
What is w in -3/7*w**3 - w**2 - 1/7 - 5/7*w = 0?
-1, -1/3
Let t(z) be the third derivative of -23/240*z**5 - 5/24*z**4 + 2*z**2 + 0 - 1/6*z**3 + 0*z - 7/480*z**6. What is c in t(c) = 0?
-2, -1, -2/7
Let b(r) = 8*r**2. Let u be b(1). Factor 2*z - 2*z**3 - 1 + 4*z**2 - 3*z**4 + 8*z**2 - u*z**2.
-(z - 1)*(z + 1)**2*(3*z - 1)
Let q(m) be the second derivative of m**8/840 + m**7/525 - m**6/300 - m**5/150 - 3*m**2/2 + 2*m. Let u(z) be the first derivative of q(z). Factor u(j).
2*j**2*(j - 1)*(j + 1)**2/5
Let a(v) be the third derivative of -v**7/2100 - v**6/900 + v**3/3 - 3*v**2. Let d(k) be the first derivative of a(k). Factor d(t).
-2*t**2*(t + 1)/5
Factor -3*d**4 - 14*d - 2*d**4 - 15*d**3 + 24*d + 5*d**5 + 5*d**2.
5*d*(d - 2)*(d - 1)*(d + 1)**2
Suppose 5*g = -4 + 14. Factor -2 - 13*s + 10*s - s**g + 0.
-(s + 1)*(s + 2)
Let y(s) = s**3 - 3*s**2 + s - 5. Let v(t) = t**3 - t**2 + t - 3. Let z(b) = -5*v(b) + 3*y(b). Suppose z(f) = 0. What is f?
-1, 0
Let a(w) = 0*w - 2*w**3 + 0*w - 3*w**2 + 0*w**2. Let u be a(-2). What is n in 0*n**2 + 0 - 1/4*n**u + 0*n + 1/4*n**5 + 0*n**3 = 0?
0, 1
Let u(b) = b**2 + b + 2. Let r be u(0). Suppose 0 = 2*i - 4, 0 = -n - n + r*i + 4. Factor n*m**3 + 4*m**2 - 4*m**3 - 2*m - 2*m**3.
-2*m*(m - 1)**2
Let g = 181/3480 - -2/87. Let r(s) be the second derivative of 0*s**2 + 1/168*s**7 + s + 1/12*s**4 + 0 + g*s**5 + 1/30*s**6 + 1/24*s**3. Factor r(n).
n*(n + 1)**4/4
Let y be (0/(-2) - (3 + -1)) + 2. Let p(q) be the second derivative of 1/40*q**5 + 0*q**3 + 0*q**4 + 1/60*q**6 + 0*q**2 + y - q. Suppose p(l) = 0. Calculate l.
-1, 0
Suppose 0 = -0*l + 2*l - 3*m - 8, 4*l + 24 = -4*m. Let g = 0 - l. Factor -8/9*n**4 + 0*n + 10/9*n**3 - 2/9*n**g + 0.
-2*n**2*(n - 1)*(4*n - 1)/9
Let r(f) = 3*f**2 + f + 1. Let d be r(-1). Find h, given that -14*h**3 - h - 27*h**4 - 10*h**d + 2*h**2 + 3*h**2 + 3*h = 0.
-1, -2/9, 0, 1/3
Let n(h) be the second derivative of -3*h - 1/60*h**4 - 1/10*h**2 - 1/15*h**3 + 0. Factor n(k).
-(k + 1)**2/5
Let p be (-16)/20*20/(-4). Factor 16*j**2 + 6*j**5 - 8*j**3 - 6*j**5 + 16*j + p*j**5 - 4*j**3 - 8*j**4.
4*j*(j - 2)**2*(j + 1)**2
Let 2/3*a**4 + 0 + 0*a + 0*a**3 + 2/3*a**5 + 0*a**2 = 0. What is a?
-1, 0
What is s in -1 - 5/6*s + 1/6*s**2 = 0?
-1, 6
Let o(b) = b**3 - b**2 - 1. Let a be o(2). Factor 0*n**3 - a*n**3 - n**2 - n**5 - 3*n**4 + 0*n**4.
-n**2*(n + 1)**3
Suppose 0 = 3*t - 4*x - 20, 13 = -5*t + 4*x + 41. What is y in 0*y + 0*y**2 - y**t + 0 + 1/3*y**3 = 0?
0, 1/3
Suppose 3*q + 2*b - 23 = -3*b, 3*q = 2*b + 16. Suppose -9*y = -0*y - 18. Factor 6*s - q*s + 2*s**y - 4*s.
2*s*(s - 2)
Let i = 122/525 + 4/75. Let c = -5 + 7. Factor -4/7*k - 2/7*k**c - i.
