 x**2 - x - q*x.
2*x*(x - 1)
Let g(y) be the first derivative of 2*y**5/55 - y**4/11 - 4. Find z such that g(z) = 0.
0, 2
Let r(f) be the third derivative of f**6/1320 + f**5/165 - f**4/264 - 2*f**3/33 - 21*f**2. Solve r(i) = 0.
-4, -1, 1
Factor -1/3*r**2 + 0 + 0*r.
-r**2/3
Let s = -305189/29372 + -5/2098. Let k = 78/7 + s. Determine u so that -3/4*u**4 + 0 + k*u**3 + 0*u + 3/2*u**2 = 0.
-1, 0, 2
Let j(v) be the second derivative of 1/6*v**4 + 0 + 4*v + 4*v**2 + 4/3*v**3. Factor j(h).
2*(h + 2)**2
Let m(a) = 4*a**2 - 6*a - 8. Let r(p) = 5*p**2 - 7*p - 9. Let y(x) = 3*m(x) - 2*r(x). Factor y(u).
2*(u - 3)*(u + 1)
Suppose -2*s + 14 - 4 = 0. Let z(a) be the first derivative of 1/8*a**2 + 1/12*a**3 + 0*a + 2 - 1/20*a**s - 1/16*a**4. Suppose z(x) = 0. Calculate x.
-1, 0, 1
Factor -25*i**2 - 11*i + i**5 + 5 - 7*i**4 - 9 + 27*i + 19*i**3.
(i - 2)**2*(i - 1)**3
Let u(s) = -11*s**3 - 17*s**2 - 6*s. Let z(f) = -17*f**3 - 26*f**2 - 9*f. Let b(j) = 8*u(j) - 5*z(j). Factor b(n).
-3*n*(n + 1)**2
Let u(i) = -3*i**3 - 8*i**2 + 5*i. Let a(x) = -x**3 - 4*x**2 + 3*x. Let q(o) = 5*a(o) - 3*u(o). Suppose q(v) = 0. Calculate v.
-1, 0
Let i = -18 - -27. Suppose 4*d - d = i. Factor v**3 + 4*v**3 - 5*v**d - v**3.
-v**3
Factor 1/3*j + 2/3 - 1/3*j**3 + 1/3*j**4 - j**2.
(j - 2)*(j - 1)*(j + 1)**2/3
Suppose -5*i = -3*i - 6. Suppose -4 - 127*r**2 + 162*r**i - 17*r**2 + 24*r + 12*r + 6*r = 0. What is r?
2/9, 1/3
Let g(a) be the third derivative of -a**5/60 + a**4/8 - a**3/3 - a**2 - 7*a. Find t such that g(t) = 0.
1, 2
Let d(x) = 2*x + 14. Let s be d(-7). Factor -2/7*t**4 + 0*t**2 + 0*t - 2/7*t**3 + s.
-2*t**3*(t + 1)/7
Let c(b) be the third derivative of -b**6/210 + b**5/105 + b**4/42 - 2*b**3/21 + 13*b**2. Let c(m) = 0. What is m?
-1, 1
Factor 24*o**3 + 4*o - 8*o - 4*o**3 - o + 15*o**2.
5*o*(o + 1)*(4*o - 1)
Suppose -28*w + 4 + 33*w - 1 - 7*w**2 - 1 = 0. What is w?
-2/7, 1
Let k(g) be the third derivative of g**7/140 - g**6/40 - 3*g**5/40 + g**4/4 - g**3/2 - 4*g**2. Let l(s) be the first derivative of k(s). Factor l(o).
3*(o - 2)*(o + 1)*(2*o - 1)
Let p(m) be the first derivative of 0*m + 1/24*m**4 - 2*m**2 - 1/60*m**5 + 2 + 0*m**3. Let b(n) be the second derivative of p(n). Determine f so that b(f) = 0.
0, 1
Determine i, given that -2/11*i + 2/11*i**2 - 4/11 = 0.
-1, 2
Let p(r) be the third derivative of -r**7/5040 + r**6/1440 - r**4/24 - 3*r**2. Let g(b) be the second derivative of p(b). Suppose g(l) = 0. What is l?
0, 1
Let n(i) be the second derivative of i**5/20 + i**4/2 + i**2 - 2*i. Let u be n(-6). Solve -o**u - o**4 - 2*o**5 - 2*o**3 - o**2 + 3*o**2 + 4*o**5 = 0 for o.
-1, 0, 1/2, 1
Let t be (3/2)/(-1*(-3)/6). Let n(x) be the third derivative of 0*x**4 - 1/140*x**7 + 1/480*x**6 + 0*x + 0*x**t - x**2 + 0 + 1/240*x**5. Factor n(m).
