o) be the first derivative of 0*o - t*o**4 + 0*o**2 - 5/3*o**3 + 6. Factor a(d).
-5*d**2*(d + 1)
Let w(m) be the first derivative of m**6/180 - m**5/30 + 2*m**3 - 2. Let y(k) be the third derivative of w(k). Factor y(d).
2*d*(d - 2)
Let h be ((-10)/(-6)*1)/(7/21). Suppose 3 = 4*i + w, -h*w - 1 = 24. Factor 3/7 + 0*q - 3/7*q**i.
-3*(q - 1)*(q + 1)/7
Let z(s) be the first derivative of -5*s**4/4 + 40*s**3/3 - 75*s**2/2 + 364. Find o such that z(o) = 0.
0, 3, 5
Let h(f) be the second derivative of f**6/6 - 11*f**5/4 - 65*f**4/12 + 55*f**3/6 + 30*f**2 - 34*f. Suppose h(s) = 0. What is s?
-1, 1, 12
Let y(h) = -h**3 - 10*h**2 + 6*h - 30. Let i be y(-9). Let j = i - -168. Find k such that -1/4*k**j - 1/2*k - 3/4*k**2 + 0 = 0.
-2, -1, 0
Let q(x) = 6*x**4 - 12*x**3 - 6*x**2 + 12*x + 15. Let w(s) = s**4 + s**3 - s**2 - s + 5. Let a(i) = q(i) - 3*w(i). Factor a(y).
3*y*(y - 5)*(y - 1)*(y + 1)
Suppose 39*f = 55 + 23. Find c such that -4/5*c**f + 4/5*c**4 + 8/5*c**3 - 8/5*c + 0 = 0.
-2, -1, 0, 1
Suppose 60/7 - 58/7*h - 2/7*h**2 = 0. What is h?
-30, 1
Let p = -9436 + 9439. Let -3/2*j + 0*j**4 - 1/8*j**5 + 7/8*j**p + 1 - 1/4*j**2 = 0. What is j?
-2, 1, 2
Let q = 1/641 - -2561/1923. Factor -2*t**3 - 1/3*t**5 - 1/3*t + 0 + 4/3*t**2 + q*t**4.
-t*(t - 1)**4/3
Let t(h) = -h**2 - 18*h + 90. Let i be t(-22). Suppose -3*d - 2/3 - 10/3*d**i = 0. What is d?
-1/2, -2/5
Let l(w) = w**3 + 6*w**2 - 9*w - 50. Let a be l(-6). Suppose -1/7*h**a + 0 - 3/7*h**2 + 3/7*h**3 + 1/7*h = 0. What is h?
0, 1
Let q be (1 - 1)*(-10)/(-190)*19. Factor -2/7*i**2 + 8/7 + q*i.
-2*(i - 2)*(i + 2)/7
Factor -1024 - 17*o - 2*o - o**2 + 10*o - 43*o - 12*o.
-(o + 32)**2
Let i(f) be the third derivative of -f**5/70 - 47*f**4/252 - 10*f**3/63 + 3*f**2 - 16*f. Find w, given that i(w) = 0.
-5, -2/9
Let d(q) = -q**2 - q + 2. Let r be d(-2). Find p such that -2 + 14 - 3*p**3 + r*p**2 - 9*p**2 = 0.
-2, 1
Let y(t) be the second derivative of 8*t**5/25 - 11*t**4/15 + 2*t**3/5 + 27*t. Factor y(c).
4*c*(c - 1)*(8*c - 3)/5
Let h be (-38)/(4 + 5 + -12). Let f = -11 + h. Factor -f*d**2 + 4/3 + 8/3*d.
-(d - 2)*(5*d + 2)/3
Let s be (-55)/(-130) + 12/(-9). Let q = s - -14/13. Factor -1/6*m**2 + 0*m + q.
-(m - 1)*(m + 1)/6
Let b(p) = -7*p**4 + 10*p**3 - 8*p**2 - 22*p + 15. Let q(s) = 8*s**4 - 9*s**3 + 7*s**2 + 23*s - 15. Let u(f) = 7*b(f) + 6*q(f). Factor u(o).
-(o - 15)*(o - 1)**2*(o + 1)
Suppose -68 = -2*i + z - 59, -z = 3*i - 6. Solve -4/5*m**2 + 12/5*m**i - 8/5*m + 0 = 0 for m.
-2/3, 0, 1
Let p(b) be the first derivative of b**6/2 + 171*b**5/5 + 630*b**4 + 784*b**3 - 209. Solve p(t) = 0 for t.
-28, -1, 0
Suppose 5*v = l + 7, -756*l + 758*l - 5*v = -4. Solve 24/7 - 166/7*g**2 - 2/7*g**l + 142/7*g**4 - 40/7*g + 6*g**5 = 0 for g.
