 w**6/450 - w**5/75 + 5*w**4/12 - 6*w. Let z(s) be the third derivative of l(s). What is i in z(i) = 0?
2
Let u(p) be the third derivative of p**6/420 + p**5/35 - p**4/12 + 25*p**2. Factor u(z).
2*z*(z - 1)*(z + 7)/7
Factor -2/9*i**2 - 4/9*i + 0.
-2*i*(i + 2)/9
Let q be 126/60 + 0 + 1*-2. Let h(p) be the first derivative of 1/25*p**5 + 1 - 1/5*p**3 + 4/5*p + 2/5*p**2 - q*p**4. Suppose h(y) = 0. Calculate y.
-1, 2
Factor 2/9*m**2 - 2/9*m**4 - 4/9*m**3 + 0 + 4/9*m.
-2*m*(m - 1)*(m + 1)*(m + 2)/9
Let g = 41 - 61. Let l be 2/g*-4*3. What is m in 0 + l*m**5 + 14/5*m**3 + 0*m - 4/5*m**2 - 16/5*m**4 = 0?
0, 2/3, 1
Factor -9/8*b**2 + 3/4 - 3/8*b + 3/8*b**3 + 3/8*b**4.
3*(b - 1)**2*(b + 1)*(b + 2)/8
Solve 144*m**3 + 143*m**2 - 1 - 4*m - 7 + 0 + 5*m**2 = 0 for m.
-1, -1/4, 2/9
Determine p, given that -15/4*p**3 - 6 - 3/2*p**4 + 15/2*p**2 + 3/4*p**5 + 3*p = 0.
-2, -1, 1, 2
Find z, given that 30*z**3 + 3*z**4 - 6*z**4 - 15*z - 8*z**5 + 12*z**2 - 3*z**4 - 6 - 7*z**5 = 0.
-1, -2/5, 1
Let u(t) = 19*t**2 - 21*t + 13. Let x(v) = 10*v**2 - 10*v + 6. Let i(k) = -6*u(k) + 11*x(k). Factor i(h).
-4*(h - 3)*(h - 1)
Let w(b) be the second derivative of b**7/84 + b**6/6 + 33*b**5/40 + 5*b**4/3 + 4*b**3/3 - 9*b. What is p in w(p) = 0?
-4, -1, 0
Let b(m) be the first derivative of -m**5/30 + m**4/18 + 2*m**3/9 + 2*m + 4. Let d(h) be the first derivative of b(h). Factor d(i).
-2*i*(i - 2)*(i + 1)/3
Let m(a) be the first derivative of -3*a**4/4 + a**3 + 8. Factor m(h).
-3*h**2*(h - 1)
Let v be (-11 - -8)/(-8 - -3). Factor -1/5*s**5 + 0 - v*s**3 + 0*s + 3/5*s**4 + 1/5*s**2.
-s**2*(s - 1)**3/5
Suppose -8 + 2 = 2*u. Let i(s) = -2*s**4 - 5*s**3 - 3*s**2 + 3*s. Let x(r) = 5*r**4 + 14*r**3 + 8*r**2 - 8*r. Let k(b) = u*x(b) - 8*i(b). Factor k(z).
z**3*(z - 2)
Let o(m) be the first derivative of -1/20*m**4 - 1/2*m**2 - 2/15*m**3 + 1/30*m**5 + 0*m - 3. Let p(b) be the second derivative of o(b). Factor p(n).
2*(n - 1)*(5*n + 2)/5
Let c be (-60)/(-14) - (-25)/((-125)/20). Factor 0*u - 2/7 + c*u**2.
2*(u - 1)*(u + 1)/7
What is x in -30*x - 24 + 24*x - 46*x - 16 + 12*x**2 = 0?
-2/3, 5
Let m(w) be the third derivative of -w**7/70 + 3*w**6/20 - 13*w**5/20 + 3*w**4/2 - 2*w**3 - 6*w**2. Factor m(h).
-3*(h - 2)**2*(h - 1)**2
Let g(n) be the third derivative of -1/9*n**3 - 1/24*n**4 + 0 + 1/20*n**5 + 6*n**2 + 0*n. Factor g(f).
(3*f - 2)*(3*f + 1)/3
Let m(d) be the third derivative of -d**8/840 - 2*d**7/525 + d**5/75 + d**4/60 + 3*d**2. Suppose m(s) = 0. Calculate s.
-1, 0, 1
Suppose 4*s + 2*w = 6*w + 44, w = -3*s + 21. Let i be (0 - 3)/((-12)/s). Find y such that y - 6*y - y**i + 4*y = 0.
-1, 0
Let n(a) be the first derivative of -a**7/1260 + a**6/2160 + a**5/180 - a**4/144 - 2*a**3 + 7. Let b(w) be the third derivative of n(w). Factor b(t).
