d/(-18)*(-5 - -2). Factor g - 4/3*v**2 + 4/3*v.
-4*(v - 2)*(v + 1)/3
Let w be (3 - 2 - 2)/1. Suppose -13 = -r - 8. Let h(l) = l**4 - 1. Let x(m) = 10*m**4 - 3*m**3 - 12*m**2 - 4*m - 5. Let c(v) = r*h(v) + w*x(v). Factor c(k).
-k*(k - 2)*(k + 1)*(5*k + 2)
Suppose -5*m = 3*a - 3 + 2, 4*a + 2*m = 6. Let k be ((-20)/45)/(a/(-9)). Let -6*n**4 + 6*n**2 - 30*n**3 + 15*n**3 + k*n**5 - 4*n + 17*n**3 = 0. What is n?
-1, 0, 1, 2
Suppose 24*u = 27*u - 6. Suppose o + 8 = 5*o. Factor o*j**2 - 4*j**u + 8*j - 6*j.
-2*j*(j - 1)
Suppose 2*u + 108 = -5*p, 4*p = -u - 47 - 40. Let k be ((-1)/(-1))/((-11)/p). Factor 11/3*d**3 + 0 - 7/3*d**k - 5/3*d**4 + 1/3*d.
-d*(d - 1)**2*(5*d - 1)/3
Let v(u) be the second derivative of u**7/63 + u**6/5 + u**5 + 23*u**4/9 + 11*u**3/3 + 3*u**2 + 71*u - 1. Factor v(c).
2*(c + 1)**3*(c + 3)**2/3
Suppose j - 2*j = 5*v - 15, 10 = 2*v. Let y = 15 + j. Suppose 2*q**3 + y*q**2 + 7*q**2 - 8*q**2 = 0. Calculate q.
-2, 0
Let a(c) be the first derivative of -c**5 + 25*c**4/4 + 5*c**3 - 65*c**2/2 - 50*c - 115. Factor a(w).
-5*(w - 5)*(w - 2)*(w + 1)**2
What is v in -32/5*v - 2/5*v**2 + 0 = 0?
-16, 0
Let k = 67 - 42. Suppose 2*v**2 - 4*v**2 - 3*v**2 - k*v - 20 = 0. Calculate v.
-4, -1
Let d be (-2950)/8 - 9/(-12). Let o = d - -2582/7. Let o - 18/7*s**2 + 3*s**3 - 3/7*s - 6/7*s**4 = 0. What is s?
-1/2, 1, 2
Let j = -132 + 247. Let l = j - 115. Find z, given that -3*z**2 + l - 9/2*z**3 + 9/2*z**5 + 0*z + 3*z**4 = 0.
-1, -2/3, 0, 1
Let h(j) = -11*j**2 + 62*j - 186. Let d(k) = -40*k**2 + 247*k - 744. Let u(b) = 6*d(b) - 22*h(b). Let u(f) = 0. What is f?
-62, 3
Let p(u) be the first derivative of -u**6/2 + 9*u**5/5 + 3*u**4/4 - 7*u**3 + 12*u - 131. Suppose p(n) = 0. What is n?
-1, 1, 2
Factor -75*m**4 + 180*m - 105*m**3 - 135*m**2 + 80*m**4 + 35*m**2 + 20*m**3.
5*m*(m - 18)*(m - 1)*(m + 2)
Factor 12*n**4 - 21*n**3 + 9*n**2 + 183*n**5 - 186*n**5 + 3*n**4.
-3*n**2*(n - 3)*(n - 1)**2
Let q = 99 - 96. Let 4 - 8 - 5 + 0 + q*h**2 + 6*h = 0. Calculate h.
-3, 1
Let j be (-12)/108*(-1)/(2/12). Suppose 0 = t + 3, 3*t + 2*t + 7 = -4*a. Factor -j*k + 2/3*k**a - 4/3.
2*(k - 2)*(k + 1)/3
Let j = 81 + -79. Find q such that 2*q**j - 2*q**4 + 2*q**3 + 0*q**5 + 4*q**5 - 3*q**3 - 3*q**5 = 0.
-1, 0, 1, 2
Let w = -44/2361 - 78440/351789. Let u = w - -5020/1043. Suppose 20/7*a**2 + 4/7*a**3 + 16/7 + u*a = 0. Calculate a.
-2, -1
Let s(o) = -12*o**2 - 154*o + 900. Let p(q) = 4*q**2 + 52*q - 300. Let z(r) = 17*p(r) + 6*s(r). Factor z(a).
-4*(a - 5)*(a + 15)
Let h be (-2242)/171 - ((-40)/(-18) + -2). Let d = h - -130/9. Factor d*s + 8/9*s**2 + 2/9*s**3 + 4/9.
2*(s + 1)**2*(s + 2)/9
Let t = 336 + -334. Let b(p) be the second derivative of 0*p**t + 0*p**3 + 0 + 9*p - 1/54*p**4 + 1/30*p**5. Factor b(d).