-3, -1, -2/3, 2/7, 1
Let b be (654/(-981))/((-2)/6). Factor -1/3*z**b + 0*z - 1/3*z**3 + 0.
-z**2*(z + 1)/3
Let j(h) = h**5 - h**2 - h + 1. Let n(s) = s**5 + 12*s**4 + 15*s**3 - 64*s**2 - 16*s + 52. Let m(y) = 4*j(y) - n(y). What is r in m(r) = 0?
-2, -1, 1, 2, 4
Let m = -107 - -113. Let y be (-2)/(-5) - 0/m. Factor -1/5*f**2 + y*f - 1/5.
-(f - 1)**2/5
Factor 0 + 2/11*h**2 + 42/11*h.
2*h*(h + 21)/11
Suppose o = 2*o - 0*o. Let v(k) be the third derivative of 1/3*k**4 - 4*k**2 + o*k - 2/3*k**3 - 1/20*k**5 + 0. Let v(s) = 0. Calculate s.
2/3, 2
Let t(l) = l**3 - 22*l**2 + 24*l - 12. Let q = -2 + 23. Let f be t(q). What is o in 24 + 882*o**2 + 66*o - f*o + 1029*o**3 + 116*o + 121*o = 0?
-2/7
Let y(u) = -4*u**2 - 6*u - 20. Let i(w) = -3*w**2 - 5*w - 17. Let k(c) = -6*i(c) + 5*y(c). Solve k(o) = 0.
-1, 1
Let b(o) = -18 + 105 + 5*o - 2*o + 9*o. Let h be b(-7). Suppose -i**h - 28/5*i - 8/5 - 22/5*i**2 = 0. Calculate i.
-2, -2/5
Let p(r) = 23*r**4 - 58*r**3 + 17*r**2 - 17*r. Let b(m) = -4*m**4 + 10*m**3 - 3*m**2 + 3*m. Let n(q) = -34*b(q) - 6*p(q). Suppose n(a) = 0. Calculate a.
0, 4
Factor -2*r**2 + 0*r**2 + 51*r + 58*r - 2*r**2 + 27*r - 1156.
-4*(r - 17)**2
Let x(c) be the second derivative of c**5/20 - 127*c**4/4 + 16129*c**3/2 - 2048383*c**2/2 + 2*c - 75. Factor x(h).
(h - 127)**3
Let b = -839 - -839. Let l(g) be the second derivative of 0 + 1/21*g**3 + 6*g - 1/14*g**4 + b*g**2. Suppose l(d) = 0. Calculate d.
0, 1/3
Factor 0*g + 0 + 2*g**2 - 2/9*g**4 + 0*g**3.
-2*g**2*(g - 3)*(g + 3)/9
Let i(f) be the third derivative of 0 + 17*f**2 + 1/2352*f**8 + 1/1470*f**7 + 0*f**3 - 1/280*f**6 + 1/84*f**4 - 1/420*f**5 + 0*f. Find n, given that i(n) = 0.
-2, -1, 0, 1
Let q(i) be the second derivative of i**5/160 - 7*i**4/48 + 13*i**3/48 - 709*i. Find k such that q(k) = 0.
0, 1, 13
Let k(h) = 5*h**4 + 11*h**3 + 34*h**2 - 107*h + 43. Let b(m) = 2*m**4 + 5*m**3 + 18*m**2 - 53*m + 22. Let s(c) = 7*b(c) - 3*k(c). Factor s(g).
-(g - 5)*(g - 1)**2*(g + 5)
Let b be (-8)/(-6)*(13 + 69/(-6)). Let f(k) be the first derivative of 0*k - 2/5*k**5 - k**2 + 2/3*k**3 + 1/2*k**4 - b. Factor f(o).
-2*o*(o - 1)**2*(o + 1)
Let k(p) be the third derivative of 0 + 0*p**5 + 37*p**2 + 3/2*p**4 + 0*p - 1/30*p**6 - 1/315*p**7 + 9*p**3. Factor k(a).
-2*(a - 3)*(a + 3)**3/3
Suppose -10*p = 34 - 64. Let t be (-7)/28 - (-1)/4. Find w such that 3/2*w + t*w**2 - 3/2*w**p - 3/4*w**4 + 3/4 = 0.
-1, 1
Let p(y) = -4*y**2 - 21*y + 22. Let l(g) = -3*g**2 - 20*g + 21. Let d(k) = -3*l(k) + 2*p(k). Solve d(q) = 0.
-19, 1
Let j be 1*0/(-3) + 0. Suppose j = -2*x - 12*x. Factor 0*l**2 + 0 + 1/3*l**4 + x*l + 0*l**3.
l**4/3
Let f(m) = -m**3 - 4*m**2 - 5*m - 4. Let g be f(-3). Factor 0 + 2/5*k**5 + 8/5*k**4 + 0*k**g + 0*k + 8/5*k**3.
