7/105 + v**6/180 - 73*v**5/270 + 8*v**4/9 - 4*v**3/3 - 3*v**2 - 3. Suppose p(o) = 0. What is o?
-6, 1
Let a(k) = -87*k**3 + 240*k**2 - 48*k - 240. Let m(y) = 35*y**3 - 96*y**2 + 19*y + 96. Let r(u) = -5*a(u) - 12*m(u). Factor r(x).
3*(x - 2)**2*(5*x + 4)
Let b = 2124/5 - 423. Let b*s**2 + 2/5 - s**3 - 7/5*s + 1/5*s**4 = 0. What is s?
1, 2
Let s(q) be the second derivative of q**5/300 - q**3/30 + q**2 - q. Let l(u) be the first derivative of s(u). Factor l(r).
(r - 1)*(r + 1)/5
Let l(c) be the first derivative of c**3/3 - c - 13. Factor l(o).
(o - 1)*(o + 1)
Let i(q) be the second derivative of -q**7/189 - q**6/27 - 7*q**5/90 + q**4/54 + 8*q**3/27 + 4*q**2/9 - 21*q. Determine c so that i(c) = 0.
-2, -1, 1
Let y be 6/((-3)/((-3)/1)). Suppose -x + 4*x = y. Suppose -1/4 + 1/4*q**x + 0*q = 0. Calculate q.
-1, 1
Let y(w) be the third derivative of w**8/45360 - w**7/7560 - w**6/1620 - w**5/20 + w**2. Let m(j) be the third derivative of y(j). Find r such that m(r) = 0.
-1/2, 2
Let r(c) = 7*c**4 - 4*c**3 - 15*c**2 + 17*c - 8. Let k(s) = 22*s**4 - 12*s**3 - 46*s**2 + 50*s - 24. Let t(f) = 3*k(f) - 10*r(f). Factor t(d).
-4*(d - 1)**3*(d + 2)
Suppose -1009 = 5*b - 1024. Factor -4/13*k**2 - 2/13 + 6/13*k**4 + 2/13*k**5 + 4/13*k**b - 6/13*k.
2*(k - 1)*(k + 1)**4/13
Suppose f = -4*f - 20. Let x be 5*(-1)/10*f. Suppose -2*y**x + 4*y - 1 - 5 - y + 5*y**2 = 0. Calculate y.
-2, 1
Let h = 645/76 + -52/19. Let k = h - 11/2. Factor 1/4*t**2 - 1/4*t**3 - 1/4*t**4 + 0 + 0*t + k*t**5.
t**2*(t - 1)**2*(t + 1)/4
Let -4/9 - 2/9*k**3 - 10/9*k - 8/9*k**2 = 0. Calculate k.
-2, -1
Let r(k) = k**4 + k**2 + k. Let a(o) = -6*o**4 - o**3 - 3*o**2 - 5*o. Let w(h) = a(h) + 5*r(h). Suppose w(d) = 0. What is d?
-2, 0, 1
Let z(m) = 7*m**2 - 9*m + 5. Let k(v) = 20*v**2 - 26*v + 14. Let w(f) = 5*k(f) - 14*z(f). Factor w(x).
2*x*(x - 2)
Let s(m) be the second derivative of -m**5/20 + m**4/3 - 2*m**3/3 + 14*m. Find r, given that s(r) = 0.
0, 2
Suppose -8*g = 7 - 23. Factor -2/3*x**g + 0*x + 0.
-2*x**2/3
Let k(z) be the first derivative of -12*z + 9/2*z**6 - 17*z**3 + 63/5*z**5 + 21/4*z**4 - 24*z**2 - 1. Suppose k(a) = 0. Calculate a.
-1, -2/3, 1
Factor -2*i**3 + 8/3*i + 2/3*i**5 - 8/3*i**2 + 0 + 4/3*i**4.
2*i*(i - 1)**2*(i + 2)**2/3
Suppose -5*y = -6*y + 5. Let o(c) be the third derivative of 2/15*c**3 + 1/150*c**y + 0 + 0*c - c**2 + 1/20*c**4. Solve o(p) = 0 for p.
-2, -1
Let x(t) = t**3 - 13*t**2 - 49*t + 20. Let z be x(16). Find v such that 0 + 18/5*v**3 - 2*v**z - 4/5*v - 14/5*v**5 + 2*v**2 = 0.
-1, 0, 2/7, 1
Let f(p) be the first derivative of p**6/30 + p**5/5 + p**4/2 + 2*p**3/3 + p**2/2 - 3*p - 1. Let w(o) be the first derivative of f(o). Factor w(z).
(z + 1)**4
Let x(j) be the third derivative of -j**8/1120 - j**7/840 + j**6/240 + j**5/120 - j**3/3 + 3*j**2. Let h(q) be the first derivative of x(q). Factor h(f).