-m**2*(2*m - 1)*(3*m + 1)/4
Let a(x) be the first derivative of -x**5/2 + x**4 + 2*x**3/3 - 1. Suppose a(h) = 0. What is h?
-2/5, 0, 2
Let a(z) be the first derivative of -6/5*z**4 + 0*z + 2 - 3/10*z**2 + 12/25*z**5 + z**3. Suppose a(w) = 0. Calculate w.
0, 1/2, 1
Suppose -3 = o, -3*o + 0*o + 3 = 4*p. Suppose 2*r**5 - 3*r**5 - 8*r + 7*r + 2*r**p = 0. What is r?
-1, 0, 1
Let f(u) = 7*u**3 - 6*u**2 + 7*u + 4. Let a(y) = y**3 + y + 1. Let o(h) = -4*a(h) + f(h). What is d in o(d) = 0?
0, 1
Suppose 0*n - 4*n = 0. Suppose n = -5*i + 10 + 5. Determine z, given that 1/4*z**4 - 1 - 5/4*z**i + 1/4*z**5 - 1/4*z**2 + 2*z = 0.
-2, 1
Let l(d) be the third derivative of -1/84*d**4 - 2*d**2 + 0*d - 2/21*d**3 + 1/420*d**6 + 1/105*d**5 + 0. Factor l(c).
2*(c - 1)*(c + 1)*(c + 2)/7
Let c(g) be the third derivative of 5*g**8/112 - 6*g**7/35 + g**6/10 + g**5/2 - 9*g**4/8 + g**3 - 2*g**2. Factor c(l).
3*(l - 1)**3*(l + 1)*(5*l - 2)
Let v be (-4)/(-1)*5/10. Solve -2*a**3 + 2*a**3 - a**3 - a - 2*a**v = 0.
-1, 0
What is j in -8/7*j + 0 - 4/7*j**2 = 0?
-2, 0
Let o(q) be the first derivative of -q**4/4 - q**3/3 + q**2/2 + q + 4. Factor o(c).
-(c - 1)*(c + 1)**2
Let w(v) = v**3 + 3*v**2 - v. Let p be w(-3). Let d = 939 + -939. What is m in d - 2/7*m**2 + 0*m + 2/7*m**p = 0?
0, 1
Let h(p) be the first derivative of -p**2 + 0*p**3 - 1 - 1/60*p**6 + 0*p**4 + 0*p**5 + 0*p + 1/105*p**7. Let s(w) be the second derivative of h(w). Factor s(l).
2*l**3*(l - 1)
Let m(z) be the third derivative of 0 + 1/120*z**6 - 1/30*z**5 + 1/24*z**4 + 0*z + 0*z**3 + 3*z**2. Determine h, given that m(h) = 0.
0, 1
Let i(r) be the first derivative of -3*r**5/20 - r**4/4 - 2*r + 2. Let q(l) be the first derivative of i(l). Factor q(c).
-3*c**2*(c + 1)
Solve -4*m**2 - 20*m + 15 + 6*m**2 + 3*m**2 = 0 for m.
1, 3
Solve 8/11*m + 1/11*m**2 + 16/11 = 0.
-4
Let t = 240 - 238. Factor 1/3 - 1/3*b**3 - 1/3*b**t + 1/3*b.
-(b - 1)*(b + 1)**2/3
Let m be 1 + 4/(-3) + (-640)/(-300). Factor 1/5 + m*g**2 + 6/5*g.
(3*g + 1)**2/5
Suppose -3*q = -w, 0*w = -4*w + 3*q + 18. Let d(y) be the first derivative of 4/3*y**3 + y**2 + 0*y**4 - 1/3*y**w + 2 + 0*y - 4/5*y**5. Factor d(i).
-2*i*(i - 1)*(i + 1)**3
Factor -8/11 - 2/11*u**3 + 2/11*u**2 + 8/11*u.
-2*(u - 2)*(u - 1)*(u + 2)/11
Let k be -14*8/(-28)*1. Determine b so that 8/7*b**3 + 8/7*b + 2/7 + 2/7*b**k + 12/7*b**2 = 0.
-1
Let o(x) be the first derivative of x**6/40 + 13*x**5/80 + x**4/3 + x**3/6 + x + 1. Let m(g) be the first derivative of o(g). Factor m(w).
w*(w + 2)**2*(3*w + 1)/4
Let s be (-66)/10 + 2/(-5). Let h(z) = z**2 + 6*z - 7. Let m(c) = -5*c + 91 - 4*c**2 + 3*c**2 - 85. Let y(w) = s*m(w) - 6*h(w). Factor y(u).
u*(u - 1)
Let l(x) = 13*x**3 - 3*x**2 - 27*x + 32. Let z(p) = 20*p**3 - 4*p**2 - 40*p + 48. Let w(o) = -8*l(o) + 5*z(o). Determine y, given that w(y) = 0.