-(t - 1)*(t + 1)*(4*t - 1)/6
Factor -9/4 + 2*q**2 + 3/2*q**3 - 3/2*q + 1/4*q**4.
(q - 1)*(q + 1)*(q + 3)**2/4
Let l(q) be the first derivative of 32/21*q**3 + 3*q**2 + 1 + 18/7*q + 2/7*q**4. Find a, given that l(a) = 0.
-3/2, -1
Let j be ((-5)/((-120)/9))/((-9)/(-12)). Let 0 - x - j*x**2 = 0. What is x?
-2, 0
Suppose -8 = -6*o + 2*o. Let p(k) = -k**2 + k - 1. Let l(a) = -3*a**2 + 3*a + 3. Let t(m) = o*p(m) - 2*l(m). Determine i, given that t(i) = 0.
-1, 2
Let v be 7/(-7) - (-8)/2. Let h = v - 1. Suppose 2*f**2 - 6*f**h + 2*f**2 = 0. Calculate f.
0
Let w(x) be the second derivative of -4*x**6/105 + 2*x**5/5 - 61*x**4/42 + 2*x**3 - 9*x**2/7 + 6*x. Factor w(k).
-2*(k - 3)**2*(2*k - 1)**2/7
Let r(a) = -9*a**4 + 11*a**3 + 14*a**2 - 60*a + 44. Let t(s) = -35*s**4 + 45*s**3 + 55*s**2 - 240*s + 175. Let j(o) = 15*r(o) - 4*t(o). Solve j(v) = 0.
-2, 1, 2
Let k(l) be the first derivative of -l**5/30 + l**4/18 + 5*l - 2. Let b(z) be the first derivative of k(z). Suppose b(f) = 0. What is f?
0, 1
Let m(k) be the second derivative of k**10/136080 - k**9/22680 + k**8/10080 - k**7/11340 - k**4/12 + 5*k. Let h(v) be the third derivative of m(v). Factor h(b).
2*b**2*(b - 1)**3/9
Let z be 3*6*(-13)/(-182). Factor 3/7*m**2 - 6/7*m + z*m**3 + 0.
3*m*(m + 1)*(3*m - 2)/7
Let n(m) be the third derivative of -m**6/720 - m**5/360 + m**4/144 + m**3/36 - 4*m**2. Factor n(v).
-(v - 1)*(v + 1)**2/6
Let r(d) be the second derivative of -1/36*d**3 - 6*d + 1/72*d**4 + 0*d**2 + 0. Factor r(w).
w*(w - 1)/6
Let t = 1/7038 - -32833/77418. Let m = t + -1/11. Factor -m*d + 0 - 1/3*d**3 + 2/3*d**2.
-d*(d - 1)**2/3
Let i = 800/7 - 114. Let n = 2/55 + 96/385. Determine z, given that 0 - n*z - i*z**2 = 0.
-1, 0
What is u in 3/5*u - 3/5*u**3 + 3/5*u**2 + 0 - 3/5*u**4 = 0?
-1, 0, 1
Let s be 4/2 - 62/(-2). Let w = -28 + s. Factor -7/5*b - 2/5*b**3 - 8/5*b**2 - 2/5 + 2/5*b**4 + 1/5*b**w.
(b - 2)*(b + 1)**4/5
Let z be 8/(-68) - (-44)/85. Let t = -6 - -6. Factor t + 0*n**3 + z*n**5 + 4/5*n**2 - 2/5*n - 4/5*n**4.
2*n*(n - 1)**3*(n + 1)/5
Let q = -1685 - -1685. Suppose 0 = -w + 2. Let 2/5*v**3 + 2/5*v**w + q*v + 0 = 0. What is v?
-1, 0
Let f(q) be the second derivative of 0 - 1/150*q**6 - 1/10*q**2 - q + 1/50*q**5 - 1/30*q**3 - 1/210*q**7 + 1/30*q**4. Let f(d) = 0. What is d?
-1, 1
Let d be 1 + 2/4*16. Factor 9*i**2 - 3*i + i**3 - 2 - d*i**2.
(i - 2)*(i + 1)**2
Let z(k) be the first derivative of -k**9/1512 - k**8/420 + k**6/90 + k**5/60 - 2*k**3/3 - 3. Let a(i) be the third derivative of z(i). Factor a(y).
-2*y*(y - 1)*(y + 1)**3
Let g(b) = 5*b**3 - 6*b**2 - 9*b + 10. Let y(x) = x**2 - x. Let p(u) = -g(u) + 4*y(u). Factor p(k).
