 2
Suppose -14*a - 12 = -10*a. Let l be (4 + (-10)/3)/((-1)/a). Suppose 1/2*n**3 - 3/2*n**l - 1/2 + 3/2*n = 0. Calculate n.
1
Let j = -1 + 1. Suppose -2*f + f + 2 = j. Factor 5*v**3 - 2*v - 2*v**3 + v**3 + 0*v**3 - f*v**5.
-2*v*(v - 1)**2*(v + 1)**2
Let k be 4/6*(450/8)/(-3). Let c = 14 + k. Find b such that -c*b**2 + 3/2 + 0*b = 0.
-1, 1
Let t(d) = d - 5. Let n be t(6). Let y(q) = 42 + 0*q**3 - 66 - q**3 + 23. Let v(h) = h**3 + 2*h**2 + 2. Let m(s) = n*v(s) + 2*y(s). Factor m(w).
-w**2*(w - 2)
Let y(r) be the second derivative of r**7/945 - r**6/60 + r**5/18 + 25*r**4/108 + 37*r**2/2 + 5*r - 3. Let v(k) be the first derivative of y(k). Factor v(l).
2*l*(l - 5)**2*(l + 1)/9
Let b = -425/3 - -143. Suppose 4 = -5*m + 4*k, 3 = 33*m - 28*m + 3*k. Factor 4/3*g**4 - 2/3*g**5 + 0*g**3 + 2/3*g - b*g**2 + m.
-2*g*(g - 1)**3*(g + 1)/3
Let l be ((-34)/51)/((-4)/30). Factor 3*o**l + 12*o**3 + 6*o**2 + 0*o**4 - 2 + o - 16*o**3 + 0*o**4 - 4*o**4.
(o - 1)**3*(o + 1)*(3*o + 2)
Let l(c) = -18*c - 2*c + 5*c - 103. Let z be l(-7). Factor -2/9*n**z + 2/9*n + 0.
-2*n*(n - 1)/9
Let i(f) be the first derivative of 3*f**3 + 105*f**2/2 - 36*f - 221. Suppose i(o) = 0. What is o?
-12, 1/3
Let h(q) be the first derivative of -q**6/12 - 2*q**5/5 - q**4/2 + q**3/3 + 5*q**2/4 + q - 254. Factor h(m).
-(m - 1)*(m + 1)**3*(m + 2)/2
Factor -56/11 + 2*i - 2/11*i**2.
-2*(i - 7)*(i - 4)/11
Suppose 0*p - p = -3. Let x be (119/(-34)*(-18)/(-21))/(2/(-8)). Suppose 2*a - x*a**4 - 44/3*a**p - 10/3*a**5 + 4/3 - 16/3*a**2 = 0. What is a?
-1, 2/5
Let y(l) be the second derivative of -5/12*l**2 + 5/72*l**4 + 0 - 5/36*l**3 + 1/24*l**5 + 12*l. Factor y(c).
5*(c - 1)*(c + 1)**2/6
Suppose -5*x - 14 = 11, -3*a - 5*x = 13. Suppose 5*k - 9 = 1. Solve -27*q**k + 6*q**3 - 6 - 4*q - 3*q**a + 9*q**3 + 25*q = 0 for q.
1, 2
Let g(f) be the third derivative of 1/8*f**4 - 1/70*f**7 - 1/2*f**3 + 6*f**2 + 0 - 1/20*f**6 + 0*f + 1/112*f**8 + 1/10*f**5. Factor g(t).
3*(t - 1)**3*(t + 1)**2
Let i(p) be the first derivative of 3*p**5/35 - 23*p**4/28 + 31*p**3/21 - 5*p**2/14 - 6*p/7 - 709. What is c in i(c) = 0?
-1/3, 1, 6
Factor 3/4*c + 0 - 17/4*c**2 + 5/4*c**4 + 9/4*c**3.
c*(c - 1)*(c + 3)*(5*c - 1)/4
Let b(y) be the first derivative of -7*y**6/3 + 66*y**5/5 - 16*y**4 - 80*y**3/3 + 48*y**2 + 32*y - 81. Find z such that b(z) = 0.
-1, -2/7, 2
Let f(c) be the first derivative of -c**5/50 - c**4/15 - c**3/15 - 17*c + 9. Let m(b) be the first derivative of f(b). Let m(p) = 0. Calculate p.
-1, 0
Let x(b) be the first derivative of -1 + 0*b**3 - 1/5*b**2 + 7*b + 1/30*b**4. Let l(t) be the first derivative of x(t). Factor l(w).
2*(w - 1)*(w + 1)/5
Let j(k) be the second derivative of k**5/80 - 85*k**4/16 + 7225*k**3/8 - 614125*k**2/8 - 240*k. Let j(d) = 0. What is d?
