m + 1)
Suppose 1 = n - 5. Let r be 14/8 + n/24. Factor -o**r - 1/3*o**4 + 0 - 1/3*o - o**3.
-o*(o + 1)**3/3
Let a(r) = r**3 - r**2 + r - 1. Let t(k) = 7*k**3 - 6*k**2 + 6*k - 6. Let j(y) = -6*a(y) + t(y). Factor j(q).
q**3
Let i be 4/(-20) - 3/(-15). Factor 14*s**2 - 3*s**3 + 6 - 8*s - 2*s**2 - 7*s + i*s**2.
-3*(s - 2)*(s - 1)**2
Let r(m) = m**3 + 3*m**2 + 4. Let q be r(-3). Let z be (-1*q)/(3 - 5). Suppose -3*v**4 + 2*v**2 + z*v**4 - 1 + 0*v**4 = 0. What is v?
-1, 1
Suppose -o = 3*o - 8. Let m(h) be the second derivative of -1/18*h**4 - h + 0 - 1/3*h**o + 2/9*h**3. Suppose m(u) = 0. What is u?
1
Let j(n) be the first derivative of 5*n**7/168 + n**6/12 - 3*n**5/10 + n**4/3 + n**3 + 1. Let t(l) be the third derivative of j(l). Find u, given that t(u) = 0.
-2, 2/5
Let b be 5/((-5)/(20/68)). Let f = b + 99/221. Solve 4/13*c + 0 - f*c**2 = 0 for c.
0, 2
Let v(n) be the first derivative of n**7/2940 - n**3 + 2. Let q(d) be the third derivative of v(d). Let q(j) = 0. What is j?
0
Let c(n) be the second derivative of -3*n**5/80 + n**4/2 - 21*n**3/8 + 27*n**2/4 + 10*n + 1. Factor c(y).
-3*(y - 3)**2*(y - 2)/4
Suppose 0 = -f - 1 + 11. Let g = 14 - f. Determine p so that 2/3*p**g - 2/3*p**2 - 1/3*p + 0 + 0*p**3 + 1/3*p**5 = 0.
-1, 0, 1
Let w(s) be the first derivative of s**7/4620 - s**6/990 + s**5/660 + s**3 + 3. Let b(k) be the third derivative of w(k). Solve b(q) = 0 for q.
0, 1
Let s be 4 + (6 - 7) - 1. Factor -1/2*q**5 + 1/2*q**s - 3/2*q**3 + 0*q + 0 + 3/2*q**4.
-q**2*(q - 1)**3/2
Let q be (1 - -1) + 268/(-133). Let a = q - -141/532. Factor 1/2*k - 1/4*k**2 - a.
-(k - 1)**2/4
Let u(q) = 9*q**3 + 7*q + 7*q**4 + 7 - 5*q**2 + 2*q**2 - 1. Let l(h) = -h**4 - h**3 + h**2 - h - 1. Let p(i) = 6*l(i) + u(i). Factor p(v).
v*(v + 1)**3
Let l(d) = -d**3 - d**2 + 1. Let k(x) = 15*x**3 - 51*x**2 + 441*x - 1041. Let m(o) = -k(o) - 12*l(o). What is p in m(p) = 0?
7
Let z = 869/63 - 95/7. Suppose 2/9*c**2 + 0 - z*c**3 + 0*c = 0. Calculate c.
0, 1
Suppose 0 = 4*n - 4*p - 12, -n - 5*p = 6 - 3. Suppose u = -n, 0 = -4*y - 4*u + u + 2. Factor -h**2 + 6*h**2 - 2*h**2 - h**y.
2*h**2
Let l = 10 + -5. Let q(p) be the third derivative of -1/20*p**4 + 0 + 2/75*p**l + 3*p**2 - 1/15*p**3 + 0*p. Factor q(x).
2*(x - 1)*(4*x + 1)/5
Let f(n) = 2*n**2 + 3*n + 2. Let p be f(-2). Suppose 8 = -p*i + 8*i. Factor 0 - 8/7*h - 10*h**3 + 48/7*h**i.
-2*h*(5*h - 2)*(7*h - 2)/7
Let o(a) = -4*a**2 + a + 3. Let i(h) = 9*h**2 - 2*h - 7. Let u(v) = v**2 + 4*v. Let y be u(-3). Let k(q) = y*i(q) - 7*o(q). What is l in k(l) = 0?
0, 1
Let c(u) be the first derivative of -u**5/15 + u**4/9 + u - 8. Let m(p) be the first derivative of c(p). Factor m(w).
-4*w**2*(w - 1)/3
Let u(b) be the third derivative of 9*b**2 + 0*b**3 + 0*b + 0 - 1/80*b**5 + 1/280*b**7 + 1/160*b**6 - 1/32*b**4. Factor u(z).
