z.
2
Let r(z) = -5*z**2 + 7. Let m(l) = -3*l + 5*l - 5*l + 2 + l. Let i be m(8). Let h(x) = 2*x**2 - 3. Let v(w) = i*h(w) - 6*r(w). Determine p, given that v(p) = 0.
0
Suppose -144*w + 33*w + 222 = 0. Factor -9/5 - 3/5*b**w - 12/5*b.
-3*(b + 1)*(b + 3)/5
Let p(h) be the third derivative of h**8/840 - 4*h**7/525 - 11*h**6/300 - h**5/25 - 31*h**2 + 2*h. Factor p(k).
2*k**2*(k - 6)*(k + 1)**2/5
Let z(r) = -16*r**3 - r**2 - r. Let f be z(-1). Factor 7*m**2 + m**2 + f*m**4 - 24*m**3 + 8*m**2 - 4*m - 3*m**5 - m**5.
-4*m*(m - 1)**4
Let c(n) be the second derivative of 0*n**2 + 0 + 1/9*n**3 - 1/12*n**4 + 1/60*n**5 - 12*n. Factor c(h).
h*(h - 2)*(h - 1)/3
Suppose 6*z - 21 = -9. Let b(i) be the first derivative of 1/2*i**z - 4/25*i**5 + 3 - 2/5*i**4 + 1/5*i**3 - 2/5*i. Find u, given that b(u) = 0.
-2, -1, 1/2
Solve 945/2*q**3 - 765*q**2 - 100 - 135/2*q**4 + 470*q = 0 for q.
2/3, 5
Suppose 4*p = 9*p - 15. Factor 4*j**p + 48*j + 26*j**2 - 24*j**2 - 26*j**2 - 32.
4*(j - 2)**3
Factor 105*i + 20 + 28*i**2 - 253*i - 4*i**3 + 104*i.
-4*(i - 5)*(i - 1)**2
Factor 78/7*g + 507/7 + 3/7*g**2.
3*(g + 13)**2/7
Let l(p) be the third derivative of 4*p**7/105 + 3*p**6/20 + p**5/5 + p**4/12 - 8*p**2 - 4*p. Factor l(u).
2*u*(u + 1)**2*(4*u + 1)
Let n = -5377/50 + 215/2. Let k = 109/225 + n. Find w such that -2/9 + k*w**2 + 4/9*w**3 - 2/9*w**4 - 2/9*w**5 - 2/9*w = 0.
-1, 1
Let u(b) = 5*b**3 + 10*b**2 + 35*b + 30. Suppose 15 = 7*o - 8*o. Let q(v) = v**2 - 1. Let a(w) = o*q(w) - u(w). Factor a(j).
-5*(j + 1)**2*(j + 3)
Let c(x) be the first derivative of 5*x**3/3 + 50*x**2 - 105*x - 177. Let c(s) = 0. Calculate s.
-21, 1
Let q(a) be the third derivative of -5*a**8/336 + 8*a**7/3 - 703*a**6/4 + 13690*a**5/3 - 253265*a**4/24 + 176*a**2. Suppose q(l) = 0. Calculate l.
0, 1, 37
Let v(m) = -m**2 + 18. Let a be v(-4). Let k(t) be the first derivative of -1/2*t**3 + 6 + 3*t + 3/4*t**a. Let k(o) = 0. Calculate o.
-1, 2
Factor 0 - 4/7*w**2 - 132/7*w.
-4*w*(w + 33)/7
Let h(f) be the third derivative of f**8/336 - f**7/70 + f**6/60 + 5*f**2 - 4*f. Determine u, given that h(u) = 0.
0, 1, 2
Let k = 148942/5 + -29977. Let r = 189 + k. Solve r*l**2 + 0*l - 2/5*l**3 + 0 = 0 for l.
0, 1
Let a(q) be the third derivative of 0*q + 49/8*q**3 + 0 - 7/2*q**4 - 39*q**2 + 29/80*q**5 - 1/80*q**6. Factor a(b).
-3*(b - 7)**2*(2*b - 1)/4
Suppose 6 = -2*h, 145*m - 4 = 140*m - 2*h. Let a(n) be the first derivative of 35/4*n**4 + 5/6*n**6 - 2 + 0*n**m - 5*n**3 - 5*n**5 + 0*n. Solve a(u) = 0 for u.
0, 1, 3
Let h(k) = 11*k**2 - k**3 + 2 - 1 + 5*k + 1 - 7*k**2. Let g be h(5). Factor -g*r**5 - 2*r - 11*r**4 + 8*r**2 - 12*r**3 + 3*r**4 + 16*r**4.
-2*r*(r - 1)**4
Suppose -60 = 87*w - 102*w. Determine j so that 0*j - 2/3*j**w + 0*j**2 - 1/3*j**3 + j**5 + 0 = 0.