85
Let t(x) be the first derivative of -1/4*x**3 + 9/8*x - 15/16*x**2 + 28. Suppose t(r) = 0. What is r?
-3, 1/2
Let w(j) = -8*j**2 - 10*j - 2. Let q(u) = 17*u**2 + 21*u + 4. Let i be (-70)/10*(-1 - -2). Let o(a) = i*w(a) - 3*q(a). Find v such that o(v) = 0.
-1, -2/5
Let z be ((-1232)/(-140) - 9)*10/(-3). Determine d, given that 0 - z*d**3 + 2*d - 4/3*d**2 = 0.
-3, 0, 1
Let l be (2/(-8))/(7/(-56)). Suppose 4*r - 10 = 9*r - 5*j, r + 6 = l*j. Solve 2 + 49/2*i**4 + 35*i**3 - 3/2*i**r - 10*i = 0 for i.
-1, 2/7
Factor 12/5 + 19/5*q + 8/5*q**2 + 1/5*q**3.
(q + 1)*(q + 3)*(q + 4)/5
Let k(c) be the first derivative of 0*c**2 + 6 - 1/16*c**4 - 6*c - 1/8*c**3. Let m(n) be the first derivative of k(n). Suppose m(b) = 0. What is b?
-1, 0
Let z(u) = 7*u**5 + 10*u**4 + 15*u**3 + 20*u**2 + 15*u + 2. Let n(f) = -f**5 + f**3 - f. Let c = 22 + -17. Let x(g) = c*n(g) + z(g). Factor x(p).
2*(p + 1)**5
Let o = 323 + -319. Let q be ((-2)/20)/(3*o/(-48)). Factor 0 + q*l**4 - 2/5*l**2 + 2/5*l**3 - 2/5*l.
2*l*(l - 1)*(l + 1)**2/5
Let h(s) be the third derivative of s**7/8820 + s**6/2520 + 17*s**4/24 - 13*s**2. Let o(v) be the second derivative of h(v). Suppose o(q) = 0. What is q?
-1, 0
Let k = -56 + 59. Factor -6*p**k - 2*p**4 - 452*p**2 + 466*p**2 + 0*p + 30*p - 36.
-2*(p - 2)*(p - 1)*(p + 3)**2
Let 490 + 2/5*x**2 + 28*x = 0. What is x?
-35
Let y = 8547 + -8547. Determine x, given that -3/2*x - 3*x**4 + y + 3/2*x**3 + 3*x**2 = 0.
-1, 0, 1/2, 1
Suppose -2*h - 5 = -7*h, q - 2*h - 16 = 0. Suppose 0*u + 5*u = -2*w + 18, q = 3*u + 3*w. Factor 0*n + 2/3*n**5 + 0 + 2/3*n**2 + u*n**4 + 2*n**3.
2*n**2*(n + 1)**3/3
Let h(s) = s**2 + s + 1. Let t be ((-1)/4 + 0)*4. Let v be 0 - 4 - (0 - -2). Let p(u) = 3*u**2 + 6*u - 18. Let o(k) = t*p(k) + v*h(k). Factor o(d).
-3*(d + 2)*(3*d - 2)
Let y be (-13 + 10 + 3)/(-7). Let t(v) be the second derivative of -1/20*v**5 + 7/12*v**3 + 7/48*v**4 + 3/8*v**2 - 8*v + y. Solve t(p) = 0 for p.
-1, -1/4, 3
Determine r, given that -4 - 3/4*r**2 + 13/2*r = 0.
2/3, 8
Factor 58*y**2 - 2*y**3 - 56*y**2 + 4*y**3 - 2*y - 2*y**4.
-2*y*(y - 1)**2*(y + 1)
Suppose 0 = -957*s + 967*s. Let s + 2/7*l**2 + 2/7*l = 0. Calculate l.
-1, 0
Let c(f) = 28*f**4 - 12*f**3 + 5*f**2 - 3*f + 9. Let n(q) = q**3 + q**2 - q + 3. Let p(u) = -2*c(u) + 6*n(u). Factor p(w).
-2*w**2*(4*w - 1)*(7*w - 2)
Let w(p) = -2*p**2 - 3*p. Suppose -2*d + 4 = -2*t, -4*t + 0*d - 5*d = 44. Let h(g) = -g**2 - g. Let z(c) = t*w(c) + 15*h(c). Suppose z(v) = 0. What is v?
0, 1
Let i(x) be the third derivative of x**7/630 - x**6/60 + x**5/15 + 5*x**4/8 - 8*x**2. Let t(r) be the second derivative of i(r). Determine n so that t(n) = 0.
1, 2
Let z(k) be the third derivative of k**8/672 - k**6/120 + k**4/48 - 85*k**2. Solve z(l) = 0.