2*d**2*(3*d - 1)/9
Let z = -1636 - -1636. Let b(t) be the second derivative of -1/10*t**6 + t - 1/4*t**4 + 0 - 3/10*t**5 + 0*t**2 + z*t**3. Suppose b(a) = 0. Calculate a.
-1, 0
Let x(t) = -2*t**2 - 2. Let n(g) = -16*g**2 - 22*g + 42. Let k(m) = -2*n(m) + 18*x(m). Let k(b) = 0. What is b?
5, 6
Let a(o) be the third derivative of -o**5/30 - o**4/12 + 2*o**3/3 + 12*o**2. Factor a(k).
-2*(k - 1)*(k + 2)
Let k(t) be the third derivative of 0 - 1/4*t**4 + 2*t**2 + 0*t + 1/30*t**5 - 4/3*t**3. Factor k(g).
2*(g - 4)*(g + 1)
Let d(g) be the second derivative of g**6/120 - 3*g**5/20 + g**4/12 + 8*g**3 + 32*g**2 - 27*g + 1. Suppose d(m) = 0. Calculate m.
-2, 8
Let j(i) be the first derivative of -2*i**3/9 - 11*i**2/3 + 8*i - 57. Find b such that j(b) = 0.
-12, 1
Let y(r) = r**5 + r**4 + r**3. Let b be 14/2 + 7 + -9. Let q(n) = 2*n**4 - n**4 - 6*n**5 + 2*n**3 + 8*n**b. Let v(c) = -3*q(c) + 5*y(c). What is a in v(a) = 0?
0, 1
Suppose 15 + 9 = 3*i. Determine r so that 7*r + i*r**2 + r - 7*r**2 - 3*r**2 = 0.
0, 4
Let k(h) be the third derivative of 0*h**3 - 13*h**2 + 1/270*h**5 + 0*h - 1/1890*h**7 + 0*h**4 + 1/1080*h**6 + 0. Factor k(d).
-d**2*(d - 2)*(d + 1)/9
Let x = 54 + -53. Let w be 0 - x - 44/(-11). Factor -2/3*a**w + a**4 + 0*a**2 + 5/3*a**5 + 0 + 0*a.
a**3*(a + 1)*(5*a - 2)/3
Let r(m) be the second derivative of -m**6/20 + 3*m**5/20 + m**4/4 + 29*m**2/2 - 10*m. Let n(h) be the first derivative of r(h). Solve n(t) = 0 for t.
-1/2, 0, 2
Determine z so that 155/3*z + 50/3 - 185/3*z**2 - 20/3*z**3 = 0.
-10, -1/4, 1
Let v = 83 + -61. Factor -52*w**4 + 9*w**3 - 40*w - 99*w**3 + 17*w**4 - 27*w**5 + v*w**5 - 100*w**2.
-5*w*(w + 1)*(w + 2)**3
Let w(m) be the first derivative of m**4/2 + 26*m**3/3 + 10*m**2 - 48*m - 175. Solve w(j) = 0.
-12, -2, 1
Factor 0 + c**2 - 9/5*c**3 + 1/5*c**5 + 0*c + 3/5*c**4.
c**2*(c - 1)**2*(c + 5)/5
Let f(a) = -a**3 - 36*a**2 - 4*a. Let y be f(0). Find q such that y - 15*q**4 + 65/4*q**3 + 5*q**5 - 15/2*q**2 + 5/4*q = 0.
0, 1/2, 1
Let p(n) be the second derivative of 6*n**2 - 8/3*n**3 + 1/3*n**4 - 9*n + 0. Factor p(f).
4*(f - 3)*(f - 1)
Let p(m) = 30*m**3 + 1200*m**2 + 13173*m + 21618. Let t(z) = -3*z**3 - 120*z**2 - 1317*z - 2162. Let c(g) = -2*p(g) - 21*t(g). Solve c(x) = 0 for x.
-19, -2
Suppose -350 = 26*q - 16*q. Let w be (637/q)/(-7) - 2*1. Factor 3/5*c**4 - 9/5*c**2 - 3/5*c**3 + 6/5 + w*c.
3*(c - 2)*(c - 1)*(c + 1)**2/5
Determine z, given that 1 - 5*z + 19 + 480*z**2 + 5*z**3 - 500*z**2 = 0.
-1, 1, 4
Find h, given that 1/2*h**2 - 3 + 5/2*h = 0.
-6, 1
Factor 1/2*u**3 - 10*u - u**2 - 12.
(u - 6)*(u + 2)**2/2
Let i be (-2961)/(-36) - (-6)/8. Let l = 85 - i. Factor 0 + 5/6*t**l + 1/3*t + 1/2*t**3.
t*(t + 1)*(3*t + 2)/6
Suppose -9*k + 12*k = 9. Suppose 2*q - o - 77 + 9 = 0, -4*o - 107 = -k*q. Find j, given that 240*j**5 + 120*j**2 - 126*j**2 + 27*j**4 - 3*j**4 - q*j**3 = 0.
