 = 0.
0
Let r(y) be the second derivative of y**7/63 + 2*y**6/135 - 4*y. Solve r(t) = 0.
-2/3, 0
Let n(d) be the first derivative of 2*d**3/3 - 2*d**2 - 6*d - 13. Determine m, given that n(m) = 0.
-1, 3
Suppose 8*i - 16*i + 24 = 0. Let w(k) be the first derivative of -2*k**2 - 2/3*k**i + 1/2*k**4 - 3 + 0*k. Suppose w(d) = 0. What is d?
-1, 0, 2
Let w(t) = -t + 3. Let p be w(0). Suppose j = -p*j + 20. Let k - j*k**3 - 4*k**2 - 3*k + 3*k**3 = 0. Calculate k.
-1, 0
Factor -2 + 2*a - 3 + 2 - 1 + 2*a**2.
2*(a - 1)*(a + 2)
Let h(l) = -l**2 + l. Let j(y) = -2*y**2 + 4*y - 2. Let b(f) = -3*h(f) + j(f). Solve b(g) = 0.
-2, 1
Let s(x) = 10*x**3 - 6*x**2 - 10*x + 6. Suppose 29 = -2*q + 1. Let h(u) = 3*u**3 - 2*u**2 - 3*u + 2. Let b(g) = q*h(g) + 4*s(g). Suppose b(d) = 0. Calculate d.
-1, 1, 2
Let o(z) = -z - 2. Let a be o(-6). Factor -2*r**5 + 8*r**2 - a*r**4 + r**2 + 2*r - 5*r**2.
-2*r*(r - 1)*(r + 1)**3
Let b(f) be the third derivative of 0 - 2/27*f**3 + 5*f**2 + 1/108*f**4 + 1/270*f**5 + 0*f. Factor b(a).
2*(a - 1)*(a + 2)/9
Let c(b) = -b**2 - 5*b + 1. Let x be c(-6). Let h be x/(-15) - 5/(-3). Find q, given that -13*q - q**2 + 1 + 5*q - q**h - 9 = 0.
-2
Suppose 24 = -3*b + 5*b. Let r(o) = b*o - 4*o + 20*o**2 + 1 - 15. Let i(q) = 7*q**2 + 3*q - 5. Let d(k) = -14*i(k) + 5*r(k). Factor d(m).
2*m*(m - 1)
Let m(r) be the third derivative of 1/6*r**3 - r**2 + 0 + 1/24*r**4 + 0*r + 1/240*r**5. Let m(w) = 0. Calculate w.
-2
Let d(p) be the first derivative of -p**5/15 - p**4/12 + p**3/9 + p**2/6 - 7. Find y such that d(y) = 0.
-1, 0, 1
Solve 5*x**2 - x**4 - 3 - 2*x**4 + x**2 = 0.
-1, 1
Let k be (-3)/(6/4*20/(-30)). Determine z so that 8/9 - 14/9*z**k + 10/9*z**2 + 32/9*z = 0.
-1, -2/7, 2
Let a(b) be the third derivative of -b**6/30 - 2*b**2. Factor a(z).
-4*z**3
Let h be 4/(-6)*(-3 - 24/(-10)). Let 2*q**3 + 0 + 6/5*q**4 + 2/5*q**2 - h*q = 0. Calculate q.
-1, 0, 1/3
Find b, given that 2*b**2 - 5*b**2 - 9*b**2 - 4*b**3 - 12*b - 4 = 0.
-1
Factor 0 + p + 11/3*p**2 - 4/3*p**3.
-p*(p - 3)*(4*p + 1)/3
Let x be (4/(-36))/(3/(-45)). Factor 1/3 - x*t + 5/3*t**4 - 10/3*t**3 - 1/3*t**5 + 10/3*t**2.
-(t - 1)**5/3
Let x be (-1)/4 + 7/12. Let n(u) = 3*u - 31. Let b be n(11). Suppose 0 + x*d**b + 0*d = 0. Calculate d.
0
Let j be (2*(-4)/10)/((-8)/20). Suppose 0*t - 1/2*t**5 - 1/3*t**j + 0 + 1/2*t**3 + 1/3*t**4 = 0. Calculate t.
-1, 0, 2/3, 1
Let b = -12 - -10. Let c be b/(-6)*27/6. Let 3/2*m**4 + 0 + 0*m - c*m**3 + m**5 - m**2 = 0. What is m?
-2, -1/2, 0, 1
Let r be (-4 + -4 + 5)/(-2 + 0). Factor -1/2*m**3 + 1 + 0*m**2 + r*m.
-(m - 2)*(m + 1)**2/2
Let a(d) be the second derivative of -d**5/5 - 4*d**4/3 - 10*d**3/3 - 4*d**2 + 16*d. Factor a(u).