-1/3, 0, 1
Let f(t) be the third derivative of -1/24*t**4 + 0*t**7 + 1/60*t**6 + 0*t**3 - 13*t**2 - 1/336*t**8 + 0*t**5 + 0*t + 0. Suppose f(h) = 0. What is h?
-1, 0, 1
Factor -12*s - 4*s**2 - 14*s + 26*s - 12*s.
-4*s*(s + 3)
Let r(d) be the third derivative of 16/105*d**7 + 0*d + 1/24*d**8 + 0*d**3 + 9*d**2 + 0*d**4 + 0 + 0*d**5 + 1/15*d**6. What is k in r(k) = 0?
-2, -2/7, 0
Let h(x) = 4*x**3 - 2*x**2 + 4*x + 3. Let z(l) = -1 + 98*l**2 - l**3 - l - 98*l**2. Let y(a) = h(a) + 3*z(a). Solve y(i) = 0 for i.
0, 1
Let h(s) = -s**2 + 179*s - 7198. Let q be h(61). Suppose -1/4*a**5 - 1/2*a**4 + 0 + 1/4*a + q*a**3 + 1/2*a**2 = 0. What is a?
-1, 0, 1
Let u be (9/2)/(-9) - (-578)/2436. Let i = 2/87 - u. Solve 2/7*a**2 - 2/7*a + 2/7*a**3 - i = 0 for a.
-1, 1
Suppose -x = -2*i - 2*i - 20, x - 3*i - 16 = 0. What is u in -23*u**2 + 4*u - 2*u**2 - x*u + 20 + 5*u**4 = 0?
-2, -1, 1, 2
Let a(t) be the first derivative of 2*t**6/3 + 24*t**5/5 + 5*t**4 - 316. Factor a(p).
4*p**3*(p + 1)*(p + 5)
Let u(i) = -128*i + 387. Let f be u(3). Find w, given that 1/8*w**f + 3/4*w**2 + 3/2*w + 1 = 0.
-2
Let d = 1025 - 1022. Let r(k) be the first derivative of 12*k + 20/3*k**d - 11 - 22*k**2 + 3*k**4. What is c in r(c) = 0?
-3, 1/3, 1
Let l(d) = d**3 + 3*d**2 + 4*d + 7. Let j be l(-2). Let k(b) be the first derivative of j*b + 9*b + 5*b**2 + 5 - 3*b**2 - 8*b**2 + b**3. Factor k(u).
3*(u - 2)**2
Suppose 3*p + 3 = 0, -305*h + 300*h + 5*p = -15. Factor 1/8*q**3 - 5/8*q**h + 3/8*q + 9/8.
(q - 3)**2*(q + 1)/8
Let q(t) be the third derivative of t**8/3360 - t**7/1260 - 11*t**4/12 + 21*t**2. Let d(o) be the second derivative of q(o). Factor d(g).
2*g**2*(g - 1)
Let c = 9706/7 - 1386. Let x = 3 - 3. Let x*s - c*s**2 + 16/7 = 0. What is s?
-2, 2
Suppose c + 8 = 4*i + 5*c, 4*c - 17 = 5*i. Let g(k) = 3*k**2 - 27*k + 51. Let y(m) = m - 1. Let f(r) = i*g(r) - 3*y(r). Factor f(w).
-3*(w - 4)**2
Let x(v) be the third derivative of -25*v**2 + 1/24*v**5 - 1/1344*v**8 + 1/24*v**3 + 1/168*v**7 - 5/96*v**4 - 1/48*v**6 + 0*v + 0. Solve x(z) = 0.
1
Let t(z) be the third derivative of -3/4*z**4 - 1/60*z**6 - 1/5*z**5 + z**2 + 0*z**3 + 0*z + 0. Factor t(n).
-2*n*(n + 3)**2
Let x(p) = 8*p**2 - 625*p + 49286. Let f(o) = -30*o**2 + 2501*o - 197148. Let i(d) = 6*f(d) + 22*x(d). Find t, given that i(t) = 0.
157
Let d(a) be the third derivative of -a**6/80 + 23*a**5/40 - 5*a**4 + 19*a**3 + 4*a**2 + 27*a. Factor d(q).
-3*(q - 19)*(q - 2)**2/2
Let w(j) = j - 1. Let l be w(3). Suppose 69 - 4*d**3 - d**4 - 5*d**2 + 0*d**l - 2*d - 69 = 0. Calculate d.
-2, -1, 0
Suppose -15 = -5*h - 5*v, -88*h + 13 = -84*h + 5*v. Factor 4/13*k**h + 0*k + 2/13*k**4 - 6/13*k**3 + 0.
