 + 2)
Suppose 11*h - 2 = 13*h. Let n be 1 - (12/10 + h). Determine c, given that 0*c + 2/5*c**4 + 0 + 2/5*c**2 + n*c**3 = 0.
-1, 0
Let w(n) be the first derivative of -3*n**3 - 1 - 2*n - 7/2*n**2 - 5/4*n**4 - 1/5*n**5. Solve w(q) = 0 for q.
-2, -1
Let g(k) be the first derivative of 3 - 1/21*k**3 - 4/7*k**2 - 16/7*k. Factor g(d).
-(d + 4)**2/7
Factor -5*b**4 + 0*b**3 + 3*b**3 + 2*b**4.
-3*b**3*(b - 1)
Suppose 16*g = 31*g - 45. Factor 3/4*a**g + 0 + 0*a + 0*a**2.
3*a**3/4
Let v(a) be the third derivative of a**6/160 - 9*a**5/80 + 27*a**4/32 - 27*a**3/8 - 5*a**2. Factor v(s).
3*(s - 3)**3/4
Let j(p) be the first derivative of -4*p**5/5 - p**4 + 4*p**3 + 2*p**2 - 8*p + 7. Find i such that j(i) = 0.
-2, -1, 1
Let x(t) be the second derivative of -t**7/1260 - 2*t**6/405 + t**5/180 + 5*t**3/6 + 10*t. Let u(w) be the second derivative of x(w). Solve u(s) = 0 for s.
-3, 0, 1/3
Let f(u) be the third derivative of -u**8/3360 + u**7/210 - u**6/30 + 2*u**5/15 + u**4/24 + u**2. Let v(s) be the second derivative of f(s). Factor v(b).
-2*(b - 2)**3
Let k(q) be the first derivative of q**6/15 - 12*q**5/25 + 6*q**4/5 - 16*q**3/15 - 36. Suppose k(b) = 0. What is b?
0, 2
Let h(z) be the third derivative of -2/35*z**7 - 2/5*z**5 + 0*z**3 + 13/60*z**6 + 0 + 0*z + 1/168*z**8 + 5*z**2 + 1/3*z**4. Factor h(l).
2*l*(l - 2)**2*(l - 1)**2
Let k(d) be the first derivative of 1/420*d**5 + 0*d + 3 + 0*d**2 - 1/1260*d**6 + 0*d**4 - 4/3*d**3. Let b(r) be the third derivative of k(r). Factor b(t).
-2*t*(t - 1)/7
Let b(i) = -3*i**2 + 6*i. Let z(m) = -6*m**2 + 12*m. Let h(k) = -9*b(k) + 5*z(k). Factor h(p).
-3*p*(p - 2)
Suppose 5*y - 4*f + 0 - 2 = 0, 5*y + 19 = -3*f. Let q be 5/18 - y/9. Let 0*l + 1/2*l**2 - q*l**5 + 1/2*l**3 - 1/2*l**4 + 0 = 0. What is l?
-1, 0, 1
Let n = 6955 - 27963/4. Let r = n - -36. Factor r*d**2 + 1/4*d - 1/4 - 1/4*d**3.
-(d - 1)**2*(d + 1)/4
Let y(j) be the first derivative of -j**4/16 - j**3/12 + 3*j**2/4 + 39. Suppose y(t) = 0. Calculate t.
-3, 0, 2
Let d(r) = r**2 - 15*r - 4. Let a be d(14). Let l = 37/2 + a. Factor 3/2*k**2 + k + l*k**3 + 0.
k*(k + 1)*(k + 2)/2
Let v be (-6)/(-4 + 2 + 0). Find f, given that 0*f**2 - 1/4*f**4 + 1/4*f**v + 0*f + 0 = 0.
0, 1
Let a(f) be the second derivative of f**5/50 - f**3/5 - 2*f**2/5 - 4*f. Factor a(u).
2*(u - 2)*(u + 1)**2/5
Let w = -30 + 10. Let h be (-10)/w*(0 - -1). Factor -h*z**5 + 3*z**4 + 1 - 9/2*z - 7*z**3 + 8*z**2.
-(z - 2)*(z - 1)**4/2
Factor 0 + 4/3*q + 6*q**2.
2*q*(9*q + 2)/3
Let n(a) = -a**2 - 2*a. Let t be n(0). Let o(x) be the second derivative of t + 0*x**2 - 1/40*x**5 + 0*x**4 + 0*x**3 + 2*x. Factor o(k).
-k**3/2
Let p(g) be the second derivative of -g**4/30 - g**3/15 + 5*g. Let p(t) = 0. What is t?
