-1/3, 0
Suppose 5*b = -2 + 27. Suppose 2*h + 30 = b*r, h - 18 = -r - 2*r. Let 15*n - 4*n**2 + r*n**2 + 6 + 5*n**3 + 10*n**2 - 2*n**3 = 0. Calculate n.
-2, -1
Let c = 1/1336 + 667/1336. Solve 0*o + 0 - c*o**2 = 0 for o.
0
Let q(x) be the second derivative of -x**5/70 - x**4/14 - 2*x**3/21 + 3*x - 7. Determine b so that q(b) = 0.
-2, -1, 0
Determine x, given that 15 + 20*x**4 + 1009 + 0*x**5 + x**5 + 1280*x + 640*x**2 + 160*x**3 = 0.
-4
Let r(t) = -t**2 + t - 4. Let o(x) = 19*x + 2. Let d be o(-1). Let c(k) = -3*k**2 + 3*k - 11. Let n(z) = d*r(z) + 6*c(z). Let n(i) = 0. Calculate i.
-1, 2
Let g(a) = a**2 + 7*a + 1. Let n be g(-7). Let -n + 8*p - 4*p**3 + 9 + 12*p**4 - 4*p + 0*p**4 - 20*p**2 = 0. What is p?
-1, -2/3, 1
Let b = -107 - -53. Let w be (-3)/b*(-8)/(-2). Factor 0*a + 0 + 2/9*a**3 - w*a**2.
2*a**2*(a - 1)/9
Let n = 36 - 33. Let k be 15/(-90)*(-4)/n. Suppose k*g**3 + 2/3*g**2 + 2/9 + 2/3*g = 0. What is g?
-1
Let w be 1 + (-2 - (-2)/(-1) - -3). Factor 0*b + w + 0*b**2 + 0*b**4 - 1/3*b**5 + 1/3*b**3.
-b**3*(b - 1)*(b + 1)/3
Let y(z) be the third derivative of 5*z**8/1344 - z**7/168 - 5*z**6/96 + z**5/48 + 5*z**4/12 + 5*z**3/6 + z**2 + 4*z. Determine o, given that y(o) = 0.
-1, 2
Let a(h) = -h**2 - h + 2. Let d(x) be the third derivative of -x**5/60 + x**4/24 + 4*x**2. Let i(p) = 2*a(p) - 4*d(p). Find q such that i(q) = 0.
1, 2
Factor 30/7*g**2 - 9/7*g**3 - 24/7 - 12/7*g.
-3*(g - 2)**2*(3*g + 2)/7
Let j(s) = s**3 - 6*s**2 - 10*s + 6. Let a(r) = -r**3 + 7*r**2 + 11*r - 7. Let q(t) = -6*a(t) - 7*j(t). Factor q(m).
-m*(m - 2)*(m + 2)
Let i(a) be the first derivative of -a**4/12 - 3*a + 2. Let b(h) be the first derivative of i(h). Suppose b(x) = 0. What is x?
0
Let g(y) = y**2 + 15*y - 1 + 0*y**2 - 16*y. Let a(s) = 4*s**2 - s - 2. Let l(u) = -a(u) + 3*g(u). Determine x so that l(x) = 0.
-1
Let f(n) be the first derivative of -n**8/112 - 11*n**7/280 - 7*n**6/120 - n**5/40 + n**3 + 5. Let w(p) be the third derivative of f(p). Factor w(a).
-3*a*(a + 1)**2*(5*a + 1)
Let n(f) = -f + 1. Let c be n(-2). Find u, given that 7*u**3 - 4*u**c + 3*u**2 - u**2 - 5*u**3 = 0.
0, 1
Let q(f) be the third derivative of -5*f**8/1512 - f**7/315 + f**6/270 - 12*f**2. Factor q(y).
-2*y**3*(y + 1)*(5*y - 2)/9
Let x = 5 + -3. Solve 36*h**x + 6 + 14*h - 41*h - 15*h**2 = 0.
2/7, 1
What is i in 1/2*i**2 - 1/2 - 1/2*i**3 + 1/2*i = 0?
-1, 1
Let -2/5*f**3 + 2/5*f + 0*f**2 + 0 = 0. What is f?
-1, 0, 1
Factor 4/5*m**2 - 12/5*m + 8/5.
4*(m - 2)*(m - 1)/5
Let b be (-1)/2*56/(-84). Solve 2/3 + b*w**2 - w = 0 for w.
1, 2
Factor 0*q + 0 - 6/13*q**4 + 0*q**2 + 4/13*q**3 - 10/13*q**5.
-2*q**3*(q + 1)*(5*q - 2)/13
Let n(v) be the third derivative of v**5/150 - v**4/20 - 4*v**3/15 + 9*v**2. Factor n(l).
