-1, 1
Let o(v) = 9*v**2 - 162*v - 153. Let n(h) = -8*h**2 + 162*h + 155. Let z(t) = 6*n(t) + 5*o(t). Factor z(x).
-3*(x - 55)*(x + 1)
Let d(k) be the third derivative of 0 - 10*k**2 + 23/108*k**4 + k - 8/27*k**3 + 1/90*k**5. Factor d(y).
2*(y + 8)*(3*y - 1)/9
Suppose -4*l - 104 = -4*d, 0 = -10*d + 5*d - 2*l + 116. Factor -d - 20*p**2 + 11 + 8 - 25*p.
-5*(p + 1)*(4*p + 1)
Suppose 4*o + 6 = -3*a, 133 - 142 = 3*o + 3*a. What is q in -4/3 + 2/3*q**5 + 8/3*q**2 - 4/3*q**4 + 2/3*q - 4/3*q**o = 0?
-1, 1, 2
Let w(m) be the third derivative of -m**6/360 - m**5/9 - m**4/2 + 3*m**2 + 34. Factor w(u).
-u*(u + 2)*(u + 18)/3
Let g(d) be the second derivative of 5*d**4/6 - 17*d**3/3 + 6*d**2 + 121*d. Factor g(w).
2*(w - 3)*(5*w - 2)
Suppose 3*s - s = 5*g - 113, -2*s = 4*g - 94. Determine w so that -g*w + 2384*w**2 - w - 2388*w**2 + 4*w**3 = 0.
-2, 0, 3
Let t(c) be the third derivative of -c**6/255 + c**5/30 + 4*c**4/51 - 5*c**3/51 + 25*c**2 - 2. Determine j so that t(j) = 0.
-1, 1/4, 5
Let s(t) = 33*t**2 - 484 + 32*t + 51*t - 32*t**2. Let f(j) = 2*j**2 + 82*j - 484. Let u(n) = -5*f(n) + 6*s(n). Factor u(g).
-4*(g - 11)**2
Solve 120/13*o**2 - 2/13*o**3 + 0 + 0*o = 0.
0, 60
Let v(i) = -2 + 12*i + 3*i**2 + 0 - 4*i**2 - 6. Let k be v(11). Factor k - 3 - 3*s**2 + 4*s + s**2.
-2*s*(s - 2)
Let 1/2 - 63/8*v**4 - 7/2*v + 27/8*v**5 + 55/8*v**2 - 3/8*v**3 = 0. What is v?
-1, 1/3, 2/3, 2
Let t(o) = -o**5 + 5*o**4 + 15*o**3 + 7*o**2 + 2*o + 2. Let z(a) = a**5 + a**4 - a**2 + a + 1. Let h(k) = -t(k) + 2*z(k). Factor h(l).
3*l**2*(l - 3)*(l + 1)**2
Let v = -1534 + 1536. Let -4/5*k**v - 1/5*k**3 + 0 - 4/5*k = 0. What is k?
-2, 0
Factor -2*i**4 + 18*i + 18*i**3 - 7*i**4 + 6*i**4 - 33*i**2.
-3*i*(i - 3)*(i - 2)*(i - 1)
Let f(n) be the second derivative of 15/2*n**3 - 1/4*n**5 + 0 - 25/2*n**2 - 5/4*n**4 - 15*n. Find h such that f(h) = 0.
-5, 1
Let q(d) be the third derivative of -d**6/360 - d**5/40 - 17*d**3/6 + d**2 + 9*d. Let b(u) be the first derivative of q(u). Let b(h) = 0. Calculate h.
-3, 0
Let r(v) be the first derivative of 4*v**3/27 + 22*v**2/9 - 16*v/3 + 64. Let r(o) = 0. Calculate o.
-12, 1
Let l be ((-75)/35 - -5)/((-4)/(-14)). Suppose 0*b = -0*b + l*b. Factor 0 + b*m - 2*m**3 + 4/7*m**2.
-2*m**2*(7*m - 2)/7
Let d(t) = 4*t - 3. Let z be d(2). Suppose h + 97 = 4*w, z*h + 0 = -2*w + 43. Let 3*x**2 + 4*x**4 - 8*x + w*x**3 + 11*x**4 + 0*x**4 + 2*x = 0. Calculate x.
-1, 0, 2/5
Let p(n) be the third derivative of n**6/30 - 6*n**5/5 + 29*n**4/6 + 32*n**3 + 139*n**2. Factor p(g).
4*(g - 16)*(g - 3)*(g + 1)
Factor -28*n**2 + 314*n - 464*n - 108 + 414*n.
-4*(n - 9)*(7*n - 3)
Let k = 20 + -15. Let l(t) be the second derivative of -3/4*t**5 + 0 + t**2 + k*t + 3/20*t**6 + 5/3*t**3 + 13/24*t**4. Factor l(v).
