Factor 1/6*q**2 + 0 - 1/3*q.
q*(q - 2)/6
Factor 0*c - 2/3*c**2 + 2/9*c**3 + 0.
2*c**2*(c - 3)/9
Let z = -30 - -30. Factor 1/5*f**2 + z + 1/5*f.
f*(f + 1)/5
Let h be 707/49 + (-6)/14. Let w be (h/168)/(1/4). Factor -2/3*v**2 - 1/3*v + 0 - w*v**3.
-v*(v + 1)**2/3
Let n(v) be the third derivative of -v**6/240 + v**5/60 - v**4/48 + 12*v**2. Let n(k) = 0. Calculate k.
0, 1
Let z be (-33)/(-390)*4 - -1. Let f = z - 7/13. Factor f*t + 6/5*t**2 + 0.
2*t*(3*t + 2)/5
Let u(b) be the first derivative of -3*b**5/80 - b**4/8 - b**3/8 - 3*b - 1. Let f(h) be the first derivative of u(h). Factor f(z).
-3*z*(z + 1)**2/4
Let c(i) be the second derivative of i**6/300 - i**5/75 + i**4/60 - 5*i**2/2 + 5*i. Let s(f) be the first derivative of c(f). Let s(m) = 0. What is m?
0, 1
Let g(a) be the first derivative of -2 - 1/10*a**4 + 1/5*a**2 - 2/25*a**5 + 0*a + 2/15*a**3. Factor g(r).
-2*r*(r - 1)*(r + 1)**2/5
Factor 4/7*o**4 + 144/7*o**2 - 40/7*o**3 - 216/7*o + 108/7.
4*(o - 3)**3*(o - 1)/7
Let k(h) be the first derivative of 0*h + 0*h**2 + 1/3*h**3 + 2. Let k(v) = 0. Calculate v.
0
Let j(c) be the second derivative of c**6/14 + 9*c**5/35 + 9*c**4/28 + c**3/7 - 8*c. Solve j(r) = 0 for r.
-1, -2/5, 0
Suppose 71 = 5*a - 4. Suppose -3*k - 5 = -d, -3*k + 2*d = -d + a. Factor -1/2*h - 1/2*h**3 - h**2 + k.
-h*(h + 1)**2/2
Let d(h) be the second derivative of -6*h + 3*h**2 + 1/2*h**3 + 0 - 1/4*h**4. Let d(i) = 0. What is i?
-1, 2
Let l(p) = -15*p**2 + 5*p - 8. Let t(v) = -7*v**2 + 2*v - 4. Let h(f) = -6*l(f) + 13*t(f). Factor h(z).
-(z + 2)**2
Let f = 9 + -6. Find t, given that -1/4*t - 1/4*t**2 + 1/4 + 1/4*t**f = 0.
-1, 1
Let g(o) = -2*o**2 + 3*o - 1. Let l(u) = u + 1. Let n(d) = g(d) + l(d). What is f in n(f) = 0?
0, 2
Let w(x) be the third derivative of x**8/560 + 3*x**7/280 + x**6/60 + x**3/6 - x**2. Let d(h) be the first derivative of w(h). Factor d(q).
3*q**2*(q + 1)*(q + 2)
Let r(t) be the first derivative of -t**7/2520 + t**6/270 - t**5/72 + t**4/36 - t**3 + 2. Let v(i) be the third derivative of r(i). Solve v(s) = 0.
1, 2
Let u(z) = 3*z**2 - 5*z + 29. Let g(l) = l**2 - 2*l + 10. Let w(i) = -17*g(i) + 6*u(i). Factor w(o).
(o + 2)**2
Let u be 8 - (0 + -2 + 4). Suppose 6*o - 6 = 3*o - s, 3*o + 5*s - u = 0. Factor -2*a**2 + 4*a + 3*a**2 + 4 + 0*a**o.
(a + 2)**2
Determine t so that -6*t + 3 - 57/4*t**2 - 21/4*t**3 = 0.
-2, -1, 2/7
Let i(d) be the third derivative of -d**5/42 + d**4/12 - 2*d**3/21 + 18*d**2. Factor i(b).
-2*(b - 1)*(5*b - 2)/7
Suppose -3*a**5 + 2*a**3 - 9*a**2 - 17*a**3 + 6*a + 9*a**4 + 2*a**3 + 10*a**3 = 0. Calculate a.
-1, 0, 1, 2
Let l = 1201/40 + -30. Let n(g) be the third derivative of 0 + 1/300*g**5 + 2*g**2 - l*g**4 + 1/15*g**3 + 0*g. Let n(r) = 0. Calculate r.
