 n(r). Find j, given that m(j) = 0.
0, 1
Factor -3*y - 3/4*y**4 + 6 - 9/2*y**2 + 15/4*y**3.
-3*(y - 2)**3*(y + 1)/4
Let y(j) be the first derivative of 0*j + 2*j**3 - 129/8*j**4 + 1 + 6*j**5 + 3*j**2. Let y(z) = 0. Calculate z.
-1/4, 0, 2/5, 2
Let c(a) = 5*a**5 - 30*a**4 + 57*a**3 - 40*a**2 - 3. Let b(h) = 10*h**5 - 60*h**4 + 115*h**3 - 80*h**2 - 5. Let s(t) = -3*b(t) + 5*c(t). What is w in s(w) = 0?
0, 2
Let i(y) = -y**5 + y**3 - y**2 - y - 1. Suppose 6*u + 22 = -2. Let h(q) = 5*q**5 + q**4 - 7*q**3 + 3*q**2 + 6*q + 4. Let m(j) = u*i(j) - h(j). Factor m(b).
-b*(b - 1)**2*(b + 1)*(b + 2)
Let t(i) be the second derivative of i**7/56 + i**6/20 - 3*i**5/40 - i**4/2 - 7*i**3/8 - 3*i**2/4 + 10*i. Factor t(s).
3*(s - 2)*(s + 1)**4/4
Let o = -75 + 151/2. Factor 1/2*g**3 + 1/2*g**2 + 0*g - o*g**5 + 0 - 1/2*g**4.
-g**2*(g - 1)*(g + 1)**2/2
Factor 5*w + 4 - 4*w**2 - 2*w**2 - 8*w + 3*w**3 + 2.
3*(w - 2)*(w - 1)*(w + 1)
Factor -3/2*c - 3/4 - 3/4*c**2.
-3*(c + 1)**2/4
Let i = 7 + -4. Solve 8*z**i + 4*z**5 - 5*z - z**5 + 10*z**4 + 0*z**5 - 2 + 2*z**3 = 0 for z.
-1, 2/3
Let s(q) be the second derivative of 0*q**2 + 0 + 2/15*q**3 + 1/25*q**5 - 2/15*q**4 + 6*q. Factor s(z).
4*z*(z - 1)**2/5
Let y = -13 - 19. Let b be 8/(-18)*48/y. Solve -b*c**2 - 2*c - 4/3 = 0.
-2, -1
Let r(z) be the first derivative of 3*z**5/35 + 9*z**4/28 + 2*z**3/7 + 8. Factor r(t).
3*t**2*(t + 1)*(t + 2)/7
Suppose 2*y - y + t = 4, 2*y + 3*t - 10 = 0. Find s such that -1 + 2*s**2 + s**3 + 3*s - s**y - 4*s**2 = 0.
1
Let a(k) be the third derivative of k**6/420 + k**5/70 - 4*k**3/21 - 8*k**2. Determine d, given that a(d) = 0.
-2, 1
Let q(v) be the first derivative of 1/42*v**4 - 1 - v + 1/70*v**5 + 0*v**2 - 1/105*v**6 - 1/21*v**3. Let h(l) be the first derivative of q(l). Factor h(s).
-2*s*(s - 1)**2*(s + 1)/7
Factor -3*v**4 + 3*v**2 + 3*v**5 - 3*v**3 + v**3 - v**3.
3*v**2*(v - 1)**2*(v + 1)
Suppose 0 = 4*d + 3*g - 28, -4*g - 29 = -13. Factor -d*h - 4 - h**2 - 5*h**2 - 2*h**3 + 2*h**2 - 4*h**2.
-2*(h + 1)**2*(h + 2)
Let a(m) be the second derivative of -m**6/6 - 5*m**5/4 - 10*m**4/3 - 10*m**3/3 - 2*m. What is q in a(q) = 0?
-2, -1, 0
Suppose 4/11 + 6/11*a + 2/11*a**2 = 0. Calculate a.
-2, -1
Let a(y) = -y**3 - 4*y**2 - 6*y - 4. Let t be a(-2). Find v, given that t*v + 0 - 2/3*v**2 + 8/3*v**3 = 0.
0, 1/4
Let d(w) be the second derivative of w**4/12 - 5*w**3/3 - 2*w. Factor d(o).
o*(o - 10)
Let n(w) be the second derivative of w**7/105 + 16*w**6/225 + 29*w**5/150 + 2*w**4/9 + 4*w**3/45 - 45*w - 1. Find y, given that n(y) = 0.
-2, -1, -1/3, 0
Let f be (1 - 0) + 3/3. Suppose 3 = 3*x + 2*h - 3, -5*h = -x + f. Determine w so that -11*w**4 + 5*w**4 - 3*w**3 + 4*w**2 - x*w + w**3 + 4*w**5 + 2*w**2 = 0.
