3*d - 4*d - 3. Let r = d + 6. Factor 2*q**3 - 4*q**4 + 3*q**2 - 4*q**r + 2*q + q**2.
-2*q*(q - 1)*(q + 1)*(2*q + 1)
Let m = 4 - 1. Let -i + 3 - m*i**2 + 4*i**4 + 3 - 6 = 0. Calculate i.
-1/2, 0, 1
Let l(y) be the second derivative of 1/30*y**4 - 5*y + 4/5*y**2 + 4/15*y**3 + 0. What is f in l(f) = 0?
-2
Let r(q) = -q + 17. Let p be r(13). Let 7/4*b**p - 1/2*b**3 - 7/4*b**2 + 0 + 1/2*b = 0. Calculate b.
-1, 0, 2/7, 1
Suppose -2*s + q = 8 - 3, q = 5. Let -1/4*l**4 - 1/2*l**3 - 1/4*l**2 + 0 + s*l = 0. Calculate l.
-1, 0
Let h(u) be the third derivative of -u**6/40 + 7*u**5/60 - 5*u**4/24 + u**3/6 + 8*u**2. Solve h(m) = 0 for m.
1/3, 1
Let o(i) be the first derivative of -i**6/600 - i**5/150 - i**4/120 + i**2 - 4. Let w(z) be the second derivative of o(z). Suppose w(g) = 0. What is g?
-1, 0
Factor -10*p + 0*p**2 - p + 4*p**2 - 5*p.
4*p*(p - 4)
Let y(j) = -6*j**3 - j**2 - 6*j. Let g(x) = 3*x**3 + 3*x. Let t(b) = 13*g(b) + 6*y(b). Determine n so that t(n) = 0.
0, 1
Let v(d) be the third derivative of -d**6/30 + 7*d**5/15 - 4*d**4/3 - 32*d**3/3 - 24*d**2. Factor v(k).
-4*(k - 4)**2*(k + 1)
Let z = 307 + -305. Factor 3/5*j**z - 4/5 + 1/5*j**3 + 0*j.
(j - 1)*(j + 2)**2/5
Let n(y) be the first derivative of -y**7/21 + y**6/15 + y**5/5 - y**4/3 - y**3/3 + y**2 - y - 3. Let s(q) be the first derivative of n(q). Solve s(o) = 0.
-1, 1
Let n(z) = z**4 - z**3 - z**2 + z. Let s(u) = 7*u**3 - 11*u**2 + u + 3. Let g(c) = 5*n(c) - s(c). Let g(v) = 0. What is v?
-3/5, 1
Find b such that 12/11 + 2/11*b**2 + 10/11*b = 0.
-3, -2
Let y be 8/(-28)*(-14)/2. Suppose -y*t = t - 12. Factor 5*g + 0*g**2 + 11 - t*g**2 - 12.
-(g - 1)*(4*g - 1)
Let p(a) = a**2 - 9*a - 7. Let m be p(11). Factor -m*t**4 + 2 + 11*t**3 - 2 + 6*t**2 - 2*t**3.
-3*t**2*(t - 1)*(5*t + 2)
Let y(j) be the first derivative of 3*j**5/5 + 3*j**4/2 + j**3 + 11. Factor y(d).
3*d**2*(d + 1)**2
Let m = 2 - 2. Suppose m = 5*z - 0*z - 25. Factor -z*q**3 + 5*q**3 + 2*q**3 + 2*q**2.
2*q**2*(q + 1)
Let a(n) be the third derivative of 1/60*n**6 + 0 - 1/10*n**5 + 0*n - 2*n**2 - 1/3*n**3 + 1/4*n**4. Find m, given that a(m) = 0.
1
Factor 9*n**2 + 9*n - n**2 - 5*n**2 + 0*n**2.
3*n*(n + 3)
Let w(t) be the second derivative of -t**8/168 + 3*t**7/140 - t**6/60 - t**5/60 + t**3 + 2*t. Let r(q) be the second derivative of w(q). Solve r(a) = 0.
-1/5, 0, 1
Suppose -30 = 3*y - 0. Let w be 1/y - 6/(-12). Suppose 8/5 + w*x**2 + 8/5*x = 0. Calculate x.
-2
Let w = 11 + -15. Let y = -2 - w. Determine r, given that -5*r**2 - 4*r - y*r + 2*r**2 = 0.
-2, 0
Solve 2 + 14/3*n**3 + 26/3*n + 34/3*n**2 = 0.
-1, -3/7
Let a(f) be the third derivative of -f**5/180 + f**4/72 + 2*f**2. Factor a(k).
-k*(k - 1)/3
Let k be (((-672)/(-70))/16)/((-12)/(-10)). Factor 1/4*y**5 - k*y**3 + 1/4 + 1/4*y + 1/4*y**4 - 1/2*y**2.
