*t**2 + d*t**3 - 1/2*t.
t*(t + 1)*(4*t - 1)/2
Let z(r) = 5*r**3 - 7*r**2 + 3*r + 3. Suppose 0 = 6*j - j + 25. Let w(b) = 13*b**2 - 5 + b**3 - 5*b - 13*b**3 + 3*b**3. Let g(s) = j*z(s) - 3*w(s). Factor g(h).
2*h**2*(h - 2)
Determine v, given that 0 + 0*v**3 + 5/2*v**2 - 5/2*v**4 + 0*v = 0.
-1, 0, 1
Let l = 23 + -21. Let s(d) be the first derivative of 0*d + 2 + 0*d**l - 2/15*d**3. Let s(j) = 0. What is j?
0
Let k(v) be the third derivative of -v**8/84 + 2*v**7/21 - v**6/3 + 2*v**5/3 - 5*v**4/6 + 2*v**3/3 - 4*v**2. Factor k(q).
-4*(q - 1)**5
Let v(p) be the second derivative of p**6/360 + p**5/60 + p**4/24 + p**3 + p. Let u(a) be the second derivative of v(a). Suppose u(i) = 0. What is i?
-1
Suppose -3*l + 8*l + 5*i - 15 = 0, -5*l - 4*i + 15 = 0. Factor 2/9*p**l - 2/9*p + 0 + 0*p**2.
2*p*(p - 1)*(p + 1)/9
Let p(w) = 47*w**4 + 25*w**3 - 7*w**2 + 5*w. Let k(u) = 165*u**4 + 87*u**3 - 24*u**2 + 18*u. Let j(t) = -5*k(t) + 18*p(t). Suppose j(o) = 0. What is o?
-1, 0, 2/7
Let a(v) = 4*v. Let h be a(1). Suppose x**4 - x**4 + 13*x**3 - 12*x**3 - x**h = 0. Calculate x.
0, 1
Let z = -12 - -21. Let u = z - 7. Factor 2/5*c**u + 2/5*c + 0.
2*c*(c + 1)/5
Let a = 398/981 - 20/109. Factor 0*w + a*w**2 + 0.
2*w**2/9
Find c, given that 0 + 1/4*c**5 + 0*c - 1/2*c**4 + 0*c**2 + 1/4*c**3 = 0.
0, 1
What is i in -32/7 - 16/7*i - 2/7*i**2 = 0?
-4
Let z(w) = 13*w**2 - 9*w + 9. Let y(u) = -6*u**2 + 4*u - 4. Let k be (3 - 1 - 3)*9. Let x(q) = k*y(q) - 4*z(q). Suppose x(v) = 0. What is v?
0
Let b(f) be the third derivative of 3*f**2 + 0*f**3 + 0 + 0*f - 1/54*f**4 + 1/270*f**5. Factor b(l).
2*l*(l - 2)/9
Let p(l) be the first derivative of -l**7/3360 - l**6/480 - l**5/240 + 2*l**3/3 + 5. Let q(n) be the third derivative of p(n). Factor q(i).
-i*(i + 1)*(i + 2)/4
Let d(i) be the second derivative of i**8/840 - i**6/180 + i**3/3 - i. Let q(w) be the second derivative of d(w). Suppose q(p) = 0. Calculate p.
-1, 0, 1
Suppose 0 + 0*t + 0*t**2 - 3/5*t**3 - 3/5*t**4 = 0. Calculate t.
-1, 0
Let x(y) = 10*y + 65. Let n be x(-6). Factor 2/5 + 32/5*t**3 + 18/5*t**4 + 12/5*t + 28/5*t**2 + 4/5*t**n.
2*(t + 1)**4*(2*t + 1)/5
Let k(c) = -c - 2. Let z be k(-5). What is h in 23*h**3 - 37*h**4 + 53*h**4 + 2*h**5 + 9*h**z = 0?
-4, 0
Let m = -1/42 - -32/21. Factor -3/4*a**2 - m*a + 3/4*a**3 + 0.
3*a*(a - 2)*(a + 1)/4
Let m(g) be the first derivative of g**4/16 + g**3/3 + 3*g**2/8 - 16. Solve m(i) = 0.
-3, -1, 0
Let j = 20 + -10. Suppose 2*u + 7 = 3*i - j, -2*u = 3*i - 1. Factor 2*k**2 + 2*k**3 - 4*k**i - k**4 - k**5 + k - 1 + 2*k**5.
(k - 1)**3*(k + 1)**2
Factor 16/3*p**3 + 10/3*p**4 + 2/3*p**2 - 4/3*p + 0.
2*p*(p + 1)**2*(5*p - 2)/3
Let o(x) be the first derivative of -x**9/4032 + x**8/2240 + x**7/1120 - x**6/480 + 4*x**3/3 - 4. Let a(w) be the third derivative of o(w). Factor a(q).