2*k**3*(k + 2)**2/5
Let t(w) = w + 35. Let d be t(-17). Let -41*k**2 + 38*k + 16*k + 45*k**2 - d*k = 0. Calculate k.
-9, 0
Suppose -3*i = 4*k - 17 + 3, -i + 4*k = 6. Factor 7*h - 5*h**4 + 10*h**i - 2*h - 5*h - 5*h**3.
-5*h**2*(h - 1)*(h + 2)
Let i be ((-27)/(-60))/((-3)/(-15)). Let v = 95 + -187/2. Let 0*r**3 - i*r**2 + 3/4*r**4 - v*r + 0 = 0. What is r?
-1, 0, 2
Let s be (-1 + 1)/((-2)/((-26)/26)). Suppose 2/3*n**3 + 2/3*n + 4/3*n**2 + s = 0. What is n?
-1, 0
Let l(d) = -d**3 + 40*d - 74*d + 33*d. Let u(j) = -2*j**3 - 3*j**2 + 3. Let w(y) = -l(y) + u(y). Factor w(p).
-(p - 1)*(p + 1)*(p + 3)
Factor 88/13 + 2/13*l**3 - 74/13*l - 16/13*l**2.
2*(l - 11)*(l - 1)*(l + 4)/13
Let c be 63 + -85 - (-4 + -21). Factor -4/3*y**4 - 8/3*y**c + 4/3*y**2 + 0 + 8/3*y.
-4*y*(y - 1)*(y + 1)*(y + 2)/3
Suppose -9 = 3*x - 0*x. Let b = 0 - x. Factor b*r**2 + 0*r + 3*r + 3*r**3 + 0*r + 3*r**2.
3*r*(r + 1)**2
Let m be -2*3/(-24) - (-60)/16. Let x(i) be the second derivative of 1/6*i**m + 0 + 1/3*i**3 + 0*i**2 + 2*i. Factor x(w).
2*w*(w + 1)
Let 408*j - 415*j - 3 - j**2 + 3*j**2 + 9 = 0. Calculate j.
3/2, 2
Let k(g) be the first derivative of 3*g**4/8 - g**3/2 - 6*g**2 + 18*g + 85. Suppose k(h) = 0. What is h?
-3, 2
Let l(t) = -t**3 + 17*t**2 + 21*t - 8. Let i be l(18). Suppose 5*q - i + 31 = 0. Solve 0*y**4 - 1/5*y**5 - 1/5*y + 0*y**2 + 0 + 2/5*y**q = 0 for y.
-1, 0, 1
Suppose 1/4*o**4 - 19/2*o + 15/4 - 5/2*o**3 + 8*o**2 = 0. What is o?
1, 3, 5
Let x be 26/(-1287)*11 + (-28)/(-45). Factor 1/5*b**3 - x*b - 1/5*b**2 + 0.
b*(b - 2)*(b + 1)/5
Let n(f) be the third derivative of f**9/40320 - f**8/2688 + f**7/480 - f**6/160 - 8*f**5/15 - 47*f**2. Let y(i) be the third derivative of n(i). Factor y(w).
3*(w - 3)*(w - 1)**2/2
Let n(q) be the first derivative of -q**7/560 + q**6/480 + q**5/160 - 11*q**3/3 + 5. Let c(d) be the third derivative of n(d). Factor c(m).
-3*m*(m - 1)*(2*m + 1)/4
Let t(c) = -10*c**3 + c**2 - 9*c. Let o = 68 - 37. Let f(i) = -o - i**3 - i + 31. Let u(r) = -18*f(r) + 2*t(r). Let u(v) = 0. What is v?
0, 1
Let y(m) be the first derivative of m**4/9 - 2*m**3/3 + 4*m**2/9 + 39. Let y(r) = 0. Calculate r.
0, 1/2, 4
Let v be (147/(-12) + 0)*-34*8. Factor 2*u**3 + 4*u**2 - v - 6*u + 3332.
2*u*(u - 1)*(u + 3)
Let z(k) be the third derivative of -k**7/14 + k**6/5 - 3*k**5/20 - 19*k**2 + 1. Factor z(j).
-3*j**2*(j - 1)*(5*j - 3)
Solve -4802/17 - 2/17*a**2 + 196/17*a = 0 for a.
49
Factor -1/7*l**3 + 30/7*l + 29/7*l**2 + 0.
-l*(l - 30)*(l + 1)/7
Let u be 14/48 + 129/344. Factor 2/3*i**2 - 4/3 + u*i.
2*(i - 1)*(i + 2)/3
Let w(d) be the first derivative of 0*d**2 - 1/6*d**3 + 15 + 1/8*d**4 + 0*d. Factor w(s).
s**2*(s - 1)/2
Suppose 2*y = 5*x - 11, 4*y - 6 + 4 = 2*x. Let n(c) be the second derivative of 0 - 2*c + 1/30*c**4 + 1/5*c**2 + 2/15*c