2*(l - 4)*(l + 1)/5
Let d(z) be the third derivative of -2*z**2 - 1/36*z**4 + 0*z + 0 - 1/45*z**5 + 1/180*z**6 + 2/9*z**3. Solve d(u) = 0.
-1, 1, 2
Suppose 2*q + 8 = 4*q. Factor o**3 - 3*o**2 + o**2 - q*o**3.
-o**2*(3*o + 2)
Let w(c) be the second derivative of -c**7/3360 + c**6/480 - c**5/160 + c**4/96 + c**3/6 - c. Let f(n) be the second derivative of w(n). Factor f(q).
-(q - 1)**3/4
Let m(s) be the third derivative of s**7/1050 - s**6/120 + 3*s**5/100 - 7*s**4/120 + s**3/15 - 20*s**2 - 2. Find f, given that m(f) = 0.
1, 2
Let n = 5 + -3. Let v(y) be the first derivative of -2 - 2/3*y**3 + 2*y**n - 2*y. Factor v(c).
-2*(c - 1)**2
Let i(k) be the first derivative of k**4/46 + 6*k**3/23 + 27*k**2/23 + 54*k/23 - 16. Factor i(c).
2*(c + 3)**3/23
Let c(z) be the first derivative of 0*z + 3 - 1/6*z**3 - 1/4*z**2. Factor c(a).
-a*(a + 1)/2
Let n = 3 + -1. Suppose -4*l + n*l = 0. Factor l*g - 4*g + 5*g - g**2.
-g*(g - 1)
Suppose 3*f - 5*r - 6 = 0, -4*f + 5*f - 3*r = -2. Let o = -5 + f. Solve 0*g**3 + 1/4*g**4 + 0*g + 1/4*g**5 + 0 + 0*g**o = 0 for g.
-1, 0
Factor 0*l**2 + 0 + 0*l - 8/11*l**3 + 8/11*l**4 - 2/11*l**5.
-2*l**3*(l - 2)**2/11
Let z(l) = 2*l**2 + 2*l - 2. Let q be z(2). Suppose -4*m + q = -6*v + 4*v, 5*m + 3*v - 7 = 0. Factor -67/4*u**m + 7/4*u**5 - 37/4*u**4 + 7*u + 73/4*u**3 - 1.
(u - 2)*(u - 1)**3*(7*u - 2)/4
Let w(y) = -y**2 + 2. Let x(c) = -4. Let h(r) = r**2 - 1. Let v(u) = 3*h(u) + x(u). Let z(j) = 2*v(j) + 7*w(j). Let z(l) = 0. What is l?
0
Let j(w) be the second derivative of w**6/1980 - w**4/33 + w**3 + 7*w. Let b(k) be the second derivative of j(k). Find m, given that b(m) = 0.
-2, 2
Let y(l) be the second derivative of -l**8/4200 + l**6/450 - l**4/60 + l**3/3 - 2*l. Let g(c) be the second derivative of y(c). Let g(t) = 0. Calculate t.
-1, 1
Let n be ((-3)/(-4))/((-10)/((-100)/105)). Let i(j) be the first derivative of -2/21*j**3 + 0*j + 2/35*j**5 - 2 - n*j**4 + 1/7*j**2. Factor i(s).
2*s*(s - 1)**2*(s + 1)/7
Suppose 3*n + 32 = 4*l - 2*n, 3*l = 5*n + 29. Factor -12*i - 3*i**5 - 39*i**3 + 36*i**2 + 24*i**4 - 6*i**4 - l + 3.
-3*i*(i - 2)**2*(i - 1)**2
Let x be (0 - 2/(-8))*8. Let 4*s**3 + 3*s - s - 2*s**4 - x*s - 2*s**2 = 0. What is s?
0, 1
Let r(o) be the first derivative of -3*o**4/16 + 7*o**3/4 - 3*o**2 - 12*o - 29. Factor r(m).
-3*(m - 4)**2*(m + 1)/4
Let g(r) = -r**2 - 16*r + 23. Let f(t) = 3*t**2 + 32*t - 45. Let s(q) = 3*f(q) + 5*g(q). Let s(k) = 0. What is k?
-5, 1
Let k(u) be the first derivative of -u**6/2 + 3*u**5/5 + 3*u**4/2 - 2*u**3 - 3*u**2/2 + 3*u - 2. Factor k(d).
-3*(d - 1)**3*(d + 1)**2
Let x be -3*(-4)/(-3) + -2. Let g(o) = -o**3 + o**2 + o + 5. Let z(s) = -2*s**3 + 2*s**2 + 2*s + 9. Let c(j) = x*z(j) + 11*g(j). Factor c(a).
(a - 1)**2*(a + 1)
Let f(v) be the first derivative of 0*v**2 + 0*v + 0*v**3 + 0*v**5 - 3 + 1/27*v**6 - 1/18*v**4. Let f(m) = 0. What is m?
