2*f + 5 - t - 2*f**2 = 0.
-1, 2
Let o(v) = 2*v**3 - 2*v**2 + 2*v. Let t(x) be the third derivative of -x**6/24 + x**5/15 - 5*x**4/24 + x**2. Let z(k) = -14*o(k) - 6*t(k). Factor z(g).
2*g*(g + 1)**2
Let i(m) be the second derivative of 4*m - 1/15*m**4 + 1/30*m**3 + 0 + 0*m**2. Factor i(d).
-d*(4*d - 1)/5
Suppose -4*c + 6 = h, -2*h - 2*h = c - 9. Solve 11*l**2 + 2*l**3 + 4 + 12*l + l**h + 2*l**3 = 0 for l.
-1
Let r(n) be the second derivative of 0 - n - 1/40*n**5 + 1/2*n**4 - 1/4*n**6 + 1/3*n**3 + 0*n**2. Find m such that r(m) = 0.
-2/3, -2/5, 0, 1
Let c(b) be the second derivative of -b**4/14 - 9*b**3/14 + 15*b**2/14 - 34*b. Factor c(s).
-3*(s + 5)*(2*s - 1)/7
Let i be (-189)/(-1176) - (-1)/8. Solve i*u**3 + 0*u**2 - 4/7*u**4 + 0 + 0*u + 2/7*u**5 = 0.
0, 1
Let b be (-1)/3 - 3/(-9). Suppose -2*t + 2*q + 2*q + 16 = b, -2*q = -5*t + 8. Factor 2*r**3 + 0*r**3 + t*r**3.
2*r**3
Let v(q) be the first derivative of -2*q**3/15 - 3*q**2/5 - 4*q/5 + 3. Factor v(r).
-2*(r + 1)*(r + 2)/5
Factor 2*w**3 - 1/2*w**5 + 0*w**4 + 0 + 0*w**2 + 0*w.
-w**3*(w - 2)*(w + 2)/2
Let p(m) = 8*m + 4. Let k(r) = -r - 1. Let h(l) = 6*k(l) + p(l). Let n be h(1). Let 2/3*i**2 - 1/3*i - 1/3*i**3 + n = 0. What is i?
0, 1
Let c(i) = -3*i**3 + 6*i**2 - 3*i + 4. Let n(w) = -2*w**3 + 5*w**2 - 2*w + 3. Let r be 1/3*(13 + -1). Let j(o) = r*n(o) - 3*c(o). Factor j(v).
v*(v + 1)**2
Factor h + 1554*h**2 + 2 - h**4 + 3*h**3 - 1557*h**2 - 2.
-h*(h - 1)**3
Suppose 3*w + 6 = 3*y, 0 = w - 4*y + 2 + 12. Let -26/7*i**4 + w*i - 36/7*i**2 - 2/7 + 6/7*i**5 + 44/7*i**3 = 0. Calculate i.
1/3, 1
Let j be (-9)/(81/(-12))*12. Suppose 4*w = 4*f + j, f + 0*f = -4*w + 11. Factor 0 - s**2 + s + 1/4*s**w.
s*(s - 2)**2/4
Let w(d) be the second derivative of -d**7/84 - d**6/60 + 4*d. Factor w(p).
-p**4*(p + 1)/2
Suppose 3*l - 4 = -1. Suppose l - 21 = -5*q. Let 1/3*s**3 + 1/3*s - 8*s**q + 0 + 2*s**2 + 16/3*s**5 = 0. What is s?
-1/4, 0, 1
Suppose -v - 4*v + 15 = 0. Let n be (4/12)/(v/2). Factor 2/3*w**4 + 2/9*w**5 + n*w**2 + 0*w + 2/3*w**3 + 0.
2*w**2*(w + 1)**3/9
Suppose 4*o - 17 = 7. Let v(t) be the third derivative of 0*t + 0 + 0*t**o + 0*t**3 + 0*t**5 - t**2 + 0*t**4 - 1/525*t**7. Suppose v(h) = 0. Calculate h.
0
Suppose 2 + k**3 - 5*k + k**2 - 4*k**4 - k**4 + 4*k**3 + 2*k**4 = 0. Calculate k.
-1, 2/3, 1
Let o(h) be the second derivative of -4/3*h**2 + 0 + 4/3*h**3 - 9*h + 1/10*h**5 - 11/18*h**4. Factor o(f).
2*(f - 2)*(f - 1)*(3*f - 2)/3
Let p(u) be the second derivative of 0 + 1/12*u**5 + 11/36*u**4 + 5*u + 7/18*u**3 + 1/6*u**2. Factor p(q).
(q + 1)**2*(5*q + 1)/3
Suppose 2*x - 3 = 3*p - 2*p, x = 3*p + 9. Factor -1/2*q + x - 1/2*q**2.