-1, 0, 1/2, 1
Let l = -3415/3 - -1125. Let n = -13 - l. Let 0*d + n - 1/3*d**2 = 0. What is d?
-1, 1
Let l = 6/77 + 5/77. Factor -1/7*i**2 + l + 0*i.
-(i - 1)*(i + 1)/7
Let a = -6 + 10. Let i(o) = -4*o**3 - o**3 + 4*o**3. Let p(d) = 3*d**3 - 3*d**2 - 3*d - 1. Let h(b) = a*i(b) + p(b). Factor h(k).
-(k + 1)**3
Suppose 14*g - 24 = 4. Factor 4/9*f + 0 - 2/9*f**g.
-2*f*(f - 2)/9
Let c = 165 + -2969/18. Let f(n) be the first derivative of 1 - 1/3*n + 1/6*n**2 - 1/15*n**5 - 1/6*n**4 + c*n**6 + 2/9*n**3. Factor f(s).
(s - 1)**3*(s + 1)**2/3
Let s(c) = -4*c - 3. Let n be s(9). Let x be n/(-12) - (-2)/(-8). Factor 0*a - 2*a**x + a**3 - a + 2*a**2.
-a*(a - 1)**2
Let i(q) be the second derivative of q**7/840 - q**6/180 - q**3/2 + 2*q. Let l(r) be the second derivative of i(r). Suppose l(h) = 0. Calculate h.
0, 2
Let i(t) be the second derivative of -t**7/13860 - t**6/3960 + 5*t**4/12 - 5*t. Let g(r) be the third derivative of i(r). What is x in g(x) = 0?
-1, 0
Determine h so that 6*h**3 - 8*h + 11*h**3 - 15*h**3 + 4*h**3 - 6*h**5 - 16*h**4 + 24*h**2 = 0.
-2, 0, 1/3, 1
Let t(h) be the second derivative of h**6/2520 - h**4/168 - h**3/3 + 2*h. Let w(a) be the second derivative of t(a). What is l in w(l) = 0?
-1, 1
Factor 3*l**4 - l**3 + 7*l**3 + l**2 + 2*l**2 + 0*l**3.
3*l**2*(l + 1)**2
Let m(w) = w**2 + w. Let r(g) = 9*g**2. Let j(d) = -8*d**2 + d. Let n(s) = 4*j(s) + 3*r(s). Let y(i) = 2*m(i) + n(i). Suppose y(z) = 0. Calculate z.
0, 2
Let i(p) be the first derivative of -p**6/48 - 3*p**5/40 - 3*p**4/32 - p**3/24 - 7. Factor i(q).
-q**2*(q + 1)**3/8
Let a be (-2)/5 + 1 + 303/(-505). Factor -4/9*m**3 + 2/3*m**2 + a*m + 0 - 2/9*m**4.
-2*m**2*(m - 1)*(m + 3)/9
Let z be 4/18 - (-387)/81. Suppose -q = -z*o - 1, o - 3*q = 2 - 5. Factor 1/5*s - 2/5*s**2 + 1/5*s**3 + o.
s*(s - 1)**2/5
Let m be 1 - (-7 - 6/(-2)). Factor -8*j - 38*j**3 + 20*j**3 - j**m - 7*j**4 - 20*j**2 + 0*j.
-j*(j + 1)*(j + 2)**3
Let t(w) be the second derivative of -w**5/160 - w**4/48 - w**3/48 - w. Factor t(n).
-n*(n + 1)**2/8
Find u such that 7/2*u**2 + 5/4*u**3 + 7/4*u - 1/2 = 0.
-2, -1, 1/5
Let r = -4 - -6. Suppose 12 = 5*v + r. Find q, given that -4*q**v + 3*q**4 - q**4 + 1 + 1 = 0.
-1, 1
Let j(h) = -7*h**3 + h**2 + 7*h - 1. Let m(s) = 6*s - 6*s**3 - 2*s**4 - 2 - s**4 + 4*s**4 + s**2. Let i(l) = 6*j(l) - 5*m(l). What is r in i(r) = 0?
-2, -1, -2/5, 1
Let a be (2/6)/((-1)/(-3)). Let m be (a/(-1))/((-2)/6). What is x in -m*x**2 + x - 2*x**3 + 7*x**2 - 3*x = 0?
0, 1
Let o(l) be the first derivative of -l**3/7 + 15*l**2/14 - 12*l/7 + 38. Suppose o(u) = 0. Calculate u.
1, 4
Suppose -10 = -5*m, -h + 1 = -m + 2. Let c(u) be the first derivative of 0*u + h + 1/8*u**4 + 1/3*u**3 + 1/4*u**2. Factor c(i).
i*(i + 1)**2/2
Solve -3*u - 3 + u**2 - 3*u**4 - 3*u**5 - 4*u**2 + 9*u**2 + 6*u**3 = 0.