(v - 2)**2*(3*v + 1)**2/2
Find d, given that -4/3*d + 1/12*d**3 + 0 - 5/4*d**2 = 0.
-1, 0, 16
Let l(a) be the first derivative of -a**4 - 4*a**3/3 + 8*a**2 + 16*a - 54. Determine s so that l(s) = 0.
-2, -1, 2
Let n(t) be the second derivative of -t**4/30 + 28*t**3/15 + 29*t**2/5 + 4*t - 22. Factor n(p).
-2*(p - 29)*(p + 1)/5
Let a be (-110)/935 + 212/68. Factor 2/3*k**4 - 2/3*k**2 + 4/3*k + 0 - 4/3*k**a.
2*k*(k - 2)*(k - 1)*(k + 1)/3
Factor -365 - 3*l**3 + 41*l + 293 + 0*l**3 - 11*l + 9*l**2.
-3*(l - 4)*(l - 2)*(l + 3)
Let o(s) = 3*s**2 + 6*s - 2. Let b be o(-3). Let b*x**3 - 3*x**2 + 2*x**2 - x**5 - 6*x**3 + x**4 = 0. Calculate x.
-1, 0, 1
Let x = -15 - 41. Let i = 284/5 + x. Find p such that -4/5*p + 0 - 1/5*p**3 - i*p**2 = 0.
-2, 0
Solve -5/4*j + 0 + 1/2*j**3 - 3/8*j**2 = 0 for j.
-5/4, 0, 2
Let c = -742 + 746. Let s(w) be the third derivative of 0*w**c - 6*w**2 + 0*w**3 + 0*w - 1/330*w**5 + 0. Find h such that s(h) = 0.
0
Factor 78*k - 1003*k**4 + 1004*k**4 - 4*k**2 - 78*k**3 - 2*k**2 + k**2 + 4*k**2.
k*(k - 78)*(k - 1)*(k + 1)
Let l(k) be the third derivative of k**6/180 - k**5/90 - k**4/9 + 4*k**3/9 + 65*k**2 - k. Find i, given that l(i) = 0.
-2, 1, 2
Let z(f) be the first derivative of -2*f**3/3 - 48*f**2 + 430. Solve z(y) = 0 for y.
-48, 0
Let -u**3 - 3*u - 6*u**2 - 28 + 6*u**2 + 10*u**2 - 10*u - 4*u = 0. Calculate u.
-1, 4, 7
Let d = -1132 - -1132. Find m such that -3/4*m**4 + 3/4*m**2 + 3/4*m + d - 3/4*m**3 = 0.
-1, 0, 1
Let l(f) be the third derivative of 0 + 4*f**2 + 0*f + 1/45*f**5 + 1/18*f**4 + 0*f**3. Factor l(m).
4*m*(m + 1)/3
Let v(c) = 18*c**2 - 4*c**3 + 2 + 12*c - 3*c**4 - c**4 + 2*c. Let o = -88 + 89. Let w(r) = r**2 - r - 1. Let x(m) = o*v(m) - 6*w(m). Solve x(j) = 0.
-1, 2
Let v(d) be the first derivative of d**4/2 - 34*d**3/3 + 63*d**2 + 162*d - 241. Factor v(a).
2*(a - 9)**2*(a + 1)
Factor 587*h + 513*h - 8893 - 5*h**2 - 51607.
-5*(h - 110)**2
Let i(w) be the first derivative of -608/21*w**3 - 19 + 128/7*w**2 - 32/7*w + 82/7*w**4 - 7/3*w**6 + 22/5*w**5. Let i(m) = 0. What is m?
-2, 2/7, 1, 2
Let s(f) = 2*f**2 + 8*f + 10. Let o be s(-2). Let a(j) be the first derivative of 2/3*j + 1/9*j**3 + 1/2*j**o + 4. Factor a(r).
(r + 1)*(r + 2)/3
Let f(u) be the first derivative of u**8/588 + 4*u**7/735 - 2*u**5/105 - u**4/42 - 9*u**2/2 + 2. Let l(o) be the second derivative of f(o). Factor l(j).
4*j*(j - 1)*(j + 1)**3/7
Let c be (-4 + 2)/((4/(-3))/2). Solve 6*r - 16*r**2 + r**c - r**2 + 8*r**2 + 2*r**3 = 0 for r.
0, 1, 2
Suppose -4*c - 18 = -4*g - 5*c, c - 2 = 0. Suppose -g*k = -9 + 1. Factor 7*a - 5*a**2 - 5*a + 12*a**k.
a*(7*a + 2)
Solve -3334*t**2 + 3320*t**2 + 26 + 2*t**3 + 0*t**3 - 20*t + 6 = 0 for t.