-2*(k + 1)**2/7
Factor 236*o**4 - 4*o**2 + 12*o - 240*o**4 + 13 - 12*o**3 - 5.
-4*(o - 1)*(o + 1)**2*(o + 2)
Let p(v) be the second derivative of v**4/42 - 22*v**3/21 - 72*v. Solve p(r) = 0.
0, 22
Let p = -24 + 0. Let r be p/(-10) - 4/10. Solve -2*y**3 + y**5 + y + 2*y**2 - 2*y**r = 0 for y.
-1, 0, 1
Let k be (2/(-4))/((-3)/30). Suppose -k - 5 = -2*z. Factor -f**3 + f + f**z + 0*f - f**3.
f*(f - 1)**2*(f + 1)**2
Let p(r) be the first derivative of -r**5/5 - 19*r**4/24 - 5*r**3/18 + 4*r**2/3 - 2*r/3 + 9. Suppose p(x) = 0. Calculate x.
-2, 1/3, 1/2
Let d(l) be the third derivative of -1/70*l**5 + 4/21*l**3 + 2*l**2 + 0*l + 0*l**4 + 0 - 1/420*l**6. Let d(u) = 0. What is u?
-2, 1
Let s be -3*(2 - 3) + -7. Let j be s/8*(-16)/12. Factor 0*k - j*k**3 + 2/3*k**2 + 0.
-2*k**2*(k - 1)/3
Let f(a) be the third derivative of a**9/4536 + a**8/3780 - a**7/3780 + 2*a**3/3 - 2*a**2. Let g(p) be the first derivative of f(p). Factor g(h).
2*h**3*(h + 1)*(3*h - 1)/9
Let x(h) be the first derivative of -h**6/15 + 2*h**4/5 + 4*h**3/15 - 3*h**2/5 - 4*h/5 - 5. Determine u so that x(u) = 0.
-1, 1, 2
Let a be 72/33 - (-8)/(-44). Factor 3/4*b**a - 1/4 - 1/2*b.
(b - 1)*(3*b + 1)/4
Let v(d) be the first derivative of d**4/16 - d**3/12 - d**2/8 + d/4 + 8. Determine n, given that v(n) = 0.
-1, 1
Let x(g) be the first derivative of g**2 + 0*g**3 + 0*g**4 - 1/60*g**6 + 0*g**5 + 4 + 0*g. Let r(z) be the second derivative of x(z). Solve r(u) = 0.
0
Let f(p) be the first derivative of 2*p**5/75 - p**4/5 + 8*p**3/15 - 8*p**2/15 + 2. Factor f(m).
2*m*(m - 2)**3/15
Let v(g) be the first derivative of -5*g**3/3 + 4*g**2 - 8*g - 3. Let c(w) = 3*w**2 - 5*w + 5. Let r(a) = -8*c(a) - 5*v(a). Factor r(b).
b**2
Let d(m) be the third derivative of m**5/210 - m**4/42 + m**3/21 + 10*m**2. Determine v so that d(v) = 0.
1
Let c(q) = 2*q + 1. Let v be 1/((-2)/(0 + -2)). Let h be c(v). Suppose 2*u - u**4 - 2*u**3 + 4*u**2 + u**4 + 3 - 4 - h*u**4 = 0. What is u?
-1, 1/3, 1
Let n(a) be the second derivative of a**3/6 + 9*a**2/2 + a. Let d be n(-9). Factor 0*r + d + 2/7*r**2 + 2/7*r**3.
2*r**2*(r + 1)/7
Let b be 1 + 63/(-12)*-2. Let y = b + -157/14. Factor 2/7*d**2 + 0 + y*d.
2*d*(d + 1)/7
Suppose 0 = -5*q - 52 + 2. Let w be q*((-7)/2)/7. Solve -4/3*s**w + 1/3*s**2 + 3*s**4 - 2*s**3 + 0 + 0*s = 0.
0, 1/4, 1
Factor -12*d**2 - 18*d + 0 - 3/2*d**3.
-3*d*(d + 2)*(d + 6)/2
Let a = -5 - -10. Let y be (-5)/a - (-10)/8. What is b in 1/4*b**2 + 0*b - y = 0?
-1, 1
Let l(i) be the third derivative of i**5/120 - i**4/48 - i**3/6 - 18*i**2. Determine z so that l(z) = 0.
-1, 2
Let h(p) = -9*p**2 + 24*p - 19. Let c(w) = 35*w**2 - 95*w + 75. Let z(r) = -4*c(r) - 15*h(r). Suppose z(v) = 0. What is v?
1, 3
Let q(w) = -w - 22. Let a be q(0). Let u = -19 - a. Factor -2/3*m**4 + 0 + 0*m + 0*m**u + 2/3*m**2.