-1/4, 0, 2/5
Suppose 0 = 2*p + 5*p. Let c(f) be the second derivative of 0 - 2/9*f**3 - 2*f - 1/6*f**4 + p*f**2 + 0*f**5 + 1/45*f**6. Let c(b) = 0. Calculate b.
-1, 0, 2
Let a be (546/13377)/(-1*3/(-7)). Let j(f) be the third derivative of -5/84*f**4 + 0 - 1/420*f**6 - a*f**3 + 0*f - 2/105*f**5 - 9*f**2. Factor j(i).
-2*(i + 1)**2*(i + 2)/7
Let y be (51/340)/((-6)/(-10)). Let w(k) be the third derivative of 1/60*k**6 - 3*k**2 + 1/10*k**5 + 0*k + 0 + y*k**4 + 1/3*k**3. Let w(b) = 0. Calculate b.
-1
Suppose -4 = -12*d + 8*d - 4*l, -4*l = 3*d - 8. Let r be d/6*(0 - 4/16). Factor -3/2 - r*g**2 + g.
-(g - 3)**2/6
Suppose 0 = 3*a + 8*a. Let j(x) be the first derivative of 1/45*x**6 - 1/30*x**4 + 2/45*x**3 + 0*x**2 + a*x - 13 - 2/75*x**5. Find m such that j(m) = 0.
-1, 0, 1
Let c(x) = -14*x**2 + 4*x - 6. Let n(s) = 2*s**2 + 1. Let l(h) = -c(h) - 6*n(h). Suppose l(g) = 0. Calculate g.
0, 2
Let q(p) = p**2 + 236*p - 1203. Let s be q(5). Let -3/8*k**s - 15/8*k - 3/2 = 0. Calculate k.
-4, -1
Let j(g) be the first derivative of -g**3/9 + 32*g**2/3 - 1024*g/3 - 134. Let j(y) = 0. Calculate y.
32
Let f(c) be the first derivative of -3*c**5/20 - c**4 + 3*c**3/2 + 6*c**2 - 8. Let r(j) be the second derivative of f(j). Factor r(h).
-3*(h + 3)*(3*h - 1)
Suppose -2*h = 5*f + 365, 229 + 121 = -5*f - 5*h. Let j = -51 - f. Find t, given that 3 - 28*t - 7 + j*t - t**2 = 0.
-2
Let m be (-4)/5 + 1312/1040. Find n, given that 2/13 - m*n + 6/13*n**2 - 2/13*n**3 = 0.
1
Let v be (24 - 23)*(1 - 1)/(-1). Suppose v = 3*u - l - 10, -u = u + l. Factor -1/3*c**3 + 1/3 - c + c**u.
-(c - 1)**3/3
Suppose 0 = 9*p - 7*p + 3*c - 7, 4*c + 4 = 4*p. Determine k so that -2/3*k**p - 1/3*k**3 + 2/3 + 1/3*k = 0.
-2, -1, 1
Let r be (-3 + (-4 - -3))*(-22)/8. Suppose -1 = 5*t - r. Determine f so that -18/17*f - 4/17*f**t + 4/17 + 18/17*f**3 = 0.
-1, 2/9, 1
Suppose 9 = 3*q - 3*f, -2*q + 2 = -5*f - 10. Suppose 0 = -2*m + 5 - q. What is a in -a + 2*a**2 - a**2 - a**2 + a**2 - m = 0?
-1, 2
Let s = -47 + 56. Suppose -2*f + s*f**2 - 13*f - 4*f**2 = 0. What is f?
0, 3
Let g = 1176 + -4701/4. Factor -1/4*l + g*l**3 + 0 + 1/2*l**2.
l*(l + 1)*(3*l - 1)/4
Suppose 0 + 0*n - 4/9*n**2 - 2/9*n**3 + 2/9*n**4 = 0. What is n?
-1, 0, 2
Let c(v) = 31*v - 211. Let u be c(7). Let l(a) be the third derivative of 0*a**4 + 1/240*a**5 + 0*a**3 + 0 + a**2 + 1/240*a**u + 0*a + 1/840*a**7. Factor l(k).
k**2*(k + 1)**2/4
Factor 108*r - 5*r**3 - 80*r**2 + 2 - 42 + 24*r**4 - 96*r**5 + 92*r**5 - 3*r**3.
-4*(r - 5)*(r - 1)**3*(r + 2)
Let m(d) be the third derivative of -d**8/1848 + 17*d**7/1155 + 7*d**6/220 - 49*d**5/330 - 2*d**4/3 - 12*d**3/11 + 400*d**2. Suppose m(t) = 0