-1, 0, 1
Let k(v) be the first derivative of -15*v**4/4 - 25*v**3/3 - 5*v**2/2 + 5*v - 9. Factor k(q).
-5*(q + 1)**2*(3*q - 1)
Let u be (14/(-49))/(-2) + -2 + 2. Factor 2/7*h**3 - 1/7*h**4 + 2/7*h**2 - u*h**5 - 1/7*h - 1/7.
-(h - 1)**2*(h + 1)**3/7
Let c be 1*-85*1/(-4). Let a = c - 21. Let 0 + 1/2*h - a*h**2 = 0. What is h?
0, 2
Factor -12 + 12 - r**2.
-r**2
Let n(o) be the second derivative of 16*o**7/21 + 8*o**6/3 + 5*o**5/2 - 5*o**4/6 - 5*o**3/3 + o**2 + 4*o. Find y such that n(y) = 0.
-1, 1/4
Let o(c) = 2*c**2 - 70*c - 648. Let h(u) = 2*u**2 + u. Let q(j) = 2*h(j) - o(j). Factor q(k).
2*(k + 18)**2
Let w = 25 + -7. Solve -4 - 10*r**5 + 7*r**2 + 20*r**4 - 23*r**2 - w*r + 12*r**3 + 16*r**5 = 0 for r.
-2, -1, -1/3, 1
Let k(x) be the second derivative of -x**5/240 - x**4/96 + x**3/12 + x**2 - x. Let u(w) be the first derivative of k(w). Let u(t) = 0. What is t?
-2, 1
Suppose 7*n = 3*n + 16. Factor 6*y**2 - 3*y**5 - 6 + 2*y**3 + 4*y**3 - y**n - 3*y - 2*y**4 + 3.
-3*(y - 1)**2*(y + 1)**3
Let y be (-30)/(-8)*24/18. Determine m, given that 0 + 18/5*m**3 + 2/5*m**y - 2*m**4 - 14/5*m**2 + 4/5*m = 0.
0, 1, 2
Suppose 0 = -l + 4*f + 3 - 12, 14 = -4*l + 5*f. Let y(o) = -o + 2. Let t be y(l). Factor 0 + 0*k - 2/3*k**t - 2/3*k**2.
-2*k**2*(k + 1)/3
Let n(f) = 2*f**2 + 1. Let r be n(1). Let k(a) be the first derivative of -1/5*a**5 + 0*a**2 + 0*a + 2/3*a**r + 2 + 1/4*a**4. Suppose k(x) = 0. What is x?
-1, 0, 2
Suppose 1 = -n + 4. Factor 6*s**2 + 0*s - 8 + 0 - n*s**3 - s**3 - 2*s**4 + 8*s.
-2*(s - 1)**2*(s + 2)**2
Determine y, given that 0 + 2/15*y**5 + 0*y**2 + 2/5*y**4 + 0*y + 4/15*y**3 = 0.
-2, -1, 0
Suppose -3 = -2*k + 3. Factor -4*c + 4*c**k - 1 - 2*c**2 + c**4 + 1 + c**4.
2*c*(c - 1)*(c + 1)*(c + 2)
Let v = 460/3 - 153. Suppose v*u - 1/3*u**2 + 2/3 = 0. Calculate u.
-1, 2
Let u(v) be the third derivative of v**8/5040 - v**5/10 + 7*v**2. Let i(w) be the third derivative of u(w). Factor i(g).
4*g**2
Suppose k - 3*u = 10 - 2, -k - 4*u + 8 = 0. Factor -1 + d - k*d**3 + 2*d**2 - 3 + 7*d + 2.
-2*(d - 1)*(d + 1)*(4*d - 1)
Let x(i) be the third derivative of i**7/420 + i**6/80 - i**5/8 + 17*i**4/48 - i**3/2 - i**2 - 9. What is o in x(o) = 0?
-6, 1
Let d(g) be the third derivative of 0*g**3 + 0*g**5 + 0*g**4 + 0*g + 0 + 1/360*g**6 + 3*g**2. Suppose d(k) = 0. What is k?
0
Suppose -2*l - 2 = 2*w + 2, 2*w + 3 = -3*l. Let p be 0/(l - -2) - -2. Factor -2*a**p + a**3 + 4*a**2 + 0*a**2.
a**2*(a + 2)
Determine w so that 0 + 4/5*w**2 + 0*w - 4/5*w**3 = 0.
0, 1
Let z(i) be the first derivative of 15*i**6/2 + 48*i**5 + 110*i**4 + 320*i**3/3 + 40*i**2 + 13. Factor z(c).
5*c*(c + 2)**2*(3*c + 2)**2
Let z be (3/30)/((-1)