-2, 1, 2
Let a(d) be the first derivative of -d**3/9 - 5*d**2/6 - 2*d + 3. Suppose a(r) = 0. Calculate r.
-3, -2
Factor -3 + 2*n**3 - 12*n**2 + 9*n + 1 + n**3 + 2*n**3.
(n - 1)**2*(5*n - 2)
Factor -27/5*c - 9/5*c**2 - 27/5 - 1/5*c**3.
-(c + 3)**3/5
Let x(o) be the second derivative of o**10/7560 - o**9/3780 - o**8/1680 + o**7/630 - 5*o**4/12 + 2*o. Let v(p) be the third derivative of x(p). Solve v(r) = 0.
-1, 0, 1
Let m(k) be the second derivative of 1/6*k**4 + 0*k**3 + 0*k**2 + 3*k + 1/10*k**5 + 0. Factor m(d).
2*d**2*(d + 1)
Suppose 0 = -3*f + 4*z + 26, z + 0 = -2. Let t be 3/9 - (-16)/f. Factor -1 + 5*s**2 - t*s**2 - s**2.
(s - 1)*(s + 1)
Let d be 205/195 - 1/2. Let u = d + 3/26. Factor 10/3*h**4 + 2/3 - u*h**5 + 20/3*h**2 - 20/3*h**3 - 10/3*h.
-2*(h - 1)**5/3
Let k(o) be the third derivative of -o**8/47040 + o**7/11760 + o**5/20 + 7*o**2. Let f(p) be the third derivative of k(p). Factor f(n).
-3*n*(n - 1)/7
Let l(u) be the first derivative of -2/3*u**6 + 18/5*u**5 - 6*u**2 + 5 + 2*u - 8*u**4 + 28/3*u**3. Let l(z) = 0. Calculate z.
1/2, 1
Let y(x) be the first derivative of -x**4/8 + x**2/4 + 8. Suppose y(c) = 0. What is c?
-1, 0, 1
Let m(v) be the third derivative of -v**8/33600 - v**7/8400 + v**6/600 - v**5/15 - 4*v**2. Let z(j) be the third derivative of m(j). Find q such that z(q) = 0.
-2, 1
Solve 4/5*m - 6/5*m**3 - 2/5*m**4 + 2/5*m**5 + 0 + 2/5*m**2 = 0 for m.
-1, 0, 1, 2
Suppose -13 = o + 5*h + 5, o - h - 6 = 0. Factor -p**2 - 3*p**2 + 3*p**2 + 0*p**o - p.
-p*(p + 1)
Suppose 4*l**4 - 21*l**3 + 14*l**3 + 11*l**3 = 0. Calculate l.
-1, 0
Let p(f) be the second derivative of 0*f**2 + 1/15*f**3 - 1/30*f**4 + 0 - 9*f. Factor p(s).
-2*s*(s - 1)/5
Let k(l) = -12*l - 3. Let z be k(-3). Factor 0*b - 5*b - b - 12*b**3 - 15*b**3 + z*b**2.
-3*b*(b - 1)*(9*b - 2)
Let -10 + 5*a**2 - 15*a - 20 + 6*a - 16*a = 0. Calculate a.
-1, 6
Factor 4/3*r**2 + 0 - 4/3*r.
4*r*(r - 1)/3
What is x in 1/2*x**2 + 1/6*x**5 + 0 - 1/3*x - 1/2*x**4 + 1/6*x**3 = 0?
-1, 0, 1, 2
Let y = 652 - 9776/15. Let r(c) be the second derivative of -1/5*c**4 - 1/5*c**2 + 0 - 2/25*c**5 + 2*c - 1/75*c**6 - y*c**3. Factor r(a).
-2*(a + 1)**4/5
Let i(k) be the second derivative of -1/5*k**2 - 8/15*k**3 - 8/15*k**4 + 0 - k. Determine u so that i(u) = 0.
-1/4
Let n(o) be the second derivative of -1/18*o**3 - 3*o + 0 - 1/6*o**2 + 1/36*o**4 + 1/60*o**5. What is x in n(x) = 0?
-1, 1
Let m(s) be the first derivative of -3*s**6/4 + 17*s**5/5 - 23*s**4/4 + 4*s**3 - s**2/4 - s + 3. Factor m(g).
-(g - 1)**4*(9*g + 2)/2
Let m(k) = k**3 - 3*k**2 + 5*k - 4. Let a be 1 - ((2 - 3) + 0). Let h be m(a). Factor -1/5*c**4 + 0*c**h + 1/5*c**3 + 0 + 0*c.
-c