n**4/16 - n**3 - 3*n**2/2 + 117*n. Factor a(x).
3*(x - 2)*(x + 1)**2*(x + 2)/4
Let z(q) be the second derivative of 0*q**2 + 2*q + 0 - 1/4*q**5 + 1/6*q**6 + 5/6*q**3 - 5/12*q**4. Find s, given that z(s) = 0.
-1, 0, 1
Let l(a) be the first derivative of 2*a**6/39 - 6*a**5/65 - 3*a**4/26 + 4*a**3/39 + 146. What is f in l(f) = 0?
-1, 0, 1/2, 2
Let u(j) = -65*j**2 + 217*j + 64. Let a(b) = -24*b - 28*b + 27*b - 29*b + 16*b**2 - 16. Let v(c) = 9*a(c) + 2*u(c). Factor v(l).
2*(l - 4)*(7*l + 2)
Let j(y) be the second derivative of y**6/360 - y**5/30 + y**4/6 + y**3/6 + 36*y. Let g(x) be the second derivative of j(x). Factor g(t).
(t - 2)**2
Let z(p) be the second derivative of -10*p + 4/5*p**2 + 0 + 2/5*p**3 + 0*p**4 - 1/25*p**5. Suppose z(h) = 0. Calculate h.
-1, 2
Suppose 0 = 4*p + p + 50. Let r = p - -12. Factor -3*c**2 - c - 5*c + 2*c**r - 2*c**2 - 3.
-3*(c + 1)**2
Let 20/9*k**4 + 28/9*k**2 + 0*k + 0 - 2/9*k**5 - 46/9*k**3 = 0. What is k?
0, 1, 2, 7
Suppose 0 = 4*d + 2*w + 3*w - 72, 18 = d + 2*w. Let b be (1/((-16)/d))/(36/(-48)). Suppose 1/2*a**2 + b - 2*a = 0. Calculate a.
1, 3
Suppose 3*h = 2*i + 18, -75*h - 24 = 2*i - 79*h. Let 0*k + i - 2/5*k**2 = 0. What is k?
0
Let f(t) = 6*t**3 - 6*t**2 - 12*t + 10. Let m(i) = 13*i**3 - 11*i**2 - 24*i + 25. Let x(d) = -5*f(d) + 2*m(d). Determine c so that x(c) = 0.
-1, 0, 3
What is d in 109/3*d - 1/3*d**3 + 13*d**2 + 70/3 - 1/3*d**4 = 0?
-5, -2, -1, 7
Suppose -15*r**3 + 57*r**3 + 64*r**3 + 900*r**4 + 16*r**2 + 134*r**3 = 0. What is r?
-2/15, 0
Let h(y) be the first derivative of y**3/3 - 13*y**2/7 - 8*y/7 - 632. Factor h(t).
(t - 4)*(7*t + 2)/7
Let t(a) = -a**2 - a - 23. Let s be t(0). Let g be s/(-12) + (-17)/(-6) + -3. Find j such that 1 + g*j - 1/2*j**2 = 0.
-1/2, 4
Let q(u) be the third derivative of -u**8/448 - 2*u**7/5 - 3133*u**6/160 + 169*u**5/40 + 301*u**4 + 784*u**3 + 867*u**2. Let q(o) = 0. What is o?
-56, -1, 2
Solve 1/3*r**2 + 48 - 8*r = 0.
12
Solve -12 - 4/3*x**3 - 5/3*x**2 + 1/3*x**4 + 12*x = 0 for x.
-3, 2, 3
Let f(j) be the second derivative of 5*j**7/42 + 13*j**6/6 + 5*j**5/2 - 10*j**4 - 2*j - 109. Find d such that f(d) = 0.
-12, -2, 0, 1
Let a(z) be the first derivative of -z**3/2 + 9*z**2/2 + 165*z/2 + 812. Factor a(p).
-3*(p - 11)*(p + 5)/2
Let u(b) be the first derivative of b**3/3 - 19*b**2 + 361*b + 121. Find h such that u(h) = 0.
19
Let n(i) be the second derivative of -5/6*i**4 + 4*i + 0 + 2/3*i**3 + 0*i**2. Factor n(u).
-2*u*(5*u - 2)
Suppose -35*y + 31*y = -10*y. Factor 1/3*d**2 + 2/3*d + y.
d*(d + 2)/3
Let w(c) be the second derivative of -c**5/15 - 3*c**4 - 54*c**3 + 17*c**2/2 + 13*c. Let y(r) be the first derivative of w(r). Find o such that y(o) = 0.