1, 2
Let w(u) be the third derivative of 0*u + 0 + 4*u**2 + 0*u**3 + 1/60*u**5 - 1/24*u**4. Factor w(x).
x*(x - 1)
Let o = 16 + -14. Let a(r) be the third derivative of -1/12*r**4 + 0*r**3 - 1/60*r**6 + 1/15*r**5 + o*r**2 + 0*r + 0. Determine p so that a(p) = 0.
0, 1
Let d be (-4)/(-30 - 2)*-134. Let t = d + 17. Solve 1/4 + t*m**2 - 1/2*m = 0 for m.
1
Let f(y) = -4*y**4 - 10*y**3 + 42*y**2 - 70*y + 32. Let a(g) = -3*g**4 - 11*g**3 + 43*g**2 - 69*g + 32. Let k(p) = 6*a(p) - 5*f(p). Factor k(r).
2*(r - 2)**4
Suppose -11 + 5 = -l. Let m(a) be the third derivative of 1/630*a**7 + 0 - 2*a**2 + 0*a**4 + 0*a**3 + 1/180*a**l + 1/180*a**5 + 0*a. Factor m(g).
g**2*(g + 1)**2/3
What is z in 81*z - 5*z**2 - 1125 - 22*z + 113*z - 22*z = 0?
15
Suppose -3*w + n - 36 = -13, -29 = 4*w - n. Let s(h) = -h - 4. Let d be s(w). Solve 4 - 5*a**3 + 3*a + 5*a - d*a**2 - 2 - 3*a**3 = 0 for a.
-1, -1/4, 1
Let k(j) = j**3 - j**2 + j. Let w(t) = 4*t**4 + 8*t**3 - 24*t**2 + 16*t. Let u(v) = -4*k(v) + w(v). Factor u(h).
4*h*(h - 1)**2*(h + 3)
Factor 8/3*s**2 + s**3 + 2/3 + 7/3*s.
(s + 1)**2*(3*s + 2)/3
Factor -192 + 171*c - 723*c**2 + 79*c + 345*c**3 + 37*c + 337*c + 3*c**5 - 57*c**4.
3*(c - 8)**2*(c - 1)**3
Find y, given that 3*y**3 + 2/3*y - 5/3*y**4 + 1/3*y**5 - 7/3*y**2 + 0 = 0.
0, 1, 2
Let r(y) be the first derivative of -2/15*y**3 + 0*y - 1 + 1/10*y**4 + 0*y**2. Let r(t) = 0. Calculate t.
0, 1
Let d(s) be the third derivative of -7*s**2 - 1/3*s**3 + 1/60*s**5 - 1/24*s**4 + 0 + 0*s. Let d(i) = 0. Calculate i.
-1, 2
Let s(m) be the third derivative of m**8/336 + 17*m**7/210 + 21*m**6/40 - 27*m**5/20 - 32*m**2. Suppose s(g) = 0. What is g?
-9, 0, 1
Let y(k) be the first derivative of -4*k**5/15 - 13*k**4/3 - 80*k**3/3 - 224*k**2/3 - 256*k/3 - 40. Factor y(h).
-4*(h + 1)*(h + 4)**3/3
Let d(r) be the first derivative of -r**8/5040 - r**7/2520 - r**3 - 3. Let i(l) be the third derivative of d(l). Suppose i(t) = 0. What is t?
-1, 0
Let n(u) be the first derivative of 4*u**5/5 + 15*u**4/4 + 16*u**3/3 + 3*u**2/2 - 2*u - 3. Factor n(o).
(o + 1)**2*(o + 2)*(4*o - 1)
Let h(i) = i**5 - 3*i**4 + 7*i**3 - 3*i**2 + 4*i. Let c(s) = -2*s**5 + 6*s**4 - 15*s**3 + 7*s**2 - 9*s. Let f(n) = 6*c(n) + 13*h(n). Solve f(k) = 0.
-1, 0, 1, 2
Let o be 15 + -17 + -20*(-1)/9. Let c(j) be the first derivative of 0*j + 1/5*j**5 + 0*j**2 + 1/12*j**4 + 1 - o*j**3. Factor c(t).
t**2*(t + 1)*(3*t - 2)/3
Suppose 32 = w + 4*z, 3*w = 4*w - 2*z - 20. Factor 6 + 3*g**2 + 19 + 3 + w*g + 20.
3*(g + 4)**2
Let c = -523/5 + 105. Factor 4/5*i**2 - c*i**3 + 0 - 2/5*i.
-2*i*(i - 1)**2/5
Let l(b) be the first derivative of b**7/1120 - b**5/160 + 2*b**3/3 - 2. Let s(v) be the third derivative of l(v). Suppose s(d) = 0. What is d?
-1, 0, 1
Let t(o) be the second derivative of 3*o**7/2 - 2*o**6 + 19*o**5/20 - o**4/6 - 25*o. Factor t(a).
a**2*(3*a - 1)**2*(7*a - 2)
Suppose 4*u = -r - 6 - 10, 2*r + 3*u + 7 = 0. Suppose 6*z**3 - r*z**4 + 3*z**4 - 2*z**4 = 0. What is z?