-2*m**2*(m - 1)*(m + 1)/3
Let g be (-4 + (-102)/(-24))*20. Suppose -i + 4/3*i**3 - 2/3 - 1/3*i**g + 2/3*i**2 + 0*i**4 = 0. Calculate i.
-1, 1, 2
Let x(t) be the third derivative of t**6/420 + t**5/105 + t**4/84 - 6*t**2. Factor x(s).
2*s*(s + 1)**2/7
Let f(c) = c**3 + 12*c**2 + 8*c - 19. Let g be f(-11). Factor 16 - 6 - 2*l**3 + g*l**2 + 8 - 30*l.
-2*(l - 3)**2*(l - 1)
Let s(x) be the third derivative of x**7/6300 - x**6/1800 - x**4/12 + 3*x**2. Let f(w) be the second derivative of s(w). Factor f(t).
2*t*(t - 1)/5
Let v(j) = -j**3 + 3*j**2 - 6*j. Let m(l) = 2*l**3 - 6*l**2 + 11*l. Let u(d) = -4*m(d) - 7*v(d). Suppose u(z) = 0. What is z?
0, 1, 2
Let s be 2*((-2)/(-2))/1. Let k = -662 - -665. Find z, given that -2/9*z**k + 0 + 2/9*z**s + 0*z = 0.
0, 1
Let f = 855 - 853. Let 0 - 1/5*s - 1/5*s**f = 0. What is s?
-1, 0
Let 0*r**4 - 3*r**4 + 99 - 18*r**3 - 39*r**2 - 36*r - 111 = 0. What is r?
-2, -1
Let m(s) be the second derivative of -s**8/3360 - s**7/315 - s**6/72 - s**5/30 + s**4/4 + s. Let k(d) be the third derivative of m(d). Factor k(v).
-2*(v + 1)**2*(v + 2)
Let i(y) be the first derivative of 2*y - 3 + 1/6*y**3 - 1/20*y**5 + 0*y**4 + 0*y**2. Let v(r) be the first derivative of i(r). Factor v(s).
-s*(s - 1)*(s + 1)
Let o(q) be the first derivative of -q**3/12 + q**2 - 51. Let o(g) = 0. Calculate g.
0, 8
Let b(w) be the first derivative of -w**6/60 - w**5/40 - 5*w + 4. Let k(f) be the first derivative of b(f). Find s such that k(s) = 0.
-1, 0
Let j(d) be the third derivative of d**6/600 - d**5/150 - 18*d**2. Factor j(u).
u**2*(u - 2)/5
Let w(v) be the first derivative of -3/2*v + 4 - 1/2*v**3 + 3/2*v**2. Suppose w(z) = 0. Calculate z.
1
Let q(r) be the first derivative of -r**7/735 - r**6/84 - 3*r**5/70 - r**4/12 - 2*r**3/21 + 3*r**2 - 7. Let x(d) be the second derivative of q(d). Factor x(p).
-2*(p + 1)**3*(p + 2)/7
Find x, given that 10*x - 12 - 2*x**3 - 2/3*x**4 + 14/3*x**2 = 0.
-3, 1, 2
Find a such that -4*a**4 - 8*a - 7*a**4 - 46*a**3 + 12*a**4 + 13*a**4 + 40*a**2 = 0.
0, 2/7, 1, 2
Let m(f) = -26*f**4 + 20*f**3 + 23*f**2 + 17*f. Let p(h) = 9*h**4 - 7*h**3 - 8*h**2 - 6*h. Let l(w) = 6*m(w) + 17*p(w). Find j such that l(j) = 0.
-2/3, 0, 1
Let b(j) be the third derivative of j**5/30 + 7*j**4/16 + 5*j**3/12 + 20*j**2. Find p such that b(p) = 0.
-5, -1/4
Let a be (-8 + 4 + 4)/(-3). Factor a + 3/7*t**2 + 3/7*t**3 - 6/7*t.
3*t*(t - 1)*(t + 2)/7
Let n be 1 - (-4 - 27/(-5))*-1. Find d, given that -84/5*d - 48/5*d**4 - n - 99/5*d**2 + 168/5*d**3 = 0.
-1/4, 2
Let l be 5/2*(-8)/(-10). Let z = l - 0. Factor 0*o**3 + 0*o + 1/2*o**4 + 0*o**z + 0 + 1/2*o**5.
o**4*(o + 1)/2
Suppose 6*p - 4*i + 915 = p, p + 183 = 3*i. Let w = p + 1283/7. Factor 0 + 0*o + w*o**2.
2*o**2/7
Let z(w) be the second derivative of 1/42*w**7 - 1/30*w**6 + 0 + 1/6*w