8*q**4 + 22*q**4.
3*q**4*(q - 1)
Factor 0*d + 0 + 1/8*d**2.
d**2/8
Suppose -j - 6 = -3*j. Find g such that -3*g**j + 2*g + 5*g**3 - 4*g = 0.
-1, 0, 1
Let r(m) be the first derivative of -m**7/105 - m**6/60 + m**2/2 - 2. Let y(z) be the second derivative of r(z). Find g such that y(g) = 0.
-1, 0
Let v(k) be the third derivative of -k**5/210 - k**4/28 - 31*k**2 + 2. Factor v(m).
-2*m*(m + 3)/7
Let s(q) be the third derivative of 1/9*q**4 + 1/168*q**8 - q**2 + 23/630*q**7 + 0 + 1/18*q**3 + 17/180*q**6 + 0*q + 2/15*q**5. Solve s(h) = 0 for h.
-1, -1/2, -1/3
Let o be (-207)/(-63) - (-2)/(-7). Let h be (-8)/(-6) - 4/o. Suppose h*d**2 - 1/2*d**4 + 0*d + d**3 + 0 = 0. What is d?
0, 2
Let h(a) be the first derivative of 7*a**5/5 + 9*a**4/4 - 4*a**3 - 2*a**2 - 7. Determine l, given that h(l) = 0.
-2, -2/7, 0, 1
Let d be (2/40*4)/(6/5). Let b(u) be the first derivative of -1/2*u**2 + d*u**3 + 1/2*u + 3. Factor b(z).
(z - 1)**2/2
Let p(t) be the third derivative of -t**2 + 0*t + 0 + 1/108*t**4 - 1/945*t**7 + 1/270*t**5 + 0*t**3 - 1/540*t**6. Suppose p(h) = 0. What is h?
-1, 0, 1
Let h be (-1 + 0)/((-10)/4). Let -h*i + 1/5*i**2 + 1/5 = 0. What is i?
1
Let f = -32 + 34. Let p(k) be the first derivative of k**2 + 0*k**3 + f - k + 1/5*k**5 - 1/2*k**4. Factor p(g).
(g - 1)**3*(g + 1)
Let i(f) be the second derivative of -f**7/945 + f**6/270 - f**5/270 - f**2/2 - 4*f. Let d(y) be the first derivative of i(y). Factor d(q).
-2*q**2*(q - 1)**2/9
Let g = -6 + 6. Suppose -3*i + 2*i + 41 = g. Factor 5*z + 4*z - 10*z**3 - 8 - i*z - 34*z**2.
-2*(z + 1)*(z + 2)*(5*z + 2)
Let u = -12 + 14. Determine x, given that 4 - u + 4 - 3*x**2 + 3*x = 0.
-1, 2
Let s(z) be the third derivative of z**8/112 + 3*z**7/35 + 3*z**6/10 + 2*z**5/5 + z**2 - 10. Solve s(m) = 0 for m.
-2, 0
Let i(v) be the third derivative of -v**5/420 - v**4/84 - v**3/42 + 7*v**2. Find t such that i(t) = 0.
-1
Suppose -40 = -6*k + 2*k. Determine h so that -6*h**4 - 2*h**3 + k*h**4 + 2*h**2 - h**2 - 3*h**2 = 0.
-1/2, 0, 1
Let l(a) be the second derivative of a**6/360 - a**5/40 + a**4/12 - a**3/3 + 4*a. Let i(j) be the second derivative of l(j). Let i(y) = 0. Calculate y.
1, 2
Suppose 0 = 4*v - 27 - 5. Let g = -6 + v. Factor 0 + 1/3*m - 1/3*m**g.
-m*(m - 1)/3
Factor -22*i**2 - 45*i**4 + 79*i**3 + 41*i**3 + 5*i**5 - 58*i**2.
5*i**2*(i - 4)**2*(i - 1)
Let n(k) = k**2 + 1 + 5 + k - 6*k. Let u be n(4). Factor -2*i**u + 6*i**2 - 5*i**2 + 1.
-(i - 1)*(i + 1)
Let q = -20 - -22. Let d(c) be the first derivative of 1 + 9/20*c**4 + c**3 + 7/10*c**q + 1/5*c. Factor d(y).
(y + 1)*(3*y + 1)**2/5
Let 75 + 9*d**2 + 45*d + 3/5*d**3 = 0. Calculate d.
-5
Let h = -69/112 - -3/7. Let k = h + 41/48. Find r such that 2/3 + k*r**2 - 4/3*r = 0.
1
Let r(s) = -s**2 + 7*s - 8. Let h be r(3). Factor 4*b**2 - 7/4*b**h + 5/4*b**3 + 0 + b.