-f*(f - 1)*(f + 1)*(3*f + 2)/2
Let i(b) = -7*b**2 + b. Let w(a) = -6*a**2 + a. Suppose -p - 18 = -4*o, 2*p + 3*o + 15 = 4*o. Let l(f) = p*w(f) + 5*i(f). Factor l(q).
q*(q - 1)
Let f be -3*(-24)/(-9) - 1. Let s = 12 + f. Determine o so that 1/2 + 3/2*o**2 - 1/2*o**s - 3/2*o = 0.
1
Suppose j - 8*j = -21. Determine b, given that 1/3*b**4 + 4/3*b + b**2 - 4/3*b**j - 4/3 = 0.
-1, 1, 2
Factor -q**2 - 8*q**3 + 11*q + 7 - 5*q + 2*q**5 - 3*q**2 - 3.
2*(q - 2)*(q - 1)*(q + 1)**3
Let t(r) = -r + 5. Let h be t(-8). Let n = h + -9. Factor -50/3*f**n - 368/3*f**2 - 80*f**3 - 64*f - 32/3.
-2*(f + 2)**2*(5*f + 2)**2/3
Suppose 4*v + k = -13 + 48, -5*v - 4*k + 52 = 0. Let 6*s**4 + 5*s**3 - v*s**3 + 2*s**5 + 7*s**5 = 0. What is s?
-1, 0, 1/3
Suppose 3*q + w - 6 = -q, 0 = -5*q - 2*w + 6. Let m(k) = -k**3 + 4*k**2 - 4*k + 2. Let s be m(2). Factor t**s + t - q - 3 + 4 - t**3 + 0*t.
-(t - 1)**2*(t + 1)
Let a be (400/(-35))/20 + (-8)/(-14). Let 2/13*b**4 + 4/13*b + a + 10/13*b**2 + 8/13*b**3 = 0. Calculate b.
-2, -1, 0
Suppose 3*r = -r + 20. Suppose -4*n = r - 13. What is a in 1/5*a - 1/5 + 1/5*a**n - 1/5*a**3 = 0?
-1, 1
Let b be ((-4)/(-14))/(192/168). Factor -1/4*l**3 - 1/4*l**4 + b*l - 1/2 + 3/4*l**2.
-(l - 1)**2*(l + 1)*(l + 2)/4
Let f = 8/17 + -6/85. Let h(m) be the first derivative of -f*m - 1/10*m**4 - 2 + 2/15*m**3 + 1/5*m**2. Suppose h(c) = 0. Calculate c.
-1, 1
Let i(k) be the second derivative of -k**6/80 + 3*k**5/80 - k**3/8 + 3*k**2/16 - 2*k. Factor i(t).
-3*(t - 1)**3*(t + 1)/8
Suppose -4*y = -14 + 2. Suppose 2 = y*d - 2*d. Factor 1/2*o**d + o + 1/2.
(o + 1)**2/2
Let v(t) = -t**5 + t**3 + 1. Let s(k) = -k**5 + 8*k**4 - 13*k**3 + 8*k**2 - 2*k - 1. Let d(r) = -2*s(r) - 2*v(r). Factor d(b).
4*b*(b - 1)**4
Let p(o) be the first derivative of o**4/42 + 2*o**3/63 - o**2/21 - 2*o/21 - 20. Factor p(l).
2*(l - 1)*(l + 1)**2/21
Let t(a) be the third derivative of a**5/210 + a**4/42 + a**3/21 - a**2. Let t(m) = 0. Calculate m.
-1
Let b(t) be the second derivative of -t**4/20 + 25*t. Find a such that b(a) = 0.
0
Suppose -7*a + 8 = -5*a. Factor 3*o**4 - o**a - 9*o**3 + o**3 + 8*o**2.
2*o**2*(o - 2)**2
Factor -2/3*m**3 + 0 + 2/3*m - 2/3*m**2 + 2/3*m**4.
2*m*(m - 1)**2*(m + 1)/3
Let f(w) be the first derivative of -4*w**5 - 7*w**4 + 4*w**3 + 14*w**2 + 8*w + 53. Suppose f(b) = 0. What is b?
-1, -2/5, 1
Let v(m) = -m**2 + 7*m - 9. Let p be v(4). Find b such that 0 + 2*b**3 - 3*b**p - 8*b + b - 5*b**2 - 3 = 0.
-3, -1
Suppose 21 = 3*o - 3*s, -3*o + 13 = -5*s - 16. Factor 4*k - 75 + 2*k**o + 6*k**2 + 75.
2*k*(k + 1)*(k + 2)
Let z be ((-2)/1)/2 + 3. Let c(d) be the third derivative of 0*d**4 - 1/10*d**5 - z*d**2 + 1/40*d**6 + 0*d**3 + 0 + 0*d. Suppose c(f) = 0. What is f?