(y - 1)**2*(y + 1)**3/4
Determine y, given that -10/7 - 18/7*y - 8/7*y**2 = 0.
-5/4, -1
Let o(f) be the third derivative of 0 + 0*f - 3/16*f**4 + 1/2*f**3 + 1/40*f**5 - 2*f**2. Factor o(z).
3*(z - 2)*(z - 1)/2
Let c(r) = r**3 - 7*r**2 + 8*r + 10. Let f be c(5). Factor f*t + 8/3*t**2 - 8/3*t**3 + 2/3*t**4 + 0.
2*t**2*(t - 2)**2/3
Let y(k) be the second derivative of -3*k**6/10 - 21*k**5/20 - 3*k**4/4 + 3*k**3/2 + 3*k**2 + 13*k. Factor y(j).
-3*(j + 1)**3*(3*j - 2)
Let s = 14 - -7. Suppose 5*a = -3*l + 24, -3*l = -0*l + 4*a - s. Factor 4*k - 5*k**l - 3*k + 4*k**2 - k**2 + 4*k**5 - 3*k**4.
k*(k - 1)**2*(k + 1)*(4*k + 1)
Let u(y) = 16*y**2 + 5*y - 11. Let c(s) = 3*s**2 + s - 2. Let k(l) = -22*c(l) + 4*u(l). What is p in k(p) = 0?
-1, 0
Let s(b) = 3*b + 9. Let v be s(-2). Determine j so that -j**v - 1/2 - 5/2*j**2 - 2*j = 0.
-1, -1/2
Factor -10/7*u**5 + 0 - 2/7*u**3 + 4/7*u**2 + 0*u - 16/7*u**4.
-2*u**2*(u + 1)**2*(5*u - 2)/7
Let o(v) be the third derivative of v**9/9072 - v**7/2520 - 2*v**3/3 + 2*v**2. Let g(b) be the first derivative of o(b). Suppose g(q) = 0. What is q?
-1, 0, 1
Let z(t) = -2*t. Let b(c) = 3*c**3 - 2*c**2 - 7*c. Let u(v) = 2*v + 2. Let x be u(2). Let d(g) = x*z(g) - 2*b(g). Factor d(m).
-2*m*(m - 1)*(3*m + 1)
Let n(q) = -3*q**2 + 14*q + 23. Let g(k) = -k + 6. Let v be g(0). Let z(a) = -a**2 + 5*a + 8. Let p(s) = v*n(s) - 17*z(s). Factor p(w).
-(w - 1)*(w + 2)
Factor -3*h + 2*h**2 + 81 + h**3 - 81.
h*(h - 1)*(h + 3)
Let w(f) be the second derivative of 1/8*f**4 + 2*f + 1/24*f**5 + 7/36*f**3 + 1/180*f**6 + 1/6*f**2 + 0. Factor w(h).
(h + 1)**3*(h + 2)/6
Let y be (-570)/(-20)*2*1. Let m = y + -283/5. Determine g so that 2/5 - m*g**2 + 2/5*g - 2/5*g**3 = 0.
-1, 1
Find r such that -16/5*r + 1 + 3/5*r**2 = 0.
1/3, 5
Let a(n) = -n**2 - 15*n - 10. Let w be a(-14). Suppose -w*j = -2*j - 4. Factor -1/3*h**j + 0*h + 0.
-h**2/3
Let j(y) = -2*y**3 - 2*y**2 - 5*y + 6. Let s(i) = i**3 + i**2 + 5*i - 5. Let x(t) = -2*j(t) - 3*s(t). Factor x(a).
(a - 1)**2*(a + 3)
Let n = 127 - 125. Let v(t) be the first derivative of -n - 1/2*t**2 + 1/12*t**3 + t. Determine w so that v(w) = 0.
2
Let s be -3 + (3/(-9))/((-21)/225). Determine y so that 0*y + 0 + 2/7*y**4 + 2/7*y**2 + s*y**3 = 0.
-1, 0
Factor 12/7*v**4 + 12/7*v**2 + 3/7*v + 0 + 3/7*v**5 + 18/7*v**3.
3*v*(v + 1)**4/7
Let i(o) be the second derivative of -3*o**7/28 + 7*o**6/10 - 61*o**5/40 + 7*o**4/6 - o**3/3 + 10*o. Suppose i(b) = 0. Calculate b.
0, 1/3, 2
Let d(z) = -z**2 - 9*z + 12. Let p be d(-10). Suppose p*y - 4 - 6 = 0. Find n such that n**5 - n**5 - 3*n**4 - 3*n**5 + 0*n**y = 0.
-1, 0
Factor 13/2*j - 6 - 1/2*j**2.
