 - 6)/3
Suppose 0 = -5*c - 2*y + 33, 2*y + 2*y = -4*c + 36. Let b(r) be the first derivative of -1/9*r**3 + 0*r**2 + 0*r**4 + 0*r - 3 + 1/15*r**c. Solve b(g) = 0.
-1, 0, 1
Suppose u - 11 - 2 = 0. Suppose -4*q + 0*q = -20, q - u = -4*r. Factor -2/7 - 16/7*i**r + 32/7*i**3 - 2*i.
2*(i - 1)*(4*i + 1)**2/7
Let o(t) be the second derivative of t**7/210 - t**6/150 - t**5/100 + t**4/60 + 18*t. Suppose o(b) = 0. What is b?
-1, 0, 1
Let c(u) be the third derivative of 0 + 1/40*u**6 + 0*u - 4*u**2 - 1/6*u**3 + 5/24*u**4 - 7/60*u**5. Factor c(z).
(z - 1)**2*(3*z - 1)
Let 6/11*a + 4/11 + 2/11*a**2 = 0. Calculate a.
-2, -1
Let l(t) be the first derivative of t**5/50 - t**4/30 - 3*t - 2. Let m(x) be the first derivative of l(x). Factor m(d).
2*d**2*(d - 1)/5
Determine d so that 0 - 6*d**3 - 2/7*d**2 + 4/7*d = 0.
-1/3, 0, 2/7
Let w(s) be the third derivative of -1/70*s**7 - 8*s**3 + 0 + 0*s + 4*s**4 - 6/5*s**5 + 4*s**2 + 1/5*s**6. Factor w(t).
-3*(t - 2)**4
Let p(a) = 48*a**3 - 52*a**2 - 4*a + 12. Let q(h) = -h**3 - h**2 - h - 1. Let m(n) = p(n) + 12*q(n). Find d, given that m(d) = 0.
-2/9, 0, 2
Factor -48/5*m**2 - 32/5 - 10*m**4 - 128/5*m + 32*m**3.
-2*(m - 2)**2*(5*m + 2)**2/5
Let m = 4 + -2. Determine z, given that -1 - 33*z**m - 2 - 20*z - 1 + 8*z**2 = 0.
-2/5
Let t(y) = -y**3 - y**2 - y. Let s(g) = 6*g**3 + 3*g**2 - 3*g. Let o(d) = s(d) + 5*t(d). Factor o(w).
w*(w - 4)*(w + 2)
Let u(d) be the second derivative of d**9/13608 + d**8/3780 - d**6/810 - d**5/540 - 7*d**3/6 + 6*d. Let h(b) be the second derivative of u(b). Factor h(p).
2*p*(p - 1)*(p + 1)**3/9
Let a be (-3)/21 + 255/21. Let s be (a/(-8))/(9/(-2)). Find m such that 0*m**2 + s*m - 1/3*m**3 + 0 = 0.
-1, 0, 1
Suppose 6 = 2*m + 6. What is y in 0*y**2 + m*y**4 + 0 - 1/4*y**3 + 1/4*y**5 + 0*y = 0?
-1, 0, 1
Let q(z) = -z**3 + 3*z**2 + z - 4. Let o be q(2). Let g(l) be the third derivative of 0 + 0*l - 3*l**o + 1/30*l**5 + 1/3*l**3 + 1/6*l**4. Factor g(j).
2*(j + 1)**2
Let y be 85/20 - (-12)/(-3). Suppose -1/2 - y*z + 1/4*z**2 = 0. Calculate z.
-1, 2
Let m(c) be the third derivative of 7*c**6/360 + c**5/60 - c**3/2 - 3*c**2. Let f(b) be the first derivative of m(b). Factor f(i).
i*(7*i + 2)
Let s(f) = 20*f**4 - 36*f**3 + 52*f**2 - 44*f + 8. Let z(d) = -d**4 - d**3 + d**2 + d. Let x(v) = s(v) + 8*z(v). Factor x(l).
4*(l - 1)**3*(3*l - 2)
Let g = -62 - -62. Let m be (-2)/(-9) + (-75)/(-27). Suppose 0*j**m + 0*j - 2/5*j**4 + 2/5*j**2 + g = 0. What is j?
-1, 0, 1
Let o(i) be the third derivative of -3*i**2 + 4/45*i**5 + 0 - 11/36*i**4 + 4/9*i**6 - 2/9*i**3 + 0*i. Factor o(n).
2*(4*n + 1)**2*(5*n - 2)/3
Factor -5*p + 16*p**3 + 13*p - 44*p**2 + 20*p**3.
4*p*(p - 1)*(9*p - 2)
Suppose 0*a - a + 2*f = -9, a + 12 = -5*f. Find v such that -v**2 + 8*v**3 - 7*v + a*v + v**2 - 4*v**5 = 0.