-9
Let s(w) be the third derivative of 27*w**6/10 + 3*w**5/5 + w**4/24 - 43*w**2 + 1. Factor s(n).
n*(18*n + 1)**2
Suppose 5*z + 22 = 2*c + c, -6 = 3*z. Factor 4*y**3 + 20*y + 4 - 16 - 16*y**2 + c.
4*(y - 2)*(y - 1)**2
Let u(m) be the first derivative of m**6/150 - 3*m**5/100 + m**4/30 + 28*m + 29. Let a(r) be the first derivative of u(r). Factor a(k).
k**2*(k - 2)*(k - 1)/5
Factor -2*z**2 + 10*z**3 - 72*z + 68*z**2 + 6*z**3 + 18*z**2.
4*z*(z + 6)*(4*z - 3)
Let y(d) be the first derivative of -d**4/34 + 8*d**3/51 - d**2/17 - 12*d/17 - 116. Factor y(p).
-2*(p - 3)*(p - 2)*(p + 1)/17
Let x(l) be the second derivative of 3*l**2 + 0 + 30*l + 121/8*l**4 - 11*l**3. Solve x(z) = 0.
2/11
Let p(s) = 11*s**4 + 18*s**3 - 24*s**2 + 34*s - 15. Let x(q) = -10*q**4 - 15*q**3 + 25*q**2 - 35*q + 15. Let o(r) = -5*p(r) - 6*x(r). Let o(m) = 0. What is m?
-3, 1
Suppose -5*i = i - 24. Let r(x) be the first derivative of 64/3*x**3 + 77/2*x**4 + i*x**2 + 98/5*x**5 + 0*x - 4. Find w, given that r(w) = 0.
-1, -2/7, 0
Let c(n) be the first derivative of n**4/24 - n**3/3 + 3*n - 1. Let l(u) be the first derivative of c(u). Find s such that l(s) = 0.
0, 4
Suppose 0 = -4*m + 28 + 4. Factor -2*x**2 + 2*x - m + x**2 - x**2 - 10*x.
-2*(x + 2)**2
Let t(z) be the second derivative of z**6/10 + 3*z**5/5 + 5*z**4/4 + z**3 + 6*z - 1. What is u in t(u) = 0?
-2, -1, 0
Let z(b) be the third derivative of -5*b**8/336 + b**7/42 + 7*b**6/8 + 47*b**5/12 + 25*b**4/3 + 10*b**3 + 118*b**2. Factor z(a).
-5*(a - 6)*(a + 1)**3*(a + 2)
Factor 4/7*i**3 - 40/7*i**2 + 36/7*i + 0.
4*i*(i - 9)*(i - 1)/7
Let y(r) be the third derivative of 0 + 0*r + 1/60*r**5 + 1/15*r**4 + r**2 + 1/600*r**6 + 2/15*r**3. Factor y(d).
(d + 1)*(d + 2)**2/5
Let h(z) be the third derivative of -z**7/525 + z**5/50 - z**4/30 - 3*z**2. Suppose h(j) = 0. What is j?
-2, 0, 1
Let d(n) be the first derivative of -10*n**3/9 - 5*n**2/12 - 39. Factor d(b).
-5*b*(4*b + 1)/6
Let u(c) = -c**3 + 4*c**2 + c - 10. Let m be u(3). Factor z**3 - z + 2*z**m - 3*z - 5*z**2.
z*(z - 4)*(z + 1)
Find c such that 332416*c - 5*c**4 + 8402*c**2 + 334*c**3 + 10078*c**2 - 23607 - 327625 + 7*c**4 = 0.
-56, 1
Let d(z) be the second derivative of z**6/255 + z**5/34 - z**4/34 - 13*z**3/51 + 10*z**2/17 - 58*z. Solve d(l) = 0 for l.
-5, -2, 1
Let p(q) be the third derivative of 0 - 50/3*q**3 + 0*q - 1/15*q**5 - 5/3*q**4 - 4*q**2. Factor p(y).
-4*(y + 5)**2
Let p = -13 - -34. Suppose 3*c + 6 = 0, 2*m + 3*c - 6 = -0*m. Factor -m*z**2 + p*z + z**2 - 6 - 4*z**2.
-3*(z - 2)*(3*z - 1)
Let x(h) be the first derivative of -4*h**3/3 + 2*h**2 + 8*h - 89. Find p such that x(p) = 0.
-1, 2
Suppose -5*p + 25 = 4*v, -v - 6*p = -p + 5. Let d = -6 + v. Determine x so that x**4 - 2*x**d + 4*x**4 = 0.
0
Let r(n) be the second derivative of -25*n + 1/40*n**5 + 0*n**2 - 1/60*n**6 + 1/24*n**4 + 0 - 1/12*n**3. What is z in r(z) = 0?