-1, 0
Let x = 3093/80 + -309/8. Let z(o) be the second derivative of -x*o**5 + 3*o + 1/8*o**3 - 3/8*o**2 + 1/16*o**4 + 0. Let z(t) = 0. Calculate t.
-1, 1
Let a(x) be the third derivative of -x**11/18480 + x**9/5040 + x**8/3780 + x**7/7560 - x**5/60 - x**2. Let b(v) be the third derivative of a(v). Factor b(w).
-2*w*(w - 1)*(3*w + 1)**3/3
Let q(g) be the second derivative of g**5/4 - 5*g**4/4 + 5*g**3/2 - 5*g**2/2 + 2*g. What is l in q(l) = 0?
1
Suppose -72 + 3*c - 3*c**2 - 20*c + c**2 - 7*c = 0. What is c?
-6
Let u = 2141/8 + -267. Let a(i) be the first derivative of -4 + 1/2*i + 1/4*i**3 - u*i**2. Determine y, given that a(y) = 0.
2/3, 1
Let z(j) be the second derivative of 3*j**5/20 + 7*j**4/6 + 10*j**3/3 + 4*j**2 - 4*j. Solve z(f) = 0 for f.
-2, -2/3
Let y be (-14 - -12)/((-34)/4). Let z = 9/34 + y. Let z*j**2 + 0*j + 0 - 1/4*j**3 = 0. Calculate j.
0, 2
Let v(c) be the second derivative of -c**5/40 - c**4/12 - c**3/12 + 16*c. Let v(y) = 0. What is y?
-1, 0
Let f be 4/1 + (3 - 6). Let y be (-3)/(-6)*4/f. Suppose 0 - 2/5*x**3 - 2/5*x**y + 0*x = 0. Calculate x.
-1, 0
Let n(a) be the second derivative of -8*a**6/3 - 18*a**5 - 135*a**4/4 + 4*a + 5. Factor n(x).
-5*x**2*(4*x + 9)**2
Factor 0 - 6/7*f + 6/7*f**3 - 2/7*f**2 + 2/7*f**4.
2*f*(f - 1)*(f + 1)*(f + 3)/7
Let l(x) be the first derivative of x**3/3 - x**2 + x - 32. Factor l(y).
(y - 1)**2
Let h = -43 + 45. Let d(y) be the second derivative of 1/60*y**5 - y + 0*y**h + 0*y**3 + 0 + 1/36*y**4. Solve d(r) = 0.
-1, 0
Let v be 6/(-21) - 237/(-168). Let s = v - 11/24. Let 0 + 0*n + s*n**4 + 2/3*n**2 + 4/3*n**3 = 0. What is n?
-1, 0
Let i(j) = -j**3 - j**2 - j - 1. Let l be i(-1). Let q be (-21)/(-14)*8/4. Factor 0 + 1/3*d**2 + d**4 - 4/3*d**q + l*d.
d**2*(d - 1)*(3*d - 1)/3
Let s(c) = c - 4. Let t = -8 + 12. Let b be s(t). Factor -u**4 + 2*u**3 + b*u**3 - u**4.
-2*u**3*(u - 1)
Determine x, given that 7/3*x**4 - 4*x**3 + x**2 + 0 + 2/3*x = 0.
-2/7, 0, 1
Let g(n) = -2*n**4 + 4*n**2 - 4*n - 2. Let o(c) = -c**4 + c**3 + 3*c**2 - 4*c - 2. Let i(a) = -3*g(a) + 4*o(a). Factor i(r).
2*(r - 1)*(r + 1)**3
Let z(o) be the second derivative of o**6/10 - 9*o**5/100 - 5*o. Factor z(y).
3*y**3*(5*y - 3)/5
Find a such that -a**3 + 1/2*a**4 + 0 + 0*a + 1/2*a**2 = 0.
0, 1
Let p = -14 - -19. Let o(g) be the second derivative of 1/18*g**4 + 0*g**2 + 0*g**3 + 1/30*g**p - 2*g + 0. Factor o(r).
2*r**2*(r + 1)/3
Factor 2160 + 5/4*x**3 + 45*x**2 + 540*x.
5*(x + 12)**3/4
Suppose 4/3*w**3 - 2/3 + 2/3*w**2 - 1/3*w**5 + 0*w**4 - w = 0. Calculate w.
-1, 1, 2
Let j be (-3*(-6)/(-9))/(-2). Let a be (1/(-2))/(j + -2). Let 9/4*q**3 - a - 6*q**2 + 13/4*q = 0. What is q?
1/3, 2
Let q(i) be the first derivative of i**3/4 - 3*i/4 - 9. Factor q(l).
3*(l - 1)*(l + 1)/4
Let k(a) = -3*a**2 - 20*a + 6. Let r(q) = -q**2 - 7*q + 2. Let o(y) = 6*k(y) - 17*r(y). Find t such that o(t) = 0.
