third derivative of q**6/15 - q**5/15 + q**2. Factor g(k).
4*k**2*(2*k - 1)
Factor -8*y**3 - y**5 + 12*y**3 + 7*y**5 - 10*y**4.
2*y**3*(y - 1)*(3*y - 2)
Factor 2/5*d**4 - 2*d**3 + 0 - 8/5*d + 16/5*d**2.
2*d*(d - 2)**2*(d - 1)/5
Let s(q) be the first derivative of 3*q**4/2 + 3*q**3 - 3*q - 6. Factor s(b).
3*(b + 1)**2*(2*b - 1)
Let w(f) be the second derivative of f**4/16 + f**3/2 - f. Factor w(i).
3*i*(i + 4)/4
Let x(n) be the third derivative of 0*n**3 + 0 - 1/20*n**5 + 1/8*n**4 + 2*n**2 + 0*n - 1/20*n**6. Determine q, given that x(q) = 0.
-1, 0, 1/2
Suppose 0*y = -3*y + 2*g + 2, -3*g - 3 = y. Suppose y*d + 4*d = 0. Factor d*u + 0 + 0*u**3 + 1/2*u**4 - 1/2*u**2.
u**2*(u - 1)*(u + 1)/2
Let q(i) be the second derivative of 3*i**5/100 - 3*i**4/20 + 3*i**3/10 - 3*i**2/10 + 6*i. Factor q(f).
3*(f - 1)**3/5
Suppose 48 - 12*f - 3*f**4 + 3*f**3 - 48 + 6*f**3 = 0. What is f?
-1, 0, 2
Let a be 4/1 - 1/1. What is h in 0*h**5 + 6*h**2 + 3*h**5 - 3*h**a - 2*h**2 - h**2 - 3*h**4 = 0?
-1, 0, 1
Let c(d) be the third derivative of -5*d**8/336 - 5*d**7/21 - 13*d**6/8 - 37*d**5/6 - 85*d**4/6 - 20*d**3 + 13*d**2. Factor c(z).
-5*(z + 1)*(z + 2)**3*(z + 3)
Let h = -2/113 + 123/565. Factor h*j**4 - 1/5*j**2 + 0*j**3 + 0*j + 0.
j**2*(j - 1)*(j + 1)/5
Suppose 6*c = -1 + 1. Let f(z) be the third derivative of 2*z**2 - 1/192*z**8 - 1/70*z**7 - 1/160*z**6 + 1/120*z**5 + 0 + c*z**3 + 0*z**4 + 0*z. Factor f(p).
-p**2*(p + 1)**2*(7*p - 2)/4
Let p(y) be the second derivative of 0 + 1/12*y**4 + 0*y**2 + 1/3*y**3 + y. What is d in p(d) = 0?
-2, 0
Let u(f) be the first derivative of 3*f**4/4 + f**3 + 3. Suppose u(b) = 0. Calculate b.
-1, 0
Let y(w) be the first derivative of 0*w**2 - 1/6*w**3 + 0*w - 3 - 1/8*w**4. Factor y(s).
-s**2*(s + 1)/2
Find a, given that -4/15*a - 2/15*a**2 + 0 + 4/15*a**3 + 2/15*a**4 = 0.
-2, -1, 0, 1
Suppose 2*f + h - 167 = 6*h, -4*h - 168 = -2*f. Let w be 6/(-16) + f/144. Suppose 2/9*g**2 + w - 4/9*g = 0. What is g?
1
Factor 96 - 3*g**4 - 96*g - 31*g**3 - 19*g**3 - 18*g**2 + 71*g**3.
-3*(g - 4)**2*(g - 1)*(g + 2)
Suppose 0 = 3*n - 7 - 2. Factor 4*o**n - 3*o + 2*o - 3*o - 2*o**4 + 0*o + 2.
-2*(o - 1)**3*(o + 1)
Suppose 0 = 4*g - 5*q - 33, 5 = -3*g - 3*q - 4. Factor 0 - 2/7*r**g + 4/7*r - 2/7*r**3.
-2*r*(r - 1)*(r + 2)/7
Let h(b) = 2*b**5 + 12*b**4 + 19*b**3 + 13*b**2 + 3*b + 1. Let i(z) = -z**5 + z**3 + z**2 + 1. Let k(l) = h(l) - i(l). Let k(p) = 0. Calculate p.
-1, 0
Let l(y) = -8*y**2 + 16*y - 8. Let k(o) = -o**3 - 23*o**2 + 48*o - 24. Let d(f) = -2*k(f) + 7*l(f). Solve d(g) = 0.
1, 2
Factor n**3 - n - 1/2*n**4 + 1/2 + 0*n**2.
-(n - 1)**3*(n + 1)/2
Let z be ((-4)/(-3))/(16/472). Let t = -39 + z. Determine r, given that -t*r - 1/3*r**2 + 2/3 = 0.