-q*(q + 1)/2
Let h be (-758)/(-12) + 1/3. Let k = -62 + h. Find x, given that k*x - 1/2 + 2*x**2 = 0.
-1, 1/4
Let l(p) be the second derivative of -p**5/4 + 5*p**4/6 - 5*p**3/6 + 5*p. Determine w, given that l(w) = 0.
0, 1
Let s(u) = u**5 - 17*u**4 - 7*u**3 - 4*u**2 + 5. Let b(p) = -2*p**5 + 18*p**4 + 6*p**3 + 4*p**2 - 6. Let o(a) = -5*b(a) - 6*s(a). What is m in o(m) = 0?
-1, 0
Let r be (-4)/(-6) - 2/3. Suppose -4*a + 2 = 2*d, r*d - 6 = 3*a + 3*d. Suppose 6 + 3*v**a + 2 - 16*v + 10*v**2 - 5*v**3 = 0. What is v?
1, 2
Let v(o) be the third derivative of -o**5/240 + o**4/32 + 7*o**2. Determine k so that v(k) = 0.
0, 3
Let g(m) be the first derivative of 1/11*m**4 + 0*m + 14/55*m**5 - 4/33*m**6 + 0*m**3 + 0*m**2 - 4. Factor g(j).
-2*j**3*(j - 2)*(4*j + 1)/11
What is n in 4/23 + 4/23*n**4 - 8/23*n**2 - 4/23*n**3 + 2/23*n + 2/23*n**5 = 0?
-2, -1, 1
Let f**3 - 3/4*f - 1/4*f**5 - 1/2 + 0*f**4 + 1/2*f**2 = 0. Calculate f.
-1, 1, 2
Suppose 0 = -2*f - 0*f - x + 1, 2*x = 5*f - 16. Suppose 7*l - 4*u = f*l + 15, -2*l = 2*u - 6. Factor 1/3*k**5 + 0 - 1/3*k**2 + 0*k + 1/3*k**4 - 1/3*k**l.
k**2*(k - 1)*(k + 1)**2/3
Let i(b) be the third derivative of 1/40*b**6 + 1/2*b**4 + 2/3*b**3 + 0 + 11/60*b**5 + 0*b - b**2. Factor i(a).
(a + 1)*(a + 2)*(3*a + 2)
Let r(q) be the second derivative of q**7/105 - q**5/25 + q**3/15 - 18*q. Solve r(c) = 0.
-1, 0, 1
Let s be (-26)/(-3) + 4/(-6). Suppose 4*z + b - s = -4*b, 0 = -3*b. Factor 0*d**5 + 11*d**4 + 3*d**2 - 4*d**5 - z*d**4 + 7*d**5 + 9*d**3.
3*d**2*(d + 1)**3
Let h(t) be the second derivative of 2/21*t**3 - 6/35*t**5 + 0 + 0*t**2 - 5/42*t**4 + 2*t. Find v such that h(v) = 0.
-2/3, 0, 1/4
Let n(v) be the third derivative of 0*v + 2*v**2 - 1/9*v**3 - 1/54*v**4 + 1/270*v**5 + 0. Factor n(h).
2*(h - 3)*(h + 1)/9
Let o(c) be the third derivative of -c**8/5880 + c**7/735 - c**6/252 + c**5/210 - 7*c**3/6 + 2*c**2. Let q(m) be the first derivative of o(m). Factor q(r).
-2*r*(r - 2)*(r - 1)**2/7
Let h(j) be the second derivative of 9*j**6/20 + 21*j**5/40 - 11*j**4/8 - 7*j**3/4 + 3*j**2/2 - 12*j. Let h(n) = 0. Calculate n.
-1, 2/9, 1
Let p(v) be the first derivative of v**8/1344 - v**7/280 + v**6/160 - v**5/240 + 2*v**2 - 5. Let s(r) be the second derivative of p(r). Factor s(i).
i**2*(i - 1)**3/4
Let c(p) = -12*p. Let j be 3/(-3)*(-3 + 6). Let r(a) = -a**2 + 23*a. Let y(i) = j*r(i) - 5*c(i). What is l in y(l) = 0?
0, 3
Suppose -48/7*n - 288/7 - 2/7*n**2 = 0. What is n?
-12
Let g(w) be the first derivative of -w**3/3 - w**2/2 + 2. Find t, given that g(t) = 0.
-1, 0
Let h(b) be the second derivative of 4*b**7/105 - 28*b**6/75 + 21*b**5/50 + 11*b**4/15 - 5*b**3/3 + 6*b**2/5 + 21*b. Suppose h(d) = 0. What is d?
-1, 1/2, 1, 6
Suppose 0 = -3*w + 5*w - 90. Let a be 1/5 + 21/w. Find y, given that 0*y**4 - 2/3*y**5 + a*y**3 + 0 + 0*y + 0*y**2 = 0.