-3*q**2*(q - 1)**2*(q + 1)/4
Let a = -14/37 + 274/333. Factor 14/9*q**3 - 32/9*q**2 + 22/9*q - a.
2*(q - 1)**2*(7*q - 2)/9
Let v be (-10)/(-45) - (0 + 0). Factor 0 - v*n**3 + 4/9*n + 2/9*n**2.
-2*n*(n - 2)*(n + 1)/9
Let k be 4 - 6 - -5 - (-12)/(-5). Factor -6/5 - 3/5*n + k*n**2.
3*(n - 2)*(n + 1)/5
Let c(m) = -m**2 - 6*m + 9. Let o be c(-7). Factor 2 - 5 + p**2 + 0 - o*p + 4.
(p - 1)**2
Let r(p) = -4 - 17*p**2 - 18*p**4 - 7 + 20*p**3 - 7*p**3. Let v(f) = -6*f**4 + 4*f**3 - 6*f**2 - 4. Let c(x) = 4*r(x) - 11*v(x). Solve c(l) = 0 for l.
0, 1/3, 1
Let q(d) be the third derivative of -5*d**8/336 - 2*d**7/35 + d**6/120 + d**5/5 + d**4/6 + d**2. Find v, given that q(v) = 0.
-2, -1, -2/5, 0, 1
Let c(p) = -3*p**3 - 3*p**2 + 6*p - 6. Let l(t) = 6*t**3 + 6*t**2 - 12*t + 13. Let d(f) = -13*c(f) - 6*l(f). Find b such that d(b) = 0.
-2, 0, 1
Let t(z) be the third derivative of 0 - 7/540*z**6 + 0*z**3 - 1/54*z**4 + 2*z**2 + 0*z - 1/30*z**5. Determine l, given that t(l) = 0.
-1, -2/7, 0
Let k(i) = -2*i - 10*i + i**2 + i. Let g be k(11). Factor 0*d + 1/2*d**2 + g.
d**2/2
Suppose -7*j - 16 = -2*o - 5*j, -4*o + 24 = -2*j. Let 0*u**3 + 0 - 2/9*u**5 + 2/9*u**o + 0*u**2 + 0*u = 0. Calculate u.
0, 1
Let u be 12/8 - (-6)/4. Suppose 4*g - 2*o = -4, -3*o - u = -3*g - 9. Find i, given that 1/2*i**4 - 1/2*i**2 + 1/2*i + g - 1/2*i**3 = 0.
-1, 0, 1
Let b be 6 + -2 - (-3 + 5). Suppose 0*p + 3*p - p + b*p**2 = 0. What is p?
-1, 0
Let g(d) be the third derivative of d**5/180 + d**4/36 - 2*d**2. Solve g(c) = 0 for c.
-2, 0
Let s = 139067/10535 - 1/2107. Let 156/5*t**3 + 27/5*t + 9/5*t**5 - 126/5*t**2 + 0 - s*t**4 = 0. What is t?
0, 1/3, 1, 3
Let f(z) be the second derivative of z**6/165 + 2*z**5/55 + 2*z**4/33 + 3*z. Factor f(r).
2*r**2*(r + 2)**2/11
Suppose -9*l = -0*l. Suppose -3/2*z**2 + l*z + 3/2 = 0. What is z?
-1, 1
Let n be 4/(-3 + 2)*-1. Let h(x) be the second derivative of -1/40*x**5 + 1/120*x**6 - 2*x - 1/8*x**2 + 0 + 1/12*x**3 + 0*x**n. Factor h(c).
(c - 1)**3*(c + 1)/4
Let n(v) = v**2 + 15*v + 29. Let q be n(-13). Factor 10/3*r + 2/3*r**q - 4/3 - 8/3*r**2.
2*(r - 2)*(r - 1)**2/3
Let 2/3*n**3 + 7*n**4 + 52/3*n**5 + 0*n + 0 + 0*n**2 = 0. Calculate n.
-1/4, -2/13, 0
Let q(b) be the first derivative of -1 - 3/7*b**2 - 1/14*b**4 + 2/7*b + 2/7*b**3. Factor q(n).
-2*(n - 1)**3/7
Let t(r) = 7*r**2 - 7*r. Let w(p) = -6*p**2 + 6*p. Let b = -3 - 2. Let j be ((-8)/10)/(2/10). Let v(m) = b*w(m) + j*t(m). Factor v(o).
2*o*(o - 1)
Suppose -o = 2*o - 9. Suppose -13*u**2 + u + 2*u**5 + 11*u**o + 6*u**2 + 2*u**5 - 13*u**4 + 4*u**3 = 0. Calculate u.
0, 1/4, 1
Let a be 16/14 + 14/(-98). Let y be 22/14 - (a - 0). Let -2/7 + y*q - 2/7*q**2 = 0. What is q?