-b*(b - 2)*(b + 1)*(7*b + 2)/4
Let h(w) be the second derivative of w**7/84 + w**6/15 + w**5/8 + w**4/12 - 5*w. Factor h(b).
b**2*(b + 1)**2*(b + 2)/2
Let d(k) be the first derivative of -4/33*k**3 + 4/55*k**5 + 0*k - 1/11*k**2 + 2 + 1/33*k**6 + 0*k**4. Find m such that d(m) = 0.
-1, 0, 1
Suppose -4*b = 2*x - 18, -x + 5*x - 18 = b. Let k = b + 0. Find c, given that c - c**2 + c**2 - c**k = 0.
0, 1
Let v(m) be the first derivative of -m**7/840 - m**6/480 + m**5/80 + 5*m**4/96 + m**3/12 - m**2/2 + 3. Let w(u) be the second derivative of v(u). Factor w(h).
-(h - 2)*(h + 1)**3/4
Let q(y) be the first derivative of 4*y**6/45 + 6*y**5/25 + y**4/15 + 7. What is i in q(i) = 0?
-2, -1/4, 0
Let o(w) be the third derivative of 17/8*w**4 + 0 + 4*w**2 - 12/5*w**5 + 0*w + 9/112*w**8 - w**3 - 19/35*w**7 + 31/20*w**6. Factor o(z).
3*(z - 1)**4*(9*z - 2)
Let a(f) be the third derivative of -f**8/336 - f**7/210 + f**6/60 + 38*f**2. Factor a(v).
-v**3*(v - 1)*(v + 2)
Factor 589*v**4 - 624*v**4 - 27*v**5 + 2*v**5 - 10*v**3.
-5*v**3*(v + 1)*(5*v + 2)
Factor -45*a + 6*a - a + 4*a**2.
4*a*(a - 10)
Let t(c) be the third derivative of -c**6/180 + 2*c**5/45 - c**4/9 + 3*c**2. Factor t(u).
-2*u*(u - 2)**2/3
Let n(k) be the third derivative of 0*k - k**2 + 1/84*k**4 - 2/21*k**3 + 0 + 1/70*k**5. Factor n(g).
2*(g + 1)*(3*g - 2)/7
Let p(r) = -5*r**3 + 17*r**2 - 37*r + 16. Let k(u) = -4*u**3 + 17*u**2 - 38*u + 16. Let l(v) = -6*k(v) + 4*p(v). Factor l(y).
2*(y - 4)**2*(2*y - 1)
Let o = 242/3 + -78. Let 0*g - o + 2/3*g**2 = 0. What is g?
-2, 2
Let y(k) be the second derivative of 2*k**6/5 + 2*k**5/5 - 4*k**4/3 - 4*k**3/3 + 2*k**2 + 3*k. Factor y(h).
4*(h - 1)*(h + 1)**2*(3*h - 1)
Let u(x) be the third derivative of -x**5/150 - 17*x**4/30 - 289*x**3/15 + x**2 + 4. Determine g so that u(g) = 0.
-17
Let b(w) = -2*w**2 + 14*w - 12. Let a(u) = 3*u**2 - 15*u + 12. Let k(o) = 6*a(o) + 7*b(o). Factor k(y).
4*(y - 1)*(y + 3)
Let j(s) = 8*s**5 + 14*s**4 + 4*s**3 - 6*s**2 - 6*s. Let r(x) = 17*x**5 + 28*x**4 + 7*x**3 - 12*x**2 - 13*x. Let w(p) = -5*j(p) + 2*r(p). Factor w(n).
-2*n*(n + 1)**3*(3*n - 2)
Factor 8 - 8*l**2 + 38*l**2 - 14*l**2 - 14*l**2 + 10*l.
2*(l + 1)*(l + 4)
Suppose -2*p - 4 = 2*w, -20*w - 4*p - 24 = -24*w. Determine c so that 8/5*c**w + 0 - 2/5*c**5 + 0*c - 6/5*c**4 + 0*c**3 = 0.
-2, 0, 1
Let l(t) be the second derivative of -t**9/3024 + t**8/840 - t**6/180 + t**5/120 - t**3/6 + t. Let k(w) be the second derivative of l(w). Factor k(a).
-a*(a - 1)**3*(a + 1)
Let p = -22 + 24. Factor a + 1/2*a**p + 1/2.