0, 2
Let q = -31/5 - -101/15. Factor 2/15*i**3 + q*i + 0 - 8/15*i**2.
2*i*(i - 2)**2/15
Let g be 16/(-20) + (-8)/(-10). Find y, given that -4*y**2 - 37/5*y**3 - 6*y**4 - 4/5*y - 9/5*y**5 + g = 0.
-1, -2/3, 0
Let o(a) = a**5 + a**4 + 5*a**3 - a**2 + 3*a + 3. Let j(y) = y**5 + y**4 + 9*y**3 - y**2 + 5*y + 5. Let k(i) = 3*j(i) - 5*o(i). Factor k(s).
-2*s**2*(s - 1)*(s + 1)**2
Let s(p) = p**2 + 3*p - 5. Let k be s(-4). Let o = 1 + k. Factor 0 + 1/2*w**3 + o*w + 0*w**2.
w**3/2
Let x(i) be the second derivative of 3*i**5/100 - i**3/10 + 3*i. Suppose x(f) = 0. What is f?
-1, 0, 1
Let w(u) be the first derivative of -2/3*u**2 + 1/6*u**4 + 2/9*u**3 + 0*u - 6. Factor w(i).
2*i*(i - 1)*(i + 2)/3
Let d(m) be the second derivative of 0*m**5 - 3*m - 1/15*m**6 + 1/6*m**4 + 0 - 1/42*m**7 + 1/6*m**3 + 0*m**2. Factor d(k).
-k*(k - 1)*(k + 1)**3
Let o = 1 + 2. Factor -3*i**o + 5*i**2 + 4*i**5 - i + 5*i**4 - 14*i**4 + 4*i**4.
i*(i - 1)**2*(i + 1)*(4*i - 1)
Factor 1/2*p**3 - p**2 + 0*p + 1/2*p**4 + 0.
p**2*(p - 1)*(p + 2)/2
Suppose 2*d = d. Let i(b) be the third derivative of 0 - 2*b**2 + 1/48*b**4 + 1/30*b**5 + 1/60*b**6 + d*b + 0*b**3. Find q such that i(q) = 0.
-1/2, 0
Factor -12*c**3 + 5*c**2 + c**2 + 8*c**3 - 4*c**2 + 2*c.
-2*c*(c - 1)*(2*c + 1)
Suppose -4*b = o - 2*b - 8, 0 = 3*o - 3*b - 6. Suppose 0 - 2/3*v - 1/3*v**5 + 5/3*v**o - 3*v**3 + 7/3*v**2 = 0. Calculate v.
0, 1, 2
Let t(i) be the first derivative of -i**6/33 - 16*i**5/55 - 21*i**4/22 - 12*i**3/11 - 24. Factor t(k).
-2*k**2*(k + 2)*(k + 3)**2/11
Let j(v) = -v**3 + v + 1. Let u be 208/(-39) - 1/(-3). Let o(r) = 8*r**3 - 9*r**2 + r - 5. Let p(d) = u*j(d) - o(d). Factor p(f).
-3*f*(f - 2)*(f - 1)
Let o be (14/(-54))/(2/(-12)). Let -4/9 - o*d - 10/9*d**2 = 0. What is d?
-1, -2/5
Let g = -28 + 85/3. Suppose -12 = -9*m + 6. Let -h**m + 2/3*h + 0 + g*h**3 = 0. Calculate h.
0, 1, 2
Let u = 101/280 - 3/40. Determine v, given that 0 + 2/7*v - 4/7*v**2 + u*v**3 = 0.
0, 1
Let c(z) = -25*z**4 - 130*z**3 + 40*z**2 + 40. Let w(q) = 2*q**4 + 10*q**3 - 3*q**2 - 3. Let d(x) = 3*c(x) + 40*w(x). Factor d(u).
5*u**3*(u + 2)
Let m = -78/25 + 118/25. Determine l so that 0 + 26/5*l**3 - 18/5*l**5 + 0*l**2 + 0*l**4 - m*l = 0.
-1, -2/3, 0, 2/3, 1
Let o be ((-6)/4 - -2)*2. Let q = o + 7. Factor 7*g**3 + 3*g**2 - q*g**3 - 2*g**2.
-g**2*(g - 1)
Let o(a) be the first derivative of -a**6/60 - a**5/15 - a**4/12 + 2*a**3/3 + 3. Let w(j) be the third derivative of o(j). Find z such that w(z) = 0.
-1, -1/3
Let w(q) = 15*q**5 - 24*q**4 - 18*q**3 + 18. Let v(g) = g**5 - g**4 - g**3 + 1. Let r(