2/5
Let d(s) be the first derivative of s**4/36 - s**3/18 - 26*s + 2. Let o(j) be the first derivative of d(j). Solve o(p) = 0.
0, 1
Suppose 3*p - 3 = -5*y + 10, y - 5*p = 25. Suppose y*w = 3*w. Factor -3*c - 9 + 1 - c + w*c + 12*c**2.
4*(c - 1)*(3*c + 2)
Suppose -c = 3*l - 10, -2*c + 4 = -3*l + 11. Factor 9*j - 4*j**l + 24 + 38*j**2 - 61*j - 6*j**2.
-4*(j - 6)*(j - 1)**2
Let -16/15 - 2/15*p**3 - 2/15*p**2 + 4/3*p = 0. What is p?
-4, 1, 2
What is v in -67*v**2 - 4*v**4 + 50*v**2 - 36*v**3 - 63*v**2 - 48*v = 0?
-6, -2, -1, 0
Let x(s) = s - 2. Suppose 2 + 13 = 3*c + v, -5*c - v + 23 = 0. Let a be x(c). Determine y, given that 5*y**a + 3*y**3 + 9*y**2 + y**2 - 12*y**2 = 0.
-1, 0
Suppose -2/9*h**2 - 800/9 - 80/9*h = 0. Calculate h.
-20
Let r = 271271/1220760 - -1/135640. Suppose -p + 6*p + 15 = 0, -3*p = 5*n - 11. Factor -r*c**2 - 4/9*c**3 - 2/9*c**n + 0 + 0*c.
-2*c**2*(c + 1)**2/9
Let o(k) = 4*k - 30. Let d be o(8). Suppose 0 = d*f + 172 - 178. Factor 0 - 1/4*c**f + 1/4*c**2 + 0*c.
-c**2*(c - 1)/4
Let t(k) be the second derivative of -k**5/24 + 5*k**4/24 - 5*k**3/18 + 133*k - 1. Suppose t(f) = 0. Calculate f.
0, 1, 2
Let t(o) be the second derivative of 3*o**7/56 - o**6/24 - o**5/3 + 5*o**4/6 - 5*o**3/6 + 14*o. Let b(z) be the second derivative of t(z). Factor b(a).
5*(a + 1)*(3*a - 2)**2
Let h(s) be the second derivative of 3*s**5/140 + s**4/28 - 3*s**3/7 + 4*s + 1. Factor h(g).
3*g*(g - 2)*(g + 3)/7
Let n(i) be the third derivative of -i**5/100 - 7*i**4/20 - 13*i**3/10 + 135*i**2 + 2*i. Factor n(z).
-3*(z + 1)*(z + 13)/5
Let c(v) be the third derivative of -v**8/10080 + v**7/5040 - v**3 + 8*v**2. Let n(q) be the first derivative of c(q). What is y in n(y) = 0?
0, 1
Let b = 2590 + -12947/5. Suppose -4*t = 5*p - 3, 0 = -3*p - 7*t + 2*t - 6. What is r in -6/5*r**2 + b*r**p + 0*r + 0 + 12/5*r**4 - 9/5*r**5 = 0?
-2/3, 0, 1
Let t(f) be the third derivative of -f**5/120 + 5*f**4/16 + 4*f**3/3 + 44*f**2 - 1. Find u such that t(u) = 0.
-1, 16
Suppose -3*l + 151 = 151. Let a(i) be the first derivative of -3/25*i**5 + 0*i + 0*i**4 - 5 + 0*i**2 + l*i**3. Factor a(y).
-3*y**4/5
Let x = -723 + 3621/5. Let i(g) be the first derivative of 0*g - 13/4*g**4 + 8/3*g**3 - 10 - 1/2*g**2 + x*g**5. Factor i(v).
v*(v - 1)**2*(6*v - 1)
Let j(c) = c**4 - 22*c**3 + 31*c**2 + 30*c + 6. Let x(u) = 2*u**4 - 43*u**3 + 59*u**2 + 60*u + 11. Let q(h) = 11*j(h) - 6*x(h). Factor q(v).
-v*(v - 15)*(v - 2)*(v + 1)
Let p be (-81)/(-72)*(48/(-54))/(-4). Let w(d) be the first derivative of -5/2*d**2 - p*d**4 + 1 - 4/3*d**3 - 2*d. Factor w(c).