-5*(k - 2)*(k - 1)*(k + 1)
Let g(x) = -x**3 - 20*x**2 - 20*x - 14. Let s be g(-19). Let y(r) be the first derivative of 2/7*r + 0*r**4 + 2/35*r**s - 3 + 0*r**2 - 4/21*r**3. Factor y(f).
2*(f - 1)**2*(f + 1)**2/7
Let o(q) be the first derivative of -q**6/18 + q**4/3 - 2*q**3/9 - q**2/2 + 2*q/3 - 30. Factor o(a).
-(a - 1)**3*(a + 1)*(a + 2)/3
Let g(s) be the first derivative of 0*s + 0*s**4 + s**2 + 1/5*s**5 + 3 - s**3. Factor g(w).
w*(w - 1)**2*(w + 2)
Let f be (-6)/42 + (-284)/(-224). Factor 3/8*p**3 + 0 + 3/4*p - f*p**2.
3*p*(p - 2)*(p - 1)/8
Let w(d) be the third derivative of 0*d + d**2 - 1/140*d**6 + 3/56*d**4 - 1/14*d**3 - 1/784*d**8 + 0 + 3/490*d**7 - 1/70*d**5. Find c, given that w(c) = 0.
-1, 1
Let i(a) be the first derivative of -1/10*a**5 - a + 1 + 1/6*a**4 - 1/15*a**6 + 1/3*a**3 + 0*a**2. Let b(g) be the first derivative of i(g). Factor b(l).
-2*l*(l - 1)*(l + 1)**2
Suppose 3*s - 1 - 11 = 0. Let r(h) be the third derivative of 1/240*h**6 + h**2 + 1/48*h**s + 0*h - 1/60*h**5 + 0*h**3 + 0. Factor r(k).
k*(k - 1)**2/2
Let g = 3 + 1. Factor 6 - 3*l**4 - 2 + 6*l + l**g - 2*l**2 - 6*l**3.
-2*(l - 1)*(l + 1)**2*(l + 2)
Let g = -21996630155/1036 - -21232271. Let j = g - -9/148. Factor -8/7*b - j*b**3 + 24/7*b**2 + 0.
-2*b*(3*b - 2)**2/7
Let s = -25 + 15. Let v be s/(-3) + (-8 - -5). Factor 0 + 1/3*y**2 - v*y.
y*(y - 1)/3
Suppose 0 = -4*w + 2*w. Suppose w = -5*a + 5 + 5. Factor 1/2*j**a + 0 - 1/2*j.
j*(j - 1)/2
Let c(q) be the second derivative of q**7/105 - q**6/60 - q**5/30 + q**4/12 - q**2 + 3*q. Let x(l) be the first derivative of c(l). What is p in x(p) = 0?
-1, 0, 1
Suppose 5*x = 2*x. Let s(m) be the third derivative of -1/6*m**4 - 3*m**2 + 0*m + 1/30*m**5 + x + 0*m**3. Determine h so that s(h) = 0.
0, 2
Let p(v) be the third derivative of -49*v**6/24 + 21*v**5/2 - 25*v**4/2 + 20*v**3/3 - 4*v**2. Suppose p(b) = 0. Calculate b.
2/7, 2
Let r(p) be the third derivative of p**7/735 - 2*p**6/105 + 8*p**5/105 - 8*p**2. Factor r(b).
2*b**2*(b - 4)**2/7
Let n(d) be the second derivative of d - 1/2*d**3 + 0 + 3/4*d**2 + 1/8*d**4. Suppose n(j) = 0. Calculate j.
1
Let b(v) be the first derivative of v**6/420 - v**5/210 - v**4/84 + v**3/21 + v**2/2 + 3. Let r(x) be the second derivative of b(x). Factor r(p).
2*(p - 1)**2*(p + 1)/7
Let v(u) = 3*u**2 + 96*u + 2. Let l be v(-32). Determine w, given that 3*w**l + 0 - 9/4*w = 0.
0, 3/4
Determine a so that 2/5*a**3 - 4/5*a**5 + 0 - 2/5*a**4 + 0*a**2 + 0*a = 0.
-1, 0, 1/2
Let d(u) be the second derivative of u**4/36 + u**3/18 - 10*u. Find s, given that d(s) = 0.
-1, 0
Let k be (0 + 3 - 3)/1. Factor 0*n + k - 2/7*n**4 + 0*n**2 + 2/7*n**5 + 0*n**3.
2*n**4*(n - 1)/7
Factor 4/5*b**3 - 8/5*b**2 + 4/5*b**4 + 0*b + 0.
4*b**2*(b - 1)*(b + 2)/5
Let q(s) be the third derivative of 1/945*s**7 - 7*s**2 + 0*s + 0 + 1/1512*s**8 + 0*s**4 - 1/270*s**