-4*(u + 1)**2*(u + 2)
Let g(f) be the second derivative of f**6/80 - 3*f**5/32 + f**4/4 - f**3/4 - 20*f. Factor g(d).
3*d*(d - 2)**2*(d - 1)/8
Suppose -3*a + 4*a - 18 = 4*x, 3*x = -5*a - 2. Let j be 4*(8 + x)/4. Factor -5/2*o**j + 0 + o - 1/2*o**2 - 4*o**3.
-o*(o + 1)**2*(5*o - 2)/2
Suppose 1/2*d - 1/2*d**3 + 0 + 0*d**2 = 0. Calculate d.
-1, 0, 1
Let d be (-185)/65 - 2/13. Let u = d + 3. Let 2/7*p**2 + u + 0*p + 2/7*p**3 = 0. What is p?
-1, 0
Find n such that 1/2 + 1/2*n**4 - 1/2*n**5 - n**2 + n**3 - 1/2*n = 0.
-1, 1
Let x = 20 - 18. Factor 0*m**2 - x*m**2 - m**2 + 4*m**4 - m**2.
4*m**2*(m - 1)*(m + 1)
Let h(c) be the second derivative of c**4/12 + 4*c**3/3 + 8*c**2 - c - 12. Factor h(n).
(n + 4)**2
Determine z, given that 13*z**4 + 8 + 48*z + 42*z**3 + 18*z**4 + 74*z**2 - 28*z**4 + 5*z**4 = 0.
-2, -1, -1/4
Let z(x) be the first derivative of -1/7*x - 1/35*x**5 + 3 + 1/7*x**4 - 2/7*x**3 + 2/7*x**2. Factor z(f).
-(f - 1)**4/7
Let i(a) = -a + 6. Let l(d) = -d + 7. Let n(r) = -6*i(r) + 5*l(r). Let q be n(5). Suppose -v**5 - 3*v**3 - q*v**4 + 3*v**5 + 5*v**3 = 0. Calculate v.
0, 1
Let l = 0 - -2. Factor -2*p**l + 2 + 0 + 3 - 3.
-2*(p - 1)*(p + 1)
Let h(v) be the third derivative of -1/4*v**4 + 0*v + 3*v**2 - 1/6*v**3 + 0 - 3/20*v**5. Solve h(m) = 0 for m.
-1/3
Let c be (-3)/12 - 26/(-40). Let p be (-1)/(-3) + 45/27. Let -c*j - 2/5*j**3 + 4/5*j**p + 0 = 0. Calculate j.
0, 1
Suppose -1/5*r**3 + 0 + 0*r - 1/5*r**2 = 0. Calculate r.
-1, 0
Let b(q) be the second derivative of -2*q**6/15 - 3*q**5/5 + 4*q**4/3 + 35*q. Find l such that b(l) = 0.
-4, 0, 1
Let y be (-1)/4 - 22/(-24). Factor 0 - y*t + 2/3*t**3 - 2/3*t**4 + 2/3*t**2.
-2*t*(t - 1)**2*(t + 1)/3
Factor 8/5 - 6/5*m - 2/5*m**2.
-2*(m - 1)*(m + 4)/5
Factor -2/11*g**4 + 0*g + 0 + 0*g**2 - 4/11*g**3.
-2*g**3*(g + 2)/11
Let s(f) be the first derivative of -f**4/18 - 2*f**3/9 - f**2/3 - 2*f/9 - 4. Let s(w) = 0. Calculate w.
-1
Factor 12/7*l**3 + 0 + 4/7*l**4 + 12/7*l**2 + 4/7*l.
4*l*(l + 1)**3/7
Let s(o) be the third derivative of 0 + 1/84*o**4 + 1/294*o**8 + 1/28*o**6 + 0*o + 13/735*o**7 + 1/30*o**5 + 3*o**2 + 0*o**3. Solve s(d) = 0 for d.
-1, -1/4, 0
Suppose v = 2*z + 2, 3*v + z - 4*z = 21. Suppose 3*y - 5*m - 15 = -0*m, 4*m = -3*y - v. Factor 2/3*j + y + 1/3*j**2.
j*(j + 2)/3
Let i = -4 + 4. Let o(w) be the first derivative of -1/10*w**5 + 0*w + 1/6*w**3 + 0*w**2 + i*w**4 - 1. Factor o(h).
-h**2*(h - 1)*(h + 1)/2
Let b(p) be the second derivative of p**6/60 - p**5/20 - p**4/8 + p**3/3 + p**2 - 26*p. Determine q so that b(q) = 0.
-1, 2
Let l(w) be the second derivative of 0 + 1/5*w**2 - 1/30*w**4 - 2*w - 7/30*w**3 + 7/100*w**5. Find q, given that l(q) = 0.
-1, 2/7, 1
Let o = -2 + 4. Factor v**3 - 5*v + 3*v**o + 5*v - 2*v**2.
v**2*(v + 1)
Let n = 416/1925 + -6/175. Factor -n*m**2 + 4/11*m**5 + 0*m + 0*m**3 + 0 + 6/11*m**4.