-2, 1
Let w(s) = -3*s**3 - s**2 + 4*s. Let f(b) = 5*b**3 + b**2 - 6*b. Suppose 11 = 3*a + 26. Let t(c) = a*f(c) - 8*w(c). Factor t(p).
-p*(p - 2)*(p - 1)
Let y(i) be the third derivative of i**2 - 1/6*i**4 + 0*i**5 - 1/105*i**7 + 1/30*i**6 + 0*i + 0 + 1/3*i**3. Determine j, given that y(j) = 0.
-1, 1
What is s in -48/5*s + 15*s**2 - 3/5*s**5 + 21/5*s**4 - 57/5*s**3 + 12/5 = 0?
1, 2
Solve -2/9*b**2 - 2/9*b**3 + 0 + 4/9*b = 0.
-2, 0, 1
Let b(s) be the first derivative of 2*s**5/25 + 3*s**4/5 + 26*s**3/15 + 12*s**2/5 + 8*s/5 - 5. Factor b(a).
2*(a + 1)**2*(a + 2)**2/5
Let h = 2 - -4. Let z(g) = -g - 2. Let k be z(-5). Solve -k*w**2 + 2 - w + h*w + 0*w = 0.
-1/3, 2
Suppose -4*g + 9*g - 25 = 0. Suppose -g*l + 5 + 5 = 0. Factor 4 + 0 - 3 - f**l.
-(f - 1)*(f + 1)
Factor 2/11*g**3 + 14/11*g**2 + 2*g + 10/11.
2*(g + 1)**2*(g + 5)/11
Let r(l) = -l + 2. Let v be r(-7). Let z(f) = -f**3 - 7*f**2 - 4*f - 4. Let d(y) = 3*y**3 + 15*y**2 + 9*y + 9. Let k(c) = v*z(c) + 4*d(c). Factor k(a).
3*a**2*(a - 1)
Let f = -9 + 11. Suppose -3*z - 24*z**3 - 12*z**4 + 5 - 15*z**f - 8 + 3 = 0. What is z?
-1, -1/2, 0
Let b(f) be the first derivative of 0*f**2 - 1/6*f**4 + 2 - 1/3*f**3 + 2*f. Let c(o) be the first derivative of b(o). Factor c(u).
-2*u*(u + 1)
Let y(b) = b + 6. Let o be y(-3). Factor -p + 5*p**4 + o*p**4 - 6*p**4 - p**5 - 2*p**2 + 2*p.
-p*(p - 1)**3*(p + 1)
Let t(h) = -h**2 - h - 1. Let w(x) = 9*x**2 + 9*x - 3. Let u(k) = -5*t(k) - w(k). Factor u(z).
-4*(z - 1)*(z + 2)
Let y(q) be the first derivative of -q**4 + 6*q**2 + 8*q - 3. What is s in y(s) = 0?
-1, 2
Suppose 3*s + 0*p + 3*p = 0, s + 3 = -2*p. Suppose -3*d + 3 = -s. Factor -2*a**d + 2*a**2 + 6*a**2 + 3*a**3.
3*a**2*(a + 2)
Let n(i) = -3*i - 10. Let c(m) = 4*m + 10. Let x(a) = 5*c(a) + 6*n(a). Let j be x(5). Factor 2/3*d**3 - 1/3*d**5 + 0 + 0*d**4 - 1/3*d + j*d**2.
-d*(d - 1)**2*(d + 1)**2/3
Let u(v) = -v**3 - v**2 - v. Let x(p) = 280*p**2 + 5410*p + 34295. Let c(z) = -5*u(z) + x(z). Determine g so that c(g) = 0.
-19
Let z(n) be the first derivative of -n**5/240 + n**4/32 + 7*n**2/2 + 9. Let u(i) be the second derivative of z(i). Factor u(k).
-k*(k - 3)/4
Let b(q) be the first derivative of 2*q**5/5 + 3*q**4/2 + 4*q**3/3 - 21. Determine x so that b(x) = 0.
-2, -1, 0
Suppose 0 = -2*f + 4*c - 24, 0 = -f - 3*c + 2*c + 3. Let n be f*4/(-32) - 0. Find x, given that -n*x**3 - 1/2*x**2 - 1/4*x + 0 = 0.
-1, 0
Let m(g) be the second derivative of -g**4/4 - 2*g**3 - 9*g**2/2 - 37*g. Factor m(a).
-3*(a + 1)*(a + 3)
Let d = 2666 - 13609/5. Let i = 56 + d. Factor -2/5*f**3 + 1/5*f + 0*f**4 + 0*f**2 + i*f**5 + 0.
f*(f - 1)**2*(f + 1)**2/5
Let v(l) be the third derivative of -l**6/300 - l**5/50 + l**4/60 + l**3/5 + 13*l**2. Solve v(s) = 0 for s.