-1, 0, 1
Suppose w - 4 = 5*w + 3*h, -2*w + 4 = 3*h. Let m = 6 + w. Factor -i**2 - 2*i**3 - 3*i**m + 10*i**2 - 8.
-2*(i - 2)**2*(i + 1)
Let g be (10/(-15))/((-1)/(-3)). Let w = 2 + g. Factor w*m**2 + m - 2*m**3 + m**2 + 0*m.
-m*(m - 1)*(2*m + 1)
Let a(k) be the second derivative of -k**4/12 - 7*k**3/6 - k**2 + k. Let d be a(-6). Factor 2*r - r - 2*r**2 - 3*r**4 + 4*r**d + r**5 + 1 - 2*r**3.
(r - 1)**2*(r + 1)**3
Let r(d) = d**3 - 6*d**2 - 3*d - 2. Let b be r(7). Suppose 8 = -4*h - 5*g + b, -3*h - 4*g + 14 = 0. Suppose -4/7*i**2 - h*i**3 + 0 + 0*i = 0. What is i?
-2/7, 0
Let p(y) be the second derivative of -2*y**6/15 - 5*y**5 - 143*y**4/3 + 338*y**3/3 + y - 1. Let p(n) = 0. What is n?
-13, 0, 1
Let s = 7746/5 + -1560. Let o = s + 12. Factor -o*t**2 - 4/5 - 14/5*t.
-2*(t + 2)*(3*t + 1)/5
Let c(t) = t**2 - 15*t - 10. Let b be c(13). Let f = b + 40. Factor 0*o + 0 + 2/5*o**2 + 4/5*o**f + 1/5*o**5 + o**3.
o**2*(o + 1)**2*(o + 2)/5
Suppose 7*b - 9*b + 14 = 4*a, 0 = -3*a + 6. Suppose 3/5*w**b + 0 - 18/5*w**2 + 27/5*w = 0. Calculate w.
0, 3
Let a be ((-7)/21)/((-2)/81). Let y = a - 13. Suppose 0 + y*x**2 + x = 0. Calculate x.
-2, 0
Let d(t) be the third derivative of -t**6/540 - t**5/90 - t**3/2 - t**2. Let g(f) be the first derivative of d(f). Factor g(u).
-2*u*(u + 2)/3
Let o(r) = r**2 + 5*r + 6. Let j be o(-4). Let f be (-3)/(-6)*j - -2. Let 12*w**f + 8*w**2 - 2*w**5 + 6*w**4 + 0*w**5 + 3*w**5 = 0. What is w?
-2, 0
Suppose c + 9 = -2*o + 7*o, 4*c - 21 = o. Suppose -c*l**3 + 2*l**2 + 2*l**3 - 2*l**2 = 0. What is l?
0
Let y be 6/(-9)*(-135)/6. Let k be ((-6)/y)/((-2)/10). Solve 2 + 1/2*u**k + 2*u = 0 for u.
-2
Let p(y) = -5*y**3 - 7*y**2 + 14*y - 11. Let a(s) = 6*s**3 + 8*s**2 - 14*s + 12. Let i(u) = 3*a(u) + 4*p(u). Let i(b) = 0. Calculate b.
-4, 1
Let q = -10197 - -71517/7. Factor 8*a + 20*a**3 - 8/7 - 50/7*a**4 - q*a**2.
-2*(a - 1)**2*(5*a - 2)**2/7
Let t be (1424/80 + -18)/(2/(-6)). Determine p, given that -t - 4/5*p - 1/5*p**2 = 0.
-3, -1
Let x be (-105)/45 + -3*(-1 + 0). Let f(q) be the first derivative of 4/3*q - 10/9*q**3 + x*q**4 - 7/3*q**2 - 2. Factor f(a).
2*(a - 2)*(a + 1)*(4*a - 1)/3
Let d be 18/(-6) - (-11 + -1). Factor -28*s + d*s**3 - 9*s**3 - 20*s**2 - 12*s**3 - 12*s**2 - 8.
-4*(s + 1)**2*(3*s + 2)
Let z(l) be the first derivative of -2*l**3/5 - l**2 - 4*l/5 + 4. Factor z(g).
-2*(g + 1)*(3*g + 2)/5
Let c = 14 + -12. Find w, given that -18*w**2 + 15*w**c - w**3 - w**3 - w**3 = 0.
-1, 0
Let a(o) be the second derivative of -o**5/15 + 4*o. Factor a(g).
-4*g**3/3
Let c be (-1 - 0)*(0 - 5)*1. Factor 28/3*o**2 + 12*o**3 + 4/3*o**c + 20/3*o**4 + 0 + 8/3*o.