2*m**2*(m + 1)**2*(2*m - 1)/11
Let t be 20/15*(-2)/(-2). Let b(d) be the second derivative of 1/18*d**4 + 4/9*d**3 + d + t*d**2 + 0. Suppose b(l) = 0. What is l?
-2
Let h(j) be the third derivative of -2/105*j**7 + j**2 + 1/336*j**8 + 1/24*j**4 + 0*j**3 + 1/20*j**6 + 0 + 0*j - 1/15*j**5. Factor h(z).
z*(z - 1)**4
Factor u**4 - 202*u**2 + 205*u**2 - 4*u**4.
-3*u**2*(u - 1)*(u + 1)
Let f(p) be the second derivative of -p**9/30240 + p**8/6720 - p**6/720 + p**5/240 - p**4/12 - 3*p. Let s(v) be the third derivative of f(v). Factor s(n).
-(n - 1)**3*(n + 1)/2
Let l(h) be the first derivative of -2*h**5/5 + h**4/2 + 2*h**3/3 - h**2 + 6. Suppose l(v) = 0. What is v?
-1, 0, 1
Let o(l) = -l**3 + 1. Let c(v) = v**3 + 6*v**2 - 6*v - 1. Let r(j) = -c(j) - 3*o(j). Find q such that r(q) = 0.
1
Suppose 0 = 5*b, b + 4*b - 10 = -5*r. Factor -7*y**r + 3*y**3 + 2*y**2 + 8*y**2 - 6*y.
3*y*(y - 1)*(y + 2)
Suppose -c - 6 = -2*d, -2*d + 14*c + 14 = 9*c. Factor 2/3*y**d + 2/3*y + 2/9*y**3 + 2/9.
2*(y + 1)**3/9
Let p(m) be the second derivative of -2*m**6/75 + 12*m**5/25 - 2*m**4 + 56*m**3/15 - 18*m**2/5 + 58*m. Factor p(z).
-4*(z - 9)*(z - 1)**3/5
Let g(x) be the first derivative of -4*x**3/3 - 8*x**2 - 16*x - 22. Factor g(q).
-4*(q + 2)**2
Let x(c) be the second derivative of 3*c**6/50 + 21*c**5/50 + 23*c**4/20 + 8*c**3/5 + 6*c**2/5 - 24*c. Suppose x(w) = 0. Calculate w.
-2, -1, -2/3
Let g = -4/45 + 22/45. Let g*u**4 - 2/5 + 4/5*u + 0*u**2 - 4/5*u**3 = 0. What is u?
-1, 1
Let p(j) = -2*j + 1. Let q(z) = -80*z**2 - 206*z - 122. Let b(u) = -3*p(u) + q(u). What is a in b(a) = 0?
-5/4
Suppose 4*f - 8*f - 31 = -3*t, t = -3*f - 7. Let g = 6 + f. Factor 2 + s**2 + 0*s**2 + s**g - 2*s - 2*s.
2*(s - 1)**2
Let o(f) be the third derivative of f**6/80 + f**5/40 - 5*f**4/16 + 3*f**3/4 + 32*f**2. Determine y so that o(y) = 0.
-3, 1
Let d(x) be the second derivative of 0*x**3 - 6*x + 0*x**2 - 3/10*x**5 + 1/10*x**6 + 1/4*x**4 + 0. Factor d(i).
3*i**2*(i - 1)**2
Let x = 1504/7 + -214. Factor -x*w + 2/7*w**2 + 4/7.
2*(w - 2)*(w - 1)/7
Factor 2/7*s - 2/7*s**3 - 3/7*s**2 + 0 + 3/7*s**4.
s*(s - 1)*(s + 1)*(3*s - 2)/7
Let v(b) be the third derivative of -b**7/315 + b**5/90 - 6*b**2. Solve v(k) = 0 for k.
-1, 0, 1
Let r = -76 - -80. Let a(k) be the second derivative of 7/8*k**4 + 5/4*k**3 - 3/2*k**2 + 0 - r*k. Factor a(x).
3*(x + 1)*(7*x - 2)/2
What is q in 8*q**2 - 2*q**3 + q**3 + 0*q**3 + 5*q**3 = 0?
-2, 0
Let w(s) = -14*s**4 - 17*s**3 - 5*s**2. Let u(q) = -99*q**4 - 120*q**3 - 36*q**2. Let c(m) = 2*u(m) - 15*w(m). Factor c(p).
3*p**2*(p + 1)*(4*p + 1)
Let y(d) be the first derivative of d**6/480 - d**4/96 + d**2/2 - 3. Let i(g) be the second derivative of y(g). Solve i(p) = 0 for p.
-1, 0, 1
Let s(o) be the thir