-(c + 1)**2*(c + 2)
Let x be (76/16 + -3)*4. Let d be (0/(-2))/(x + -5). Solve 0 - 2/9*q**3 + d*q + 0*q**2 = 0 for q.
0
Let j(u) be the second derivative of 3*u**7/280 - 19*u**6/240 + u**5/20 + 29*u**4/12 - u**2/2 + 5*u + 1. Let n(g) be the third derivative of j(g). Factor n(v).
3*(v - 2)*(9*v - 1)
Let z(c) be the second derivative of -c**6/12 - 3*c**5/8 - 5*c**4/24 + 5*c**3/4 + 5*c**2/2 - 40*c. Solve z(u) = 0 for u.
-2, -1, 1
Let m(k) be the first derivative of k**6/420 + k**5/210 - k**4/42 - 11*k**2 - 26. Let y(l) be the second derivative of m(l). Factor y(j).
2*j*(j - 1)*(j + 2)/7
Let c(t) be the third derivative of -t**6/40 - 3*t**5/10 + 15*t**4/8 - 4*t**3 + t**2 + t. Suppose c(o) = 0. Calculate o.
-8, 1
Let u(n) be the first derivative of 2*n**3/21 - 10*n**2/7 + 48*n/7 - 253. Let u(s) = 0. Calculate s.
4, 6
Let z(r) be the third derivative of r**5/15 - 20*r**4/3 + 800*r**3/3 + 4*r**2 + 34. Factor z(i).
4*(i - 20)**2
Let r(s) = s + 21. Let y be r(-15). Let k = y + -4. Factor -1/4*a**k + 1/2*a - 1/4.
-(a - 1)**2/4
Let 576 - 32*o**3 + 31*o + o**4 + 4*o**5 + o**4 + 33*o - 288*o**2 + 34*o**4 = 0. Calculate o.
-9, -2, 2
Suppose -1171 + 1113 = -29*c. Suppose 0*i**c + 2/11*i**4 + 2/11*i**3 + 0*i + 0 = 0. Calculate i.
-1, 0
Suppose 2*p - 3*u + 28 = -3*p, 0 = 5*p - 2*u + 27. Let q = p - -7. Factor 0 + 2 - 2*w**3 + 6*w**q + 73*w - 79*w.
-2*(w - 1)**3
Let h(m) = m**3 - 2*m**2 - 12*m + 16. Let n be h(4). Determine q so that 0*q**2 + 2/15*q**5 + 0*q - 2/15*q**4 + 0*q**3 + n = 0.
0, 1
Let u = 18 + -9. Let d be (-648)/(-252) - 3/(-7). Determine b so that 0*b - d*b**3 + 7 - 1 + u*b = 0.
-1, 2
Let d(s) be the first derivative of s**4/6 - s**3/2 - s**2 - 17*s + 13. Let g(h) be the first derivative of d(h). Factor g(r).
(r - 2)*(2*r + 1)
Let d = -85 - -79. Let y(i) = 2*i**3 + 11*i**2 - 6*i + 2. Let s be y(d). Factor -36/5*r**s - 2/5 + 54/5*r**4 + 0*r**3 + 16/5*r.
2*(r + 1)*(3*r - 1)**3/5
Let j(v) be the second derivative of -2*v**7/21 + 12*v**6/5 - 81*v**5/5 - 30*v + 3. Factor j(q).
-4*q**3*(q - 9)**2
Let b = 106379/5 - 21275. Suppose 8/5*j - b*j**2 - 23/5*j**4 - 6*j**3 + 0 - j**5 = 0. Calculate j.
-2, -1, 0, 2/5
Let j(z) be the first derivative of 5/3*z**3 + 15/2*z**2 + 0*z - 21. Factor j(l).
5*l*(l + 3)
Suppose 4*o - 97 = -33. Suppose 5*g - o = 3*c, 2*g + g - 21 = -2*c. Let -3*r + 0 - 2*r**3 - 6 + g*r + 7 - r**2 = 0. Calculate r.
-1, -1/2, 1
Let o = -85/8 + 271/24. Suppose 0 + 2/9*g**2 - o*g = 0. Calculate g.
0, 3
Let z(g) be the third derivative of -g**7/42 - 5*g**6/4 + g**5/4 + 115*g**4/6 + 50*g**3 + 429*g**2. Factor z(s).