3*z*(z - 1)*(z + 1)**2/4
Factor 2205/4*m**2 + 5 - 105*m.
5*(21*m - 2)**2/4
Let a(s) be the second derivative of s**4/15 - 4*s**3/3 + 10*s**2 + 11*s. Suppose a(v) = 0. Calculate v.
5
Let l(p) be the second derivative of -2*p**6/27 + 17*p**5/45 - 7*p**4/9 + 22*p**3/27 - 4*p**2/9 + 5*p. Factor l(r).
-4*(r - 1)**3*(5*r - 2)/9
Let f(o) be the second derivative of o**7/84 + o**6/20 + o**5/20 - o**4/12 - o**3/4 - o**2/4 + 34*o. Determine n so that f(n) = 0.
-1, 1
Find t such that 8*t**5 - 4*t**2 + 4*t**4 + t**3 + t + t**3 - 11*t**5 = 0.
-1, 0, 1/3, 1
Let j = 557 - 555. Factor j + 1/2*q**2 + 2*q.
(q + 2)**2/2
Factor 1/4*q**4 + 0 + 1/4*q - 1/4*q**3 - 1/4*q**2.
q*(q - 1)**2*(q + 1)/4
Suppose -3*y - 8 = -5*y. Let l(h) be the first derivative of -22/5*h**3 - 4*h**y - 32/25*h**5 - 2*h**2 - 2 - 2/5*h. Solve l(x) = 0.
-1, -1/4
Let t(f) = -f**4 + 6*f**3 + 7*f**2. Let k(w) = w**3 + w**2. Let o(j) = -40*k(j) + 5*t(j). Suppose o(v) = 0. Calculate v.
-1, 0
Factor 8 + 2*t**2 - 3*t**2 - 2*t**2 + 4.
-3*(t - 2)*(t + 2)
Let x = -22 - -28. Factor 3*n - 12*n**2 + 20*n - 8*n - x + 3*n**3.
3*(n - 2)*(n - 1)**2
Let q(t) be the first derivative of t**6/900 + t**5/300 - 2*t**3/3 + 1. Let x(h) be the third derivative of q(h). Factor x(w).
2*w*(w + 1)/5
Factor -1244*m - 1598 + 725*m**3 - 962 - 1680*m - 760*m**2 + 5*m**5 - 1236*m - 110*m**4.
5*(m - 8)**3*(m + 1)**2
Suppose 3*r - 82 = -5*n, 8*r - 3*r - 48 = -2*n. Let p = -11 + n. What is x in 0*x + 1/2*x**p + 0 - 1/2*x**2 = 0?
0, 1
Find b, given that -2*b - 1 - 3/4*b**2 = 0.
-2, -2/3
Let p be 2 + 0 + 1 + 1. Let f = 11/7 + -1. Let 0 + 0*w - 2*w**3 - f*w**2 - 10/7*w**p = 0. Calculate w.
-1, -2/5, 0
Suppose 8*k + 7 = 23. Factor -10/7*n + 2/7 + 2*n**k - 6/7*n**3.
-2*(n - 1)**2*(3*n - 1)/7
Let a(j) be the first derivative of 2*j**5/55 - 3*j**4/11 + 26*j**3/33 - 12*j**2/11 + 8*j/11 - 1. Find m, given that a(m) = 0.
1, 2
Let k(a) = -7 + 3*a**2 + 3*a**2 - a - 2*a - a**3. Let u be k(5). Solve -3*p - 2*p**5 + 4*p**u - 3*p + 4*p = 0 for p.
-1, 0, 1
Let o = 27 - 24. Let 0*h**2 + 0 - 2/9*h**5 + 0*h**o + 0*h + 2/9*h**4 = 0. Calculate h.
0, 1
Let u(d) be the second derivative of -d**5/4 - 15*d**4/4 + 25*d**3/3 + d + 5. What is n in u(n) = 0?
-10, 0, 1
Let g be 2*-3*2/(-6). Suppose -4*w = -5*q + 30, w + 3 = 4*q + g*w. Suppose -q*y**3 - 2*y + 2*y**4 + 2*y = 0. Calculate y.
0, 1
Let p(r) = -3*r - 25. Let g be p(-9). Factor -2/9*k**3 + 0*k + 0*k**g + 2/9*k**4 + 0.
2*k**3*(k - 1)/9
Determine a so that 43*a**3 - 79*a**2 - 63*a + 6*a**3 - 101*a + 24 + 345*a**2 = 0.
-6, 2/7
Let v be 2/(-3) + (-32)/(-12). Let n be (3/v)/(12/2). Factor -1/2*u**2 - 1/4*u - n*u**3 + 0.