-1, 0, 1
What is x in -1/3*x**4 + 1/3*x**2 + 0 - x + x**3 = 0?
-1, 0, 1, 3
Let k(r) be the third derivative of -r**5/30 - 10*r**4/3 + 28*r**3 + 10*r**2 - 58*r. Factor k(a).
-2*(a - 2)*(a + 42)
Suppose 0 = -48*m + 174 + 162. Let u(h) be the second derivative of -1/105*h**m - 11*h + 0*h**4 + 0*h**6 + 1/25*h**5 - 1/15*h**3 + 0*h**2 + 0. Factor u(q).
-2*q*(q - 1)**2*(q + 1)**2/5
Let q = 80 + -115. Let k be 80/q + 2 + 37/7. Solve 0 + 0*h - h**2 - 7/4*h**k - 5/4*h**4 + 4*h**3 = 0.
-2, 0, 2/7, 1
Let y(x) be the third derivative of x**7/105 - x**5/10 - x**4/6 + 76*x**2. Solve y(k) = 0.
-1, 0, 2
Let y(a) be the third derivative of -12*a**2 - 5/8*a**4 + 5/3*a**3 + 0 + 1/12*a**5 + 0*a. Let y(g) = 0. Calculate g.
1, 2
Let v(w) be the second derivative of w**6/50 - 9*w**5/100 + w**4/10 - 131*w + 2. Solve v(r) = 0 for r.
0, 1, 2
Let l(n) be the first derivative of -4/3*n**3 - 144*n - 16 + 24*n**2. Let l(h) = 0. What is h?
6
Let q(a) be the first derivative of a**5/90 + a**4/12 - 7*a**2/2 - 8. Let j(i) be the second derivative of q(i). Factor j(x).
2*x*(x + 3)/3
Let a(h) be the second derivative of 25*h**6/6 - 45*h**5 - 65*h**4 - 80*h**3/3 - 89*h. Factor a(w).
5*w*(w - 8)*(5*w + 2)**2
Let s = -36 - -40. Factor -132*g - 10 + 112*g - 6 - s*g**2.
-4*(g + 1)*(g + 4)
Let h be -6 + (-404)/(-44) - 3. Let v be 5*((-489)/165 + 3). Solve 0 + v*o**2 + h*o**3 - 4/11*o = 0 for o.
-2, 0, 1
Let b be (-5)/(-3) + (-6)/(-18). Factor 5*q**b - q**3 + 10*q**3 + 15*q**4 + 6*q**3 + 5*q**5.
5*q**2*(q + 1)**3
Let f(z) be the third derivative of -4*z**2 + 0 - 1/4*z**3 - 1/40*z**5 - 1/8*z**4 + 0*z. Factor f(p).
-3*(p + 1)**2/2
Let c(z) be the first derivative of -z**6/8 + 21*z**5/20 - 57*z**4/16 + 25*z**3/4 - 6*z**2 + 3*z - 388. Factor c(f).
-3*(f - 2)**2*(f - 1)**3/4
Let d be (2 - (-36)/(-8))/(165/(-20) + 7). Factor 1/5*m**d - 4/5*m - 1.
(m - 5)*(m + 1)/5
Suppose -w - 3*q + 18 = 0, 3*w - 5*q - 14 = -4*q. Suppose -w*h = -7*h. Factor -1/2*z**3 - z - 3/2*z**2 + h.
-z*(z + 1)*(z + 2)/2
Suppose -180*d**2 - 81 + 205*d**2 - 5*d**3 + 40*d + 21 = 0. Calculate d.
-2, 1, 6
Solve 3/7*d**4 + 0*d + 0 + 3/7*d**2 - 6/7*d**3 = 0.
0, 1
Let 4/5*x + 18/5*x**2 - 18/5*x**4 + 0 - 4/5*x**3 = 0. What is x?
-1, -2/9, 0, 1
Let r be (-9)/2*(0 + (-4)/9). Factor 3023*t - 327*t**r - 876*t**3 - 12 - 294*t**3 - 675*t**4 - 2867*t.
-3*(t + 1)**2*(15*t - 2)**2
Factor 302/5*l - 2/5*l**3 + 148/5*l**2 + 152/5.
-2*(l - 76)*(l + 1)**2/5
Let c(i) be the second derivative of -i**7/21 + 7*i**6/15 - 9*i**5/5 + 10*i**4/3 - 8*i**3/3 - 23*i + 1. Suppose c(x) = 0. What is x?
0, 1, 2
Let g(s) = 2*s + 1. Suppose 0 = -10*z + 6*z + 4. Let w be g(z). Determine c so that c**2 - 3*c + 3*c - 3*c - 9*c**w + 11*c**2 = 0.
0, 1/3,