-2, 1
Let a(h) = -4*h**4 - h**3 + 5*h**2 - 5. Let u(c) = 3*c**4 + c**3 - 4*c**2 + 4. Let r = -6 - -10. Let t(p) = r*a(p) + 5*u(p). Find x such that t(x) = 0.
0, 1
Let s be (-2)/6 - (0 - (-76)/(-84)). Factor -2/7*p + s - 2/7*p**2.
-2*(p - 1)*(p + 2)/7
Let f(m) = m**2 - 7*m - 8. Let y be f(8). Let u(x) = x**3 + x + 3. Let a be u(y). Factor 2/7*d**4 - 2/7*d - 6/7*d**a + 0 + 6/7*d**2.
2*d*(d - 1)**3/7
Let d(x) be the third derivative of -x**8/168 - x**7/30 - 3*x**6/40 - x**5/12 - x**4/24 + 2*x**2. Factor d(p).
-p*(p + 1)**3*(2*p + 1)
Let n(s) = 3 + 3 + 13 - 3 + 2*s. Let b be n(-8). Factor 2/3*p**2 + 0 + b*p.
2*p**2/3
Let l(g) = 21*g**3 - 44*g**2 + 33*g - 10. Let q(x) = 105*x**3 - 219*x**2 + 165*x - 51. Let v(y) = -21*l(y) + 4*q(y). Let v(z) = 0. What is z?
2/7, 1
Let g(t) be the third derivative of 7*t**5/150 - t**4/6 + t**3/5 - 4*t**2. Factor g(z).
2*(z - 1)*(7*z - 3)/5
Let k(v) = -v - 9. Let j be k(-12). Factor -3*i - 2*i + 2*i**j + 3*i.
2*i*(i - 1)*(i + 1)
Let s(j) = 4*j**2 - 2*j**4 - 13 + 11 - 4*j**4. Let g = -2 - -6. Let a(v) = -v**4 - v**3 + v**2 + v - 1. Let o(f) = g*a(f) - s(f). What is d in o(d) = 0?
-1, 1
Let k(j) = -j + 11. Let r be k(10). Let h(n) be the first derivative of 1/8*n**4 + 0*n + r - 1/6*n**3 + 1/10*n**5 - 1/4*n**2. Let h(b) = 0. Calculate b.
-1, 0, 1
Let w(q) = -2*q - 32. Let i be w(-20). Let s be (1/i)/(7/28). Find d such that -1/2*d + d**4 + d**3 - 2*d**2 - s*d**5 + 1 = 0.
-1, 1, 2
Let o(r) be the third derivative of -r**7/2940 - r**6/630 - r**5/420 + r**4/8 + r**2. Let w(b) be the second derivative of o(b). Solve w(j) = 0 for j.
-1, -1/3
Let z(l) = 2*l**4 + 11*l**3 - 7*l + 7. Let y(w) = 2*w**4 + 10*w**3 - 6*w + 6. Let q(r) = -7*y(r) + 6*z(r). Factor q(s).
-2*s**3*(s + 2)
Suppose -4*w + 6*h + 27 = h, -w + 3*h + 12 = 0. Factor 0*q**w - q**4 + 0*q**3 - q**3 + 3*q**2 - q**2.
-q**2*(q - 1)*(q + 2)
Let o(i) = 15*i**3 + 11*i**2 - 56*i + 19. Let m(l) = 3*l**3 + 2*l**2 - 11*l + 4. Let u(p) = 11*m(p) - 2*o(p). What is j in u(j) = 0?
-2, 1
Let k = 10/89 - 92/2403. Let y(i) be the first derivative of 2 - k*i**3 + 2/45*i**5 + 0*i + 1/18*i**4 - 1/9*i**2. Suppose y(n) = 0. What is n?
-1, 0, 1
Solve -3/5*p**4 + 3/5*p**3 - 3/5*p + 3/5*p**2 + 0 = 0 for p.
-1, 0, 1
Let i be 39/(-60) + 6/9. Let d(v) be the third derivative of 0*v**3 + 0*v + 3*v**2 + 0*v**5 + 0 + 1/12*v**4 - i*v**6. Determine c so that d(c) = 0.
-1, 0, 1
Let z(s) be the third derivative of 1/75*s**5 + 1/45*s**3 + s**2 + 0 + 0*s + 1/225*s**6 + 1/1575*s**7 + 1/45*s**4. Determine i, given that z(i) = 0.
-1
Factor 0*o - 2/15*o**2 + 2/15.
-2*(o - 1)*(o + 1)/15
Let m(i) be the first derivative of 2*i**2 - 1 - i**3 - 1/5*i**5 - i**4 + 4*i. Suppose m(