(a + 1)**2/2
Let q(h) be the third derivative of -h**7/210 - h**6/120 - 2*h**3/3 - 3*h**2. Let j(w) = -w**4 - w**3 - 5. Let r(v) = 4*j(v) - 5*q(v). Factor r(x).
x**3*(x + 1)
Let v(a) be the second derivative of a**8/420 + a**7/105 + a**6/72 + a**5/120 - a**3/3 - 2*a. Let s(f) be the second derivative of v(f). Factor s(k).
k*(k + 1)*(2*k + 1)**2
Let z be 3/(-4)*(0 - 4). Let x(w) = 2*w**3 + 3*w**2 - 5*w - 3. Let c(u) = 2*u**3 + 2*u**2 - 4*u - 2. Let n(k) = z*c(k) - 2*x(k). Suppose n(q) = 0. What is q?
-1, 0, 1
Let f(z) be the second derivative of 0 + 2/9*z**4 + 8*z + 1/90*z**6 + 0*z**2 - 2/9*z**3 - 1/12*z**5. Factor f(r).
r*(r - 2)**2*(r - 1)/3
Let u = 8 + -5. Suppose 0 = 5*x - c - 36, 16 = u*x - 0*x - 2*c. What is a in 3 - 7 + a**2 - 6*a**2 - x*a - a**3 = 0?
-2, -1
Let m be 3/(-15) - 6/(-15). Factor -1/5*r**3 + m - 1/5*r**2 + 1/5*r.
-(r - 1)*(r + 1)**2/5
Factor 4*p**2 - p**5 - 8*p**3 + 0*p**5 - p**2 + p**2 + 5*p**4.
-p**2*(p - 2)**2*(p - 1)
Let d(g) be the second derivative of g**6/1260 + g**3/6 + 4*g. Let z(c) be the second derivative of d(c). Suppose z(t) = 0. Calculate t.
0
Let q(n) be the second derivative of -5*n**7/42 + n**5/4 + 2*n. Suppose q(y) = 0. What is y?
-1, 0, 1
Let d(w) be the second derivative of w**8/5880 + w**7/980 + w**6/420 + w**5/420 - w**3/6 + w. Let m(c) be the second derivative of d(c). Factor m(p).
2*p*(p + 1)**3/7
Let f(w) be the second derivative of w**6/180 + w**5/120 - w**4/72 - w**3/36 + 5*w. Factor f(m).
m*(m - 1)*(m + 1)**2/6
Let t be (-16)/(-3) + 1/(-3). Let m = -5 + t. Determine w so that 2*w**4 + 10*w**2 + m*w**4 + 4*w**4 - 14*w**3 - 2*w = 0.
0, 1/3, 1
Let c(m) = -20*m**3 + 24*m**2 - 28*m - 16. Let u(k) = -k**2 - 1. Let t(x) = c(x) - 20*u(x). What is a in t(a) = 0?
1/5, 1
Let w = -202 + 809/4. Let p(f) be the second derivative of 1/30*f**6 - 1/3*f**3 + 0 - w*f**4 + 0*f**2 + 0*f**5 - 2*f. Find h, given that p(h) = 0.
-1, 0, 2
Let h be (-5)/2*(-18)/15. Factor -h*n**2 + 15 - 6*n - 5 - 16 - 3*n.
-3*(n + 1)*(n + 2)
Suppose 0 = 4*j - 3*j + 3*o + 1, 0 = -4*o - 4. Suppose 0*b**5 - b**4 + 3*b**j - 2*b**4 - 3*b**5 + 3*b**3 = 0. Calculate b.
-1, 0, 1
Let l(h) be the first derivative of h**5/180 - h**4/72 - h**3/9 + h**2 - 1. Let a(c) be the second derivative of l(c). Find q, given that a(q) = 0.
-1, 2
Determine n, given that 0*n**2 + 12/5*n**3 + 0 + 4/5*n**4 - 16/5*n = 0.
-2, 0, 1
Let r(d) = -d**2 + d + 2. Let g be r(-1). Let s(a) be the third derivative of -1/180*a**5 + 0*a - 1/72*a**4 + g - 2*a**2 + 0*a**3. Factor s(w).
-w*(w + 1)/3
Let b = 7 + -7. Let i(a) be the second derivative of 0 + 1/48*a**4 - 1/8*a**2 + b*a**3 - 2*a. Solve i(p) = 0.
-1, 1
Let k(x) = 6*x**2 - 4*x + 13. Let h(t) = -5*t**2 + 5*t - 12. Let b(i) = 5*h(i) + 4*k(i). Factor b(g).
-(g - 8)*(g - 1)
Let v(c) = -c + 2*c**2 + 3 - c**2 + 0. Let b be v(0). Determine m, given that 2*m**4 + 0*m - 4 - 4*m**b + 4*m + 2 = 0.
-1, 1
Let l(x) be the thi