-2, 1, 8
Suppose 4*k - 48 = a, 0*a = 4*k - 2*a - 48. Let -3*s**5 - 12*s**2 + 8*s**4 + 4*s**4 - 9*s**3 + k*s - 15 + 15 = 0. What is s?
-1, 0, 1, 2
Let j(q) be the third derivative of 0*q**3 + 0*q**4 - 22*q**2 + 0 - 1/210*q**7 + 0*q**5 + 0*q + 1/336*q**8 - 1/60*q**6. Factor j(s).
s**3*(s - 2)*(s + 1)
Let x(r) = -19*r**4 - 203*r**3 - 999*r**2 - 1599*r - 384. Let j(m) = -40*m**4 - 408*m**3 - 1998*m**2 - 3199*m - 769. Let l(i) = -6*j(i) + 13*x(i). Factor l(k).
-(k + 3)**2*(k + 21)*(7*k + 2)
Let k(a) be the first derivative of -a**7/42 + a**6/45 + a**5/20 - a**4/18 + a + 5. Let o(m) be the first derivative of k(m). Suppose o(g) = 0. What is g?
-1, 0, 2/3, 1
Suppose 35*c = 32*c + 18. Let i(g) be the first derivative of -4/5*g**3 - 3 - 2/5*g - 1/5*g**c - 1/5*g**4 + 14/25*g**5 + g**2. Solve i(m) = 0.
-1, 1/3, 1
Let 24/5 + 12/5*o**2 + 1/5*o**3 + 7*o = 0. Calculate o.
-8, -3, -1
Determine l so that -18*l + 162 + 1/2*l**2 = 0.
18
Let h(q) = -q**2 - 1. Let b be 6*(7/(-2))/(-7). Let z(t) = t**2 + 4 + t + 8*t**2 + t**2 - b*t**2. Let p(r) = 6*h(r) + z(r). What is w in p(w) = 0?
-2, 1
Let o(j) be the second derivative of j**5/20 - j**4/6 + 2*j**3/3 - 3*j**2/2 + 28*j. Let i be o(1). What is u in 1/2*u**4 - u**3 + i*u + 0 + 1/2*u**2 = 0?
0, 1
Factor 0*q - 12*q**2 + 3/4*q**3 + 0.
3*q**2*(q - 16)/4
Solve -44/7*w + 114/7 + 2/7*w**2 = 0 for w.
3, 19
Let j = 28 - 12. Let c = 18 - j. Factor 2*n**4 - 14/3*n**3 - 2/3*n + 0 + 10/3*n**c.
2*n*(n - 1)**2*(3*n - 1)/3
Let m(y) be the first derivative of y**3/6 + 17*y**2/4 + 110. Suppose m(i) = 0. What is i?
-17, 0
Let s = 9 + 57. Let z = s + -63. Factor -2/5 - 2/5*j**4 - 8/5*j**z - 12/5*j**2 - 8/5*j.
-2*(j + 1)**4/5
Let n = 21 - 20. Suppose -2*f + 5 = v - n, 5*v + 3*f = 30. Solve -11*x**2 - v*x**2 + 20*x**2 - 12 = 0.
-2, 2
Let g(x) be the second derivative of x - 3/100*x**5 - 1/10*x**4 - 1/10*x**3 - 7 + 0*x**2. Factor g(k).
-3*k*(k + 1)**2/5
Let h = -128 - -137. Suppose -1 = h*z - 19. Suppose -4/5*c**z + 16/5*c**3 - 7/5*c**4 + 0 + 0*c = 0. What is c?
0, 2/7, 2
Let o(t) be the first derivative of -5*t**4/12 - 25*t**3/6 - 10*t**2 + 7*t - 21. Let l(g) be the first derivative of o(g). Suppose l(h) = 0. What is h?
-4, -1
Factor -6*h**3 + h**3 - 75*h**2 + 0*h + 9*h**3 - h**3 - 78*h.
3*h*(h - 26)*(h + 1)
Let p(g) = 2*g**3 + 2*g**2 + 31*g - 33. Let y be p(1). Factor -72*r**4 - 40/3*r**y - 4/3*r - 36*r**5 + 0 - 48*r**3.
-4*r*(r + 1)*(3*r + 1)**3/3
Let m(k) be the first derivative of k**3 + 3/16*k**2 + 17 + 15/32*k**4 - 3/4*k. Determine c, given that m(c) = 0.
-1, 2/5
Let t(o) = -o**4 - o**2 + o. Let r(m) = m**5 - 3*m**4 + 11*m**3 - 3*m**2 - 3*m. Let h(k) = r(k) + 3*t(k). Solve h(b) = 0.
0, 1, 2, 3
Let d be (2 + 0)/(903/4816). What is v in -128/3 - d*v - 2/3*v**2 = 0?
-8
Let l = -91/114 + 12/19. Let n = l - -5/12. Suppose -1/4*p**2 + n + 0*p = 0.