-1, 0, 1
Let z(q) be the first derivative of q**4/10 + 7*q**3/3 + 36*q**2/5 - 9*q + 486. Suppose z(v) = 0. Calculate v.
-15, -3, 1/2
Suppose 8*x - 28 + 4 = 0. Solve 262*d - 16*d**4 - 9*d**4 - 197*d + 55*d**2 - 30 - 65*d**x = 0.
-3, -1, 2/5, 1
Let i(r) be the first derivative of r**6/2 + r**5 - r**4/4 - 5*r**3/3 - r**2 + 72. Factor i(o).
o*(o - 1)*(o + 1)**2*(3*o + 2)
Let a(q) be the third derivative of -1/180*q**5 - 1/1080*q**6 + 3*q**2 + 1/1890*q**7 + 0 + 0*q + 1/216*q**4 + 1/27*q**3. Let a(j) = 0. What is j?
-1, 1, 2
Let x be (0 + 46)*(-10)/(-4). Factor 159*u**4 + 145*u**5 - 20*u**5 - 434*u**4 + x*u**2 - 20 + 95*u**3 - 40*u.
5*(u - 1)**3*(5*u + 2)**2
Let v = -13264/5 - -2653. Let v*j**2 - 1/5*j + 0 = 0. Calculate j.
0, 1
Let o(r) = -18*r**2 + 382*r - 81. Let f be o(21). Factor 1/6*c**f + 5/6*c + c**2 + 0.
c*(c + 1)*(c + 5)/6
Let 94/3*l + 2/3*l**2 - 196/3 = 0. Calculate l.
-49, 2
Let w be (-34)/(-9) - 4/(-18). Let z be (2 + (-1 - 2))*(2 - w). Factor 3/4*l**z + 1/2*l + 0 + 1/4*l**3.
l*(l + 1)*(l + 2)/4
Factor 54*a**2 + 3*a + 3*a**3 - 2*a**3 - 7*a - 51*a**2.
a*(a - 1)*(a + 4)
Suppose -3*s + 2*w = 2*s - 1836, -1468 = -4*s + 2*w. Let m = s - 2570/7. Determine c, given that 3/7 - m*c + 3/7*c**2 = 0.
1
Let f(g) be the second derivative of g**6/40 - g**5/20 - 5*g**2 + g. Let h(d) be the first derivative of f(d). Let h(s) = 0. Calculate s.
0, 1
Let m(v) be the second derivative of -v**7/3780 + v**6/540 + v**4/12 + 2*v. Let p(l) be the third derivative of m(l). Factor p(t).
-2*t*(t - 2)/3
Let w(h) = h + 8. Let c be w(-8). Suppose -3*a + d + 33 = -c*a, -33 = -2*a - 3*d. Factor 13*l - 2*l**2 + a + 15 + 5*l**2 + 5*l.
3*(l + 3)**2
Let j(m) be the third derivative of -7/270*m**5 + 1/945*m**7 - 1/108*m**6 + m**2 + 2 + 5/108*m**4 + 0*m + 2/9*m**3. Find f, given that j(f) = 0.
-1, 1, 6
Let q be 4/10*(-25)/(-220). Let n(a) be the first derivative of -2/33*a**3 - 1/33*a**6 + 0*a**2 + 2/55*a**5 - 8 + q*a**4 + 0*a. Factor n(t).
-2*t**2*(t - 1)**2*(t + 1)/11
Factor -12000/7*d + 30000/7 + 3/7*d**4 + 1800/7*d**2 - 120/7*d**3.
3*(d - 10)**4/7
Factor 0 + 8*i**3 + i - 11/2*i**2 - 7/2*i**4.
-i*(i - 1)**2*(7*i - 2)/2
Let b(f) be the first derivative of -f**6/960 + f**4/64 + f**3/24 - 10*f**2 - 27. Let c(z) be the second derivative of b(z). Factor c(o).
-(o - 2)*(o + 1)**2/8
Suppose 0 = -5*l + s - 2, 12*s - 9*s - 6 = -2*l. Factor -3/2*b**3 - 9/2*b - 6*b**2 + l.
-3*b*(b + 1)*(b + 3)/2
Let b = -47552/35 - -6796/5. Suppose 6/7*w**2 + 2*w**3 - 6/7*w**4 - b*w - 10/7*w**5 + 0 = 0. What is w?
-1, 0, 2/5, 1
Let y(x) be the third derivative of x**5/160 + 13*x**4/64 + 11*x**3/8 - 17*x**2. Let y(c) = 0. What is c?
-11, -2
Suppose u + 11 = 2*x, -29*x + 27*x - 2*u = -14. Let q(c) be the first derivative of 0*c**2 + 36/5*c