-5*(s - 2)*(s + 1)**2*(s + 30)
Let n(c) be the third derivative of 0 - 1/5*c**5 + 0*c**3 + 0*c + 2/35*c**7 + 16*c**2 + 1/30*c**6 - 1/6*c**4. Find q, given that n(q) = 0.
-1, -1/3, 0, 1
Suppose -2 = -2*f + 6. Suppose -f*q + 20 = 0, -s - 12 = -0*s - 3*q. Factor 2/9*h**s + 0*h + 0 - 2/9*h**2.
2*h**2*(h - 1)/9
Let c(a) = 5*a**2 - 42*a + 18. Let b be c(8). What is s in 3/7*s**b + 9/7 + 12/7*s = 0?
-3, -1
Let t(g) = 27*g**2 - 32*g**3 - 5*g + 2*g**2 + 12*g**3 - 4*g. Let b(j) = 121*j**3 - 175*j**2 + 55*j - 1. Let q(o) = -6*b(o) - 39*t(o). Factor q(a).
3*(a - 1)*(3*a - 2)*(6*a + 1)
Let n(d) = 18*d + 270. Let v be n(-15). Let l(k) be the third derivative of v*k - 8*k**2 - 4/3*k**3 + 0 - 1/15*k**5 - 1/2*k**4. Suppose l(i) = 0. Calculate i.
-2, -1
Suppose -t = -6*t - 3*q + 24, -5*t - 4*q + 27 = 0. Let w be (1 + 2 + -6 + t)/1. Factor -1/9*v - 1/9*v**3 + 2/9*v**2 + w.
-v*(v - 1)**2/9
Let t(j) = 1025*j**2 + 11*j + 34. Let n be t(-8). Let l be 6/4 - n/(-468). Factor 184/9*d - 84*d**2 + l*d**3 - 686/9*d**4 - 16/9.
-2*(d - 1)*(7*d - 2)**3/9
Let i(g) be the first derivative of -g**3/27 + 40*g**2/3 - 1600*g - 209. Factor i(v).
-(v - 120)**2/9
Let t(y) = 2*y**2 - 74*y - 26. Let i(w) = -w**2 + 73*w + 26. Let x(l) = 7*i(l) + 6*t(l). Factor x(n).
(n + 13)*(5*n + 2)
Let s(j) be the first derivative of -24*j**4 + 2376*j**3 - 88209*j**2 + 2910897*j/2 - 443. Factor s(f).
-3*(4*f - 99)**3/2
Let s(y) be the first derivative of 33 + 3/4*y**2 + 2*y - 1/6*y**3. Suppose s(x) = 0. What is x?
-1, 4
Let d(y) = -y**4 + y**3 - 2*y**2 - y - 1. Let w(p) = 4*p**4 - 9*p**3 + 48*p**2 - 55*p + 32. Let h(g) = -15*d(g) - 3*w(g). Determine a so that h(a) = 0.
-9, 1, 3
Let u(o) be the second derivative of o**6/30 + o**5/10 - 5*o**4/12 - o**3 - 156*o. Find f such that u(f) = 0.
-3, -1, 0, 2
Suppose 0 = -a + 4*p - 9, 5*p - 7 - 8 = 0. Solve -20*w - 8*w**4 - 8*w**3 + 23*w**a + 3*w**4 = 0 for w.
-1, 0, 2
Let i(k) be the first derivative of 25*k**4/4 - 80*k**3/3 - 25*k**2/2 + 80*k + 129. Factor i(n).
5*(n - 1)*(n + 1)*(5*n - 16)
Let o(p) be the first derivative of -4*p**3/21 - 4*p**2/7 + 12*p/7 - 165. Suppose o(q) = 0. What is q?
-3, 1
Let i(r) = 4*r**3 - 35*r**2 + 23*r - 16. Let x(s) = -25*s**3 + 210*s**2 - 140*s + 95. Let n(k) = -35*i(k) - 6*x(k). Suppose n(w) = 0. What is w?
1/2, 1, 2
Let g = 533/505 + 55/101. Factor 2/5*b**2 + g*b + 8/5.
2*(b + 2)**2/5
Let u = 199/66 + -83/33. Solve u*c**2 - 2 + 3/2*c = 0 for c.
-4, 1
Let j(c) be t