2*k**2*(k - 2)*(k - 1)/13
Suppose 2/5*n**3 - 88/5*n + 16/5*n**2 + 96/5 = 0. What is n?
-12, 2
Factor 9*s**2 + 1092*s + 90 - 2*s**3 - 1170*s + 0*s**3 + 13*s**2.
-2*(s - 5)*(s - 3)**2
Let j = 59/165 - 4/165. Find f, given that 1/6*f**3 - 1/6*f**5 + 0*f - j*f**4 + 0 + 1/3*f**2 = 0.
-2, -1, 0, 1
Let b be (261/(-15) - -18)/((-1)/(-10)). Let v be (-2)/(-4) + 3/2. Find s such that b*s**2 - s**4 - v*s**2 - 7*s**2 + 3*s**3 + s = 0.
0, 1
Suppose -4 = -3*z + 107. Let c = z + -27. Determine g so that 0*g**2 - 2*g + g**2 + 2 + c*g - 11*g = 0.
1, 2
Let x(m) be the first derivative of 0*m**4 + 6 + 0*m - 2*m**2 - 1/20*m**5 + 1/2*m**3. Let s(y) be the second derivative of x(y). Factor s(b).
-3*(b - 1)*(b + 1)
Let d(z) be the third derivative of z**9/12096 - z**8/1344 + z**7/504 - z**5/60 + z**4/2 - 2*z**2 + 10*z. Let y(n) be the third derivative of d(n). Factor y(l).
5*l*(l - 2)*(l - 1)
Let l(t) be the first derivative of 1/2*t**2 + 1/4*t**4 + 3 + 0*t + 17/12*t**3. Factor l(r).
r*(r + 4)*(4*r + 1)/4
Let u(q) be the second derivative of -q**7/840 + q**6/72 - q**5/15 + q**4/6 - 11*q**3/3 - 23*q. Let r(v) be the second derivative of u(v). Factor r(s).
-(s - 2)**2*(s - 1)
Let g(y) = -y**4 - y**2 - y + 2. Let o(u) = -6*u**5 - 18*u**4 - 39*u**3 - 6*u**2 + 18*u - 12. Let q(j) = 9*g(j) + o(j). Suppose q(h) = 0. What is h?
-2, -1, 1/2
Let b = -839/2 - -1679/4. Let z(d) be the first derivative of -1/5*d**5 + b*d**4 + d**3 + 2*d - 2 - 5/2*d**2. Find x, given that z(x) = 0.
-2, 1
What is c in 1/2*c + 2*c**4 + 1/2*c**5 - 4*c**2 + 2 - c**3 = 0?
-4, -1, 1
Let r(d) be the first derivative of -4*d**3/3 - 20*d**2 + 96*d - 406. Factor r(p).
-4*(p - 2)*(p + 12)
Let y be (12/(-63))/((-4)/(-224)*-404 + 7). Factor -10/9*v**3 + 38/9*v**2 - 32/9*v - y.
-2*(v - 2)**2*(5*v + 1)/9
Factor 392 + 1/2*f**2 - 28*f.
(f - 28)**2/2
Suppose 4*c + 38 - 54 = 0. Solve -2/3*a**5 - 2/3*a - 4*a**2 + 4/3*a**3 + 2 + 2*a**c = 0.
-1, 1, 3
Let f(x) be the second derivative of -x**5/30 - 4*x**4/9 - 5*x**3/9 + 14*x**2/3 - 2*x + 5. Factor f(j).
-2*(j - 1)*(j + 2)*(j + 7)/3
Let m be -14 + 153/63 + 12. Determine s so that -1/7*s**5 + 1/7*s**4 + 0 - 5/7*s**2 + 2/7*s + m*s**3 = 0.
-2, 0, 1
Suppose -22*w - 4*w**4 - 859*w**3 - 24*w + 863*w**3 + 10*w + 36*w**2 = 0. Calculate w.
-3, 0, 1, 3
Let h(x) be the first derivative of 7*x**5/20 + x**4/8 - 7*x**3/4 + x**2 + x - 49. Suppose h(c) = 0. Calculate c.
-2, -2/7, 1
Let t(b) be the third derivative of 55/4*b**4 + 0 + 0*b - 15*b**3 - 121/24*b**5 + 21*b**2. Find n, given that t(n) = 0.
6/11
Let r = 57 - 55. Factor r*u**2 - 1 + 13*u**3 + 5*u - 17*u**2 - 4*u**4 - 2*u + 4*u.
-(u - 1)**3*(4*u - 1)
Let z(t) be the first derivative of -t**2/2 - 3*t - 12. Let q be z(-7). Let 6/5*i + 2/5*i**5 + 0 - q*i**2 + 24/5*i**3 - 12/5*i**4 = 0. Calculate i.
0, 1, 3
Let o(w) be the third derivative of w**