4*o*(o + 1)**3*(o + 2)/3
Let s(o) be the second derivative of o**5/60 + o**4/36 - o**3/18 - o**2/6 - 6*o. Factor s(t).
(t - 1)*(t + 1)**2/3
Suppose 2*f - 20 = 3*c, -5*f - c + 37 = 4. Solve 0*b**2 - 11*b - 2*b**2 - 2 + f*b = 0 for b.
-1
Let w(y) be the third derivative of 0*y + 0*y**5 + 0*y**4 + 0 + 0*y**6 - 1/735*y**7 - y**2 + 0*y**3. Find j, given that w(j) = 0.
0
Let j(a) = 10*a**2 - 13*a. Let y(x) = -x**2 + x. Let f(g) = 4*j(g) + 44*y(g). Solve f(r) = 0 for r.
-2, 0
Let j = 659/3 + -218. Suppose -3*k + 10/3*k**2 + 4/3*k**3 + j*k**5 + 2/3 - 4*k**4 = 0. Calculate k.
-1, 2/5, 1
Let k be ((-4)/(-32))/((-3)/(-36)). Solve 0 - k*p**2 - 1/2*p**3 - p = 0 for p.
-2, -1, 0
Let w(t) be the third derivative of -t**6/30 + t**4/6 + 18*t**2. Suppose w(u) = 0. Calculate u.
-1, 0, 1
Let o(u) be the first derivative of -u**5/80 + u**4/8 - 3*u**3/8 - 2*u**2 - 5. Let b(k) be the second derivative of o(k). Solve b(q) = 0 for q.
1, 3
Suppose 0*l - 5*l = z - 3, 2*z - 6 = -2*l. Determine b, given that b**2 + l*b + 3*b**3 + 3*b - 4*b - b**4 + 0*b - 2*b**5 = 0.
-1, 0, 1/2, 1
Find g such that 0 + 0*g**2 - 2/7*g**3 + 0*g + 2/7*g**4 = 0.
0, 1
Let y be ((-10)/(-12) + 9/(-6))*-3. Factor 4/5 + 2/5*w**3 - 6/5*w + 0*w**y.
2*(w - 1)**2*(w + 2)/5
Let k(l) = -l - 5. Let y be k(-8). Let m(d) be the third derivative of 0*d - d**2 - 2/25*d**5 + 1/15*d**y + 0 - 1/60*d**4. Factor m(x).
-2*(3*x + 1)*(4*x - 1)/5
Let y = 69 + -47. Let o be (3 + y/(-4))*-2. Factor 1/2*g**2 - 1/2*g**3 + 1/4*g - 1/4*g**4 + 1/4*g**o - 1/4.
(g - 1)**3*(g + 1)**2/4
Let z(p) be the first derivative of p**6/42 + p**5/5 + 4*p**4/7 + 8*p**3/21 - 8*p**2/7 - 16*p/7 + 3. Solve z(j) = 0.
-2, 1
Suppose -13*u + 9 = -10*u. Factor 0*v - 2/3*v**u - 1/3*v**4 - 1/3*v**2 + 0.
-v**2*(v + 1)**2/3
Let u(c) be the third derivative of -c**5/30 + c**4/12 + 2*c**3 + 21*c**2. What is q in u(q) = 0?
-2, 3
Let b(m) be the first derivative of -m**7/63 - 2*m**6/45 - m**5/30 - 2*m - 3. Let l(a) be the first derivative of b(a). Factor l(g).
-2*g**3*(g + 1)**2/3
Let k(q) be the first derivative of -1/6*q**2 + q - 4/9*q**4 - 4/9*q**3 - 1. Let c(m) be the first derivative of k(m). Let c(r) = 0. What is r?
-1/4
Let a(p) be the second derivative of -1/4*p**3 + 3/8*p**4 + 2*p - 3/40*p**5 - 3/20*p**6 + 0 + 1/14*p**7 + 0*p**2. Suppose a(v) = 0. What is v?
-1, 0, 1/2, 1
Let b(k) = 6*k**3 + 30*k**2 + 35*k + 11. Let o(j) = -2*j**3 - 10*j**2 - 12*j - 4. Let l(w) = 2*b(w) + 7*o(w). Factor l(n).
-2*(n + 1)**2*(n + 3)
Let z be 9/(-6)*16/(-1068). Let l = z - -168/445. Determine g so that 2/5*g**3 - l*g + 2/5*g**2 - 2/5 = 0.
-1, 1
Let q(c) = -8*c**2 + 14*c + 2. Let g(i) = 2*i - 2*i**2 - i + i**2. Let r(m) = 10*g(m) - q(m). Let r(k) = 0. What is k?
-1
Let x(v) be the third derivative of 0*v - 1/60*v**5 + 1/24*v**4 + 0 - 5*v**2 + 0*v**3. Determine h, given that x(h) = 0.
0, 1
Let s(p