-3, -1, 1
Let h(p) = -10*p**2 + 12. Let v(q) = -q**2 - q - 1. Let d be v(0). Let i(f) = -f**2 + 1. Let u(s) = d*h(s) + 12*i(s). Factor u(l).
-2*l**2
Let u(a) = a**3 + 5*a**2 - a - 8. Let g(l) = -l**3 - 9*l**2 + l + 16. Let h(i) = 3*g(i) + 7*u(i). Factor h(v).
4*(v - 1)*(v + 1)*(v + 2)
Let j = 11 - 4. Let v(k) be the third derivative of 1/60*k**6 + 0*k - 2*k**2 + 1/140*k**j + 0*k**4 + 0*k**3 + 1/120*k**5 + 0. Factor v(d).
d**2*(d + 1)*(3*d + 1)/2
Let f(r) be the third derivative of r**5/150 - r**4/15 + 10*r**2. Factor f(i).
2*i*(i - 4)/5
Let r(f) = 3*f**2. Let g = -7 - -8. Let u be r(g). Factor 4/5 + 2/5*q**u + 8/5*q**2 + 2*q.
2*(q + 1)**2*(q + 2)/5
Let f(v) = -v**3 - 1. Let h(d) = d**4 + 6*d**3 + 5. Let a be ((-5)/(-2) + -2)*10. Let m(l) = a*f(l) + h(l). Let m(p) = 0. What is p?
-1, 0
Let c(q) be the first derivative of -q**6/33 + 3*q**4/22 - 4*q**3/33 + 9. Determine b so that c(b) = 0.
-2, 0, 1
Let k(j) be the second derivative of -1/12*j**4 + j + 0 - 1/2*j**2 - 1/3*j**3. Find v, given that k(v) = 0.
-1
Let p(c) = -2*c**2 - 4*c + c**2 + 3*c. Suppose 0 = -2*m + m + 1. Let q(b) = -10*b + 2. Let l(o) = m*q(o) - 4*p(o). Solve l(k) = 0 for k.
1/2, 1
Let u(m) be the third derivative of -m**8/448 + m**7/140 + m**6/80 - m**5/10 + 7*m**4/32 - m**3/4 - 16*m**2. Factor u(t).
-3*(t - 1)**4*(t + 2)/4
Let h = -682 - -682. Suppose -3/4*b**2 - 3/8*b**3 - 3/8*b + h = 0. Calculate b.
-1, 0
Suppose 8*l - 9 = 5*l. Find h such that -h**2 + 3*h**3 - h - 3*h**l + 3*h**3 + h**4 - 2*h**3 = 0.
-1, 0, 1
Let n(k) be the second derivative of -k**4/78 + k**3/13 - 2*k**2/13 - 9*k. Suppose n(r) = 0. What is r?
1, 2
Factor 8/5*j**3 + 16/5 - 16/5*j + 4/5*j**4 - 12/5*j**2.
4*(j - 1)**2*(j + 2)**2/5
Find x, given that 0*x + 4/5*x**2 - 4/5 = 0.
-1, 1
Let v be (136 + -137)/(2*(-1)/6). Find h, given that 24/7*h**2 + 6/7*h**4 + 2/7 + 20/7*h**v + 12/7*h = 0.
-1, -1/3
Suppose -1/7*i**4 - 1/7*i**2 + 2/7*i**3 + 0*i + 0 = 0. What is i?
0, 1
Let y(p) be the third derivative of p**7/4200 - p**6/1800 + p**3 - 2*p**2. Let d(v) be the first derivative of y(v). Factor d(l).
l**2*(l - 1)/5
Let k = -99 - -139. Factor -21*p**4 - 4 - k*p**2 + 4*p**5 + p**4 + 40*p**3 + 2*p + 18*p.
4*(p - 1)**5
Let h(p) = p**4 + 13*p**3 - 19*p**2 + 5*p + 3. Let y(k) = 12*k**4 + 144*k**3 - 210*k**2 + 54*k + 34. Let i(b) = 68*h(b) - 6*y(b). Factor i(v).
-4*v*(v - 2)**2*(v - 1)
Let c(v) be the second derivative of -v**6/240 + v**5/60 - v**4/48 + v**2 + 3*v. Let g(r) be the first derivative of c(r). Determine t so that g(t) = 0.
0, 1
Let s(q) = -84*q**2 + 39*q - 4. Let a(u) = 335*u**2 - 155*u + 16. Let k(d) = 6*a(d) + 22*s(d). Determine i so that k(i) = 0.
2/9
Let g(b) = b**3 + 4*b**2 + 3*b + 4. Let p be g(-3). Suppose p*a = 3*k, 0 = -k + 6*k - 5*a. Factor 0*d**3 - 2/9 - 2/9*d**4 + k*d + 4/9*d**2.
-2*(d - 1)**2