-u*(u + 1)**2/4
Let k(t) = 6*t**2 + 5*t. Let n(m) = 2*m + 2. Let g be n(5). Let a(y) = 15*y**2 + 12*y. Let x(v) = g*k(v) - 5*a(v). Find b such that x(b) = 0.
0
Let p(y) be the second derivative of 0 - 8/15*y**3 - 1/5*y**4 - 1/25*y**5 - y**2 + 2*y - 1/300*y**6. Let t(f) be the first derivative of p(f). Factor t(w).
-2*(w + 2)**3/5
Suppose -8*h + 44 = 44. Let h*y**2 + 1/5*y - 1/5*y**3 + 0 = 0. Calculate y.
-1, 0, 1
Factor -10/3*a - 8/3*a**2 - 2/3*a**3 - 4/3.
-2*(a + 1)**2*(a + 2)/3
Let w(h) be the second derivative of 6*h + 0 + 2*h**2 + 1/15*h**6 + 1/2*h**5 + 7/3*h**3 + 3/2*h**4. Factor w(j).
2*(j + 1)**3*(j + 2)
Let q(j) be the first derivative of -3 + 16*j + 1/2*j**4 + 12*j**2 + 4*j**3. Let q(c) = 0. Calculate c.
-2
Let v be 3/10*25/30. Suppose 0*u + 3*j = 5*u - 9, -2*u = 5*j + 15. Factor -1/4*l + v*l**2 - 1/4*l**4 + u + 1/4*l**3.
-l*(l - 1)**2*(l + 1)/4
Factor 0 - n**2 + 0*n - 1/3*n**3.
-n**2*(n + 3)/3
Let d = -383 - -387. Determine r so that -1/5 + 0*r**3 + 2/5*r**2 - 1/5*r**d + 0*r = 0.
-1, 1
Let q(u) be the first derivative of -u**4/2 - 4*u**3 - 9*u**2 - 8*u - 67. Solve q(f) = 0 for f.
-4, -1
Let c(m) be the first derivative of m**6/1080 + m**5/360 - m**4/36 - m**3 + 2. Let q(d) be the third derivative of c(d). Factor q(g).
(g - 1)*(g + 2)/3
Let l(y) be the second derivative of 7*y**6/75 + y**5/10 - y**4/15 + 6*y. Factor l(h).
2*h**2*(h + 1)*(7*h - 2)/5
Let b(t) be the first derivative of 3/7*t**2 + 0*t - 3/7*t**3 - 5 + 0*t**4 + 3/35*t**5. Find y such that b(y) = 0.
-2, 0, 1
Let l(d) be the second derivative of -2*d**2 + d**3 + 0*d**6 + 0 + 2*d - 2/5*d**5 + 1/3*d**4 + 1/21*d**7. Determine t so that l(t) = 0.
-2, -1, 1
Let h(a) = a**3 + 4*a**2 - 7*a - 7. Let j be h(-5). Let d = 6 - 4. Solve -3*t**2 - t + j*t + t**d = 0.
0, 1
Let m(p) be the second derivative of p**4/12 - p**3/2 - 2*p**2 + 36*p. Factor m(f).
(f - 4)*(f + 1)
Let k(u) be the third derivative of u**7/280 + u**6/40 + 3*u**5/40 + u**4/8 - u**3 + u**2. Let y(n) be the first derivative of k(n). Find b such that y(b) = 0.
-1
Let v = 4 - 2. Let p be (-1 + -1)*(v + -4). Suppose 2 + 5*b - 7*b**3 - b - 2*b**p + 3*b**3 = 0. Calculate b.
-1, 1
Solve 0*z - 3/8*z**2 - 3/8*z**3 + 0 = 0 for z.
-1, 0
Let h be (2/6)/((-66)/(-1056)). Factor -1/3*p**2 - h + 8/3*p.
-(p - 4)**2/3
Let g(m) be the third derivative of m**8/84 - 11*m**7/210 + m**6/120 + 13*m**5/60 - 5*m**4/24 - m**3/3 + 7*m**2. What is x in g(x) = 0?
-1, -1/4, 1, 2
Let y(b) be the first derivative of b**4/16 - b**3/12 - b**2/8 + b/4 + 15. What is c in y(c) = 0?
-1, 1
Let f be (9/12)/((-3)/(-12)). Suppose -5*g**4 + 7*g**4 + 2*g**3 - f*g**4 = 0. Calculate g.
0, 2
Let v = -146 - -10951/75. Let m(i) be the second derivative of 0 - 1/210*i**7 - 1/100*i**5 + v*i**6 + 0*i**3 - 2*i + 0*i**2 + 0*i**4. Solve m(n) = 0.
0, 1
Let n be (2*-3)/(-1) + -2. Find k, 