-1, 1
Let d(p) be the third derivative of -4*p**2 + 1/112*p**8 + 7/20*p**5 + 0*p + 1/14*p**7 + 0 + 9/40*p**6 + 1/4*p**4 + 0*p**3. Factor d(y).
3*y*(y + 1)**3*(y + 2)
Let t = 223/3 - 74. Find y such that -t*y**5 + 1/3*y**3 + 0 + 1/3*y**4 - 1/3*y**2 + 0*y = 0.
-1, 0, 1
Let a(v) = 3*v**4 - 5*v**3 + 3*v**2 + v - 2. Let s(o) = 2*o**4 - 4*o**3 + 3*o**2 + o - 2. Let l(g) = 3*a(g) - 4*s(g). Factor l(u).
(u - 1)**2*(u + 1)*(u + 2)
Let m be (-2 - 6/(-3))/(-2). Find j, given that -2*j**3 - 2*j + 0*j**2 + 4*j + m*j**2 = 0.
-1, 0, 1
Let h be 3/(-18) + 237/18. Suppose -4 = 3*f - h. Factor -3*z - f - 3/4*z**2.
-3*(z + 2)**2/4
Let s be 1/(-2)*(-20)/(-1150). Let a = 233/345 + s. Solve 4/9*w - 2/3*w**2 - 2/9*w**5 + a*w**4 + 0 - 2/9*w**3 = 0 for w.
-1, 0, 1, 2
Let w(l) be the third derivative of -l**7/2940 + l**6/630 - l**5/420 + l**3/3 + l**2. Let f(m) be the first derivative of w(m). Factor f(b).
-2*b*(b - 1)**2/7
Let d be ((-16)/6)/((-5)/120). Let w be -1 + d/20 + 1. Factor 2/5*q**3 + 24/5*q + 12/5*q**2 + w.
2*(q + 2)**3/5
Let r(t) be the first derivative of 4*t**3/3 + 10*t**2 + 14. Determine a so that r(a) = 0.
-5, 0
Let b(x) be the third derivative of 0*x**4 + 0*x**3 + 0 + 1/30*x**6 + 4/35*x**7 + 0*x**5 + 0*x - 6*x**2. Let b(y) = 0. What is y?
-1/6, 0
Let c be -8 - 2/(-4)*4. Let l = c - -11. Determine z, given that 5*z + 10*z**3 + 5*z**4 - 5*z**5 + 4*z**2 + 6*z**2 + 6*z**l + 1 = 0.
-1
Suppose 0 - y**3 + 4/3*y + 4/3*y**4 - 4/3*y**2 - 1/3*y**5 = 0. What is y?
-1, 0, 1, 2
Factor -108/5 - 3/5*q**2 - 36/5*q.
-3*(q + 6)**2/5
Let y(w) be the third derivative of w**7/1470 + w**6/140 + 13*w**5/420 + w**4/14 + 2*w**3/21 - 15*w**2. Let y(x) = 0. Calculate x.
-2, -1
Suppose 0*i + 6*i = 54. Let n be i/(-3) - -10 - 3. Factor 0 - 2/3*w**3 - 1/3*w**n + 2/3*w + 1/3*w**2.
-w*(w - 1)*(w + 1)*(w + 2)/3
Let p(l) = -15*l + 60. Let d be p(4). Let -4/7*n**3 + d*n + 0 - 2/7*n**2 - 2/7*n**4 = 0. What is n?
-1, 0
Let c be 6/(-1 - 14/(-8)). Let a(m) = -4*m**4 - m**3 + 4*m**2 - 9*m. Let q(v) = 6*v**4 + 2*v**3 - 6*v**2 + 14*v. Let g(d) = c*a(d) + 5*q(d). Factor g(r).
-2*r*(r - 1)**2*(r + 1)
Suppose 4*w = -w - 3*j + 6, 3*w - 12 = j. Factor -4*x**2 + w + 6*x - 2*x**2 + 4*x**2 - 7.
-2*(x - 2)*(x - 1)
Let r be 4/(-18) + 2000/2520. Suppose 0 - 2/7*z + r*z**2 + 0*z**3 - 4/7*z**4 + 2/7*z**5 = 0. What is z?
-1, 0, 1
Let f(l) = -13*l**3 + 5*l**2 + 16*l + 4. Let t(d) = 25*d**3 - 10*d**2 - 32*d - 8. Let i(s) = -11*f(s) - 6*t(s). Let i(v) = 0. Calculate v.
-1, -2/7, 2
Let k be 36/10 + ((-561)/55)/17. Factor 4/3*t**k - 8*t**2 - 32/3 + 16*t.
4*(t - 2)**3/3
Suppose x + 4*d = 2*d + 8, -3*x + 2*d = 8. Factor y**2 - 2/5*y**3 + x - 2/5*y.
-y*(y - 2)*(2*y - 1)/5
Let o(h) = -h**2 - 8*h - 9. Let i be o(-6). Let t(q) be the third de