0, 2
Let b(w) be the first derivative of -7*w**6/25 - 29*w**5/50 - 2*w**4/15 + 4*w**3/15 + 4*w + 8. Let f(x) be the first derivative of b(x). Solve f(n) = 0 for n.
-1, -2/3, 0, 2/7
Let v(m) = -4*m**5 - m**4 - 4*m**3 + 10*m**2 + 4*m - 5. Let r(g) = g**5 - g**4 + g**3 - 1. Let n(f) = 3*r(f) + v(f). Factor n(a).
-(a - 1)**2*(a + 2)**3
Let c(i) be the first derivative of 6 - 3*i**4 - 4*i**3 - 2*i**2 + 0*i - 4/5*i**5. What is v in c(v) = 0?
-1, 0
Let o be ((-6)/3)/4 + (-5)/(-2). Determine h so that 3*h**5 - 11/4*h**4 + 0*h**o + 0*h + 0 + 1/2*h**3 = 0.
0, 1/4, 2/3
Find c, given that -c**4 - 1 + 3*c**3 - 3/2*c - 3/2*c**5 + 2*c**2 = 0.
-1, -2/3, 1
Find k such that 0*k + 1/5*k**5 + 0*k**4 - 3/5*k**3 - 2/5*k**2 + 0 = 0.
-1, 0, 2
Let b(k) be the first derivative of 2 + 1/12*k**3 - 1/2*k + 3/8*k**2 - 3/16*k**4 + 1/20*k**5. Find m, given that b(m) = 0.
-1, 1, 2
Let i(z) = -904*z**3 + 804*z**2 + 176*z - 36. Let s(c) = 129*c**3 - 115*c**2 - 25*c + 5. Let j(b) = -3*i(b) - 20*s(b). Factor j(n).
4*(n - 1)*(3*n + 1)*(11*n - 2)
Let h(t) be the first derivative of 5*t**4/8 - 5*t**3/3 - 25*t**2/4 + 15*t - 22. Factor h(s).
5*(s - 3)*(s - 1)*(s + 2)/2
Let w = -9 + 14. Solve 0*z**2 + 3*z**2 + 3 - 4*z - 5*z**2 - w = 0 for z.
-1
Let n be (-2)/(-1)*19/7. Let q = n + -100/21. Factor q - 7/3*c + 7/3*c**3 - 2/3*c**2.
(c - 1)*(c + 1)*(7*c - 2)/3
Let c(a) be the second derivative of a**8/224 - a**7/35 + a**6/16 - a**5/20 + 3*a**2/2 + 2*a. Let v(l) be the first derivative of c(l). What is s in v(s) = 0?
0, 1, 2
Determine r, given that 15*r**4 + 45/4*r**5 - 25*r**3 + 55/4*r - 25/2*r**2 - 5/2 = 0.
-2, -1, 1/3, 1
Let y be -4*1/(-6)*198/96. Let o(q) be the first derivative of -y*q**4 + 9/10*q**5 - 1/2*q - 5/24*q**6 + 1 + 3/8*q**2 + 2/3*q**3. Factor o(n).
-(n - 1)**4*(5*n + 2)/4
Let c = -3 - -5. Suppose -2*m + 4 = -6*m - 3*r, 16 = 4*m - 2*r. Factor -4*b**2 + m*b + b**2 + b**c + 4*b**2.
2*b*(b + 1)
Let g(v) be the second derivative of -2*v + 1/12*v**4 + 0*v**2 + 0 + 0*v**3. Factor g(j).
j**2
Suppose -3*w + 1 - 10 = 0. Let x be w*((-1)/(-3) + -1). Factor -t + 2*t + t**2 - x*t.
t*(t - 1)
Let f(d) be the first derivative of d**7/14 + d**6/5 - d**4/2 - d**3/2 + 2*d + 2. Let m(v) be the first derivative of f(v). Suppose m(g) = 0. What is g?
-1, 0, 1
Let c(b) = 2*b - 3*b**4 - 5*b**2 + b**3 + 11*b**2 + 0*b**2. Let n(y) = -6*y**4 + 2*y**3 + 11*y**2 + 3*y. Let p(f) = 10*c(f) - 6*n(f). Solve p(x) = 0 for x.
-1, 0, 1/3, 1
Let f(v) = 10*v**5 - 4*v**4 - 7*v**2 + 7. Let d be (-3)/6 - 13/2. Let x(u) = 3*u**5 - u**4 - 2*u**2 + 2. Let y(w) = d*x(w) + 2*f(w). Solve y(t) = 0.
-1, 0
Suppose 6*j - 60 = j. Let p = -8 + j. Suppose 1/4*f**p + 1/4*f**2 + 0*f - 1/2*f**3 + 0 = 0. What is f?
0, 1