-(j - 12)*(j - 1)/2
Let m = 17 + -33. Let k be ((-4)/m)/((-21)/(-72)). Suppose 4/7 + k*j - 4/7*j**2 = 0. What is j?
-1/2, 2
Let t(o) be the first derivative of 3 + 0*o**3 + o + 1/24*o**4 - 1/4*o**2. Let s(h) be the first derivative of t(h). Suppose s(g) = 0. Calculate g.
-1, 1
Factor 8/3 + 2/3*b**2 + 10/3*b.
2*(b + 1)*(b + 4)/3
Let d(n) be the first derivative of -3/4*n**4 + 5 - 1/3*n**3 + 3/2*n**2 + 2*n - 1/5*n**5. Solve d(a) = 0.
-2, -1, 1
Let r(y) be the third derivative of -3*y**8/784 + 11*y**7/490 - 19*y**6/840 + y**5/140 - y**2 + 8. Find u such that r(u) = 0.
0, 1/3, 3
Let s be (-4)/(-10) - 14/10. Let j be ((s/2)/(-1))/1. Factor -1/2 + 2*t - 3*t**2 + 2*t**3 - j*t**4.
-(t - 1)**4/2
Let z be (12/24)/((-2)/(-12)). Solve 5/4*i - 7/4*i**2 + 3/4*i**z - 1/4 = 0.
1/3, 1
Let q be -7 + 56/7 + -1. Let -9/7*k**4 + 0*k**2 + q - 3/7*k**5 + 0*k + 0*k**3 = 0. Calculate k.
-3, 0
Solve -4/7*n**5 + 16/7*n**3 + 8/7*n**2 + 0*n**4 - 12/7*n - 8/7 = 0 for n.
-1, 1, 2
Let r(g) be the first derivative of -g - 4/3*g**2 + g**5 + 2 + 11/18*g**4 - 5/9*g**6 - 4/3*g**3. Let t(l) be the first derivative of r(l). Factor t(p).
-2*(p - 1)**2*(5*p + 2)**2/3
Let o(n) be the first derivative of -n**3/15 - 3*n**2/10 + 22. Suppose o(c) = 0. Calculate c.
-3, 0
Determine u, given that -13*u - 7*u**5 + 42*u**4 + 10*u - 4*u**5 - 58*u**3 + 32*u**2 - 3 + 1 = 0.
-2/11, 1
Let s be (-2 - 1)/(3/2). Let a be -1 - (2 + -1 + s). What is l in 0*l + 0*l**2 - 1/4*l**5 + 1/4*l**3 + 0 + a*l**4 = 0?
-1, 0, 1
Let v be (5/(-5))/(2/(-6)). Suppose -10*f**3 + f**4 + 3*f**v + f**2 + 9*f**3 = 0. Calculate f.
-1, 0
Let a(q) be the first derivative of -q**8/6720 + q**7/1680 - q**6/1440 + 5*q**3/3 + 4. Let v(y) be the third derivative of a(y). Factor v(k).
-k**2*(k - 1)**2/4
Let w(a) be the third derivative of a**6/160 + 3*a**5/80 + 3*a**4/32 + a**3/8 - 12*a**2. Factor w(s).
3*(s + 1)**3/4
Let d(z) = -9*z**2 - z + 12. Let t(r) = 4*r**2 - 6. Let c(a) = 3*d(a) + 5*t(a). Let x(j) = -j**2. Let w(k) = c(k) - 4*x(k). Find h, given that w(h) = 0.
-2, 1
Let v(l) be the second derivative of -l**10/10080 + l**8/1120 - l**6/240 - l**4/4 + 4*l. Let a(n) be the third derivative of v(n). Suppose a(p) = 0. What is p?
-1, 0, 1
Determine n so that 8*n**2 + 0 - 4/3*n**3 - 12*n = 0.
0, 3
Let y**3 + 0*y**3 + 5 + 6*y**3 + 23*y**2 + 20*y - 1 = 0. What is y?
-2, -1, -2/7
Let h(a) be the first derivative of 0*a - 1/11*a**2 + 4 - 2/33*a**3. Factor h(v).
-2*v*(v + 1)/11
Let o(l) = -l + 12. Let x be o(10). Let r(u) be the first derivative of 0*u**4 + 1/4*u + 0*u**2 - x - 1/6*u**3 + 1/20*u**5. Factor r(s).
(s - 1)**2*(s + 1)**2/4
Let -8*b**5 - b**2 + b**2 + 4 + 9*b**5 - 8*b + 7*b**3 + b**2 - 5*b**4 = 0. Calculate b.
-1, 1, 2
Let y(j) = 46*j**2 + 5*j - 2. Let w(p) = p + 2. Let q be w(-4). Let o(g) = 47*g**2 + 6*g - 2. Let s(v) = q*o(v) + 3*y(v). Find a such tha