1
Let y(m) = 2*m**2 + 1. Let i be y(-1). Let u = 7 - i. Solve 3*z + u - 6 - 2*z**2 + z**2 = 0.
1, 2
Suppose 12 = -5*p + 5*b - 3, p + 4*b = 7. Let r(v) be the first derivative of -v + 6. Let a(o) = -3*o**2 + 12*o - 15. Let s(j) = p*a(j) + 3*r(j). Factor s(h).
3*(h - 2)**2
Let a be 9/(-21) + (-96)/(-28). Suppose -a = -2*t + 1. Solve 0 + 3/2*i**3 - 1/2*i - i**t = 0.
-1/3, 0, 1
Let u be (2/(-33))/(9/6 + -2). Let r(g) be the first derivative of u*g**3 + 1/11*g**2 + 0*g + 1 + 1/22*g**4. Let r(a) = 0. Calculate a.
-1, 0
Factor 8/15*j**2 - 2/15*j**3 - 8/15*j + 0.
-2*j*(j - 2)**2/15
Let t(p) = -p**2 + 3*p**2 - 3*p**2 + 2 + 4*p. Let u be t(4). Solve 0 - 65*h**3 + 225/2*h**4 - 2*h**u + 4*h = 0.
-2/9, 0, 2/5
Let u = 33 + -19. Suppose -3*o + 1 = -u. Factor -2*y**3 - o*y**3 - 4 + 3*y**2 - 8*y**2 + 16*y.
-(y - 1)*(y + 2)*(7*y - 2)
Factor 2*b**3 - b**3 - 9*b + 2 + 6*b.
(b - 1)**2*(b + 2)
Let v be (6/5)/(6/20). Let w(y) be the second derivative of 0 + 0*y**3 + 1/12*y**v + 2*y - 1/2*y**2. Determine m so that w(m) = 0.
-1, 1
Suppose 3*h - 16 + 1 = 0. Suppose -h*d + 2*w - 15 = -w, 0 = -2*w + 10. Factor d + 2/5*q + 6/5*q**3 + 8/5*q**2.
2*q*(q + 1)*(3*q + 1)/5
Let o be ((-5)/10)/(2/(-64)*6). Factor -2*c**3 + o*c + 0*c**2 + 2/3*c**4 + 0.
2*c*(c - 2)**2*(c + 1)/3
Let s(i) be the third derivative of -1/1050*i**7 + 0*i**3 - 1/300*i**6 + 0*i**4 + 0 - 1/300*i**5 - 4*i**2 + 0*i. Solve s(r) = 0 for r.
-1, 0
Suppose 2/9 - 4/9*c + 2/9*c**2 = 0. Calculate c.
1
Let l be 6/4*(-16)/(-12). Factor m**2 + m - 3*m - 1 - m**3 - l*m + 5*m.
-(m - 1)**2*(m + 1)
Let b = 113/348 + 1/116. Let g(z) be the third derivative of 0*z + b*z**3 + 5/8*z**4 + 0 + 2/5*z**5 - z**2 - 2/15*z**6. Factor g(h).
-(h - 2)*(4*h + 1)**2
Let y be 12/16*(3 - -1). Factor -16/3 - 8*p - 4*p**2 - 2/3*p**y.
-2*(p + 2)**3/3
Let x(f) be the second derivative of f**6/90 - f**5/12 + f**4/6 + 2*f**3/9 - 4*f**2/3 + 4*f. Find c, given that x(c) = 0.
-1, 2
Let h be (16/20)/(-2)*15. Let z(m) = m**3 + 8*m**2 + 11*m - 4. Let g be z(h). Factor 0*l - 1/3*l**5 + 2/3*l**4 + 0*l**g - 1/3*l**3 + 0.
-l**3*(l - 1)**2/3
Let s = 3 - -5. Let c = s - 8. Factor 0*i**2 + 2/5*i**4 + 0 + c*i - 2/5*i**3.
2*i**3*(i - 1)/5
Let h(o) be the third derivative of 6*o**2 + 1/300*o**6 - 1/30*o**5 + 7/60*o**4 + 0*o + 0 - 1/5*o**3. Factor h(r).
2*(r - 3)*(r - 1)**2/5
Let f(g) be the third derivative of 1/6*g**4 + 1/105*g**7 + 1/20*g**6 - 4*g**2 - 1/168*g**8 + 0*g + 0 + 0*g**3 - 1/6*g**5. Find c, given that f(c) = 0.
-2, 0, 1
Let x(y) = y**2 - y. Let t(u) = -4*u**3 - 8*u**2 + 20*u. Let k(j) = t(j) + 12*x(j). Determine p, given that k(p) = 0.
-1, 0, 2
Let l be (3312/80)/(3/10). Let s = l - 684/5. Find b, given that 0 + 3/5*b**2 - s*b = 0.
0, 2
Suppose -2*a + 13 = 3. Let y(r) be the second derivative of -1/60*r**a -