-1, 0, 1
Let t be ((-3)/4)/(9/(-4)). Let h(w) be the third derivative of t*w**3 + 1/4*w**4 - 3*w**2 + 0*w + 1/10*w**5 + 1/60*w**6 + 0. Suppose h(i) = 0. Calculate i.
-1
Let g be (-2 - (-2 - -1)) + 0. Let a(p) = -p**3 - p**2 - p - 1. Let w be a(g). Factor w*x + x**2 + 8*x**3 + 2*x + 9*x**2.
2*x*(x + 1)*(4*x + 1)
Let c = -1/54 + 14/27. Determine y so that c + 1/4*y**2 - 3/4*y = 0.
1, 2
Find t, given that 10*t - 1 + 81/4*t**3 - 117/4*t**2 = 0.
2/9, 1
Suppose -2*j = -j + 2*v + 8, 0 = 4*j + 4*v + 16. Factor 9*i**2 + j*i**3 + 2*i**3 - 13*i**2.
2*i**2*(i - 2)
Factor 0*a**3 + 0 + 8/7*a**4 - 6/7*a**2 - 2/7*a.
2*a*(a - 1)*(2*a + 1)**2/7
Let n be ((-11)/2)/((-2)/4). Let m = n - 9. Factor 0*v**m - 2/9 + 2/9*v**4 + 4/9*v - 4/9*v**3.
2*(v - 1)**3*(v + 1)/9
Suppose n = -3*n + 2*b + 8, 2*n = -5*b + 4. Factor i**n + 1 + 1 - 2 - i**4.
-i**2*(i - 1)*(i + 1)
Let q(v) be the second derivative of -v**4/60 + 11*v**3/30 - v**2 - 19*v. Let q(g) = 0. Calculate g.
1, 10
Let l(g) be the third derivative of -1/16*g**4 + 8*g**2 + 1/40*g**5 + 0 + 0*g + 0*g**3. Find s such that l(s) = 0.
0, 1
Factor -7*p**2 + 16*p**3 - 13*p**3 + 3*p + p**2.
3*p*(p - 1)**2
Suppose -3*g - m + 4*m - 153 = 0, -g - 71 = -5*m. Let c be -3 + 3/((-42)/g). Factor -c*w**5 + 0*w**3 + 0*w**2 + 0*w + 0 + 2/7*w**4.
-2*w**4*(w - 1)/7
Suppose 65 = 4*c + 5*n, 0*n - 29 = -2*c + n. Let l = 19 - c. Determine i, given that 2/7*i**l - 2/7*i - 2/7*i**2 + 2/7*i**3 + 0 = 0.
-1, 0, 1
Let s(p) be the first derivative of 2*p**5/65 + p**4/13 - 2*p**2/13 - 2*p/13 - 6. Factor s(c).
2*(c - 1)*(c + 1)**3/13
Let h(u) = -u - 1. Let o be h(-3). Let t be 2/10 - (-57)/15. Factor 2*k + 2*k**2 + 2*k - t - 3*k**o.
-(k - 2)**2
Let y(g) be the second derivative of g**9/60480 + g**8/13440 - g**6/1440 - g**5/480 + g**4/2 - 9*g. Let v(z) be the third derivative of y(z). Factor v(b).
(b - 1)*(b + 1)**3/4
Let q(c) be the third derivative of c**9/12096 - c**8/3360 - c**7/2520 - 5*c**4/24 + 2*c**2. Let y(u) be the second derivative of q(u). Factor y(v).
v**2*(v - 2)*(5*v + 2)/4
Suppose 8 = -2*b, h + 3*b + 14 = -b. Suppose h*d + 1/2*d**3 + 2*d**2 + 0 = 0. Calculate d.
-2, 0
Determine x, given that -2/5*x**3 + 2/5*x + 2/3*x**4 - 2/3*x**2 + 0 = 0.
-1, 0, 3/5, 1
Factor 5/3*u**3 + 1/6*u**4 + 16/3 + 6*u**2 + 28/3*u.
(u + 2)**3*(u + 4)/6
Let j(l) be the first derivative of -l**4/42 + 2*l**3/21 - 5. Factor j(f).
-2*f**2*(f - 3)/21
Let s(m) = 2*m**2 + 13*m + 1. Let n be s(-7). Find a such that n + 1/2*a**2 - 4*a = 0.
4
Let t(l) be the third derivative of l**6/30 - 2*l**5/15 - 2*l**4/3 + 16*l**3/3 + 11*l**2. Solve t(s) = 0.
-2, 2
Let b(d) = -d**3 + d. Let t(p) = 6*p**3 - 9*p**2 + 3*p. Let j(c) = 3*b(c) + t(c). Find k such that j(k) = 0.
0, 1, 2
Suppose -10*r + 3*r = 0. Let u(k) be the third derivative of r + 1/72*k**4 - 1/18*