)/((-23)/4 + 5). Let h = -1 - -1. Find p, given that 0*p**c + 0*p**2 + h + 2/7*p + 2/7*p**5 - 4/7*p**3 = 0.
-1, 0, 1
Let x(n) be the first derivative of 4*n**3/9 - n**2/4 + 20. Let x(j) = 0. Calculate j.
0, 3/8
Let u = -19 + 9. Let m = u - -24. Solve 5*d**2 + d + m*d**3 - 4*d**2 + d + 2*d**5 + 8*d**2 + 9*d**4 = 0.
-2, -1, -1/2, 0
Let m(f) be the second derivative of f**7/10080 + f**6/1440 + f**4/12 - f. Let q(a) be the third derivative of m(a). Determine l so that q(l) = 0.
-2, 0
Let a(g) = g**2 + 4 - 2*g**2 - 7*g + 10*g. Let w be a(4). Find r, given that 2*r**5 + w*r**5 - 2*r**3 + 2*r**4 - 2*r**2 + 0*r**2 = 0.
-1, 0, 1
Let b be ((-3)/12)/((-2)/4). Let u(k) be the first derivative of -b*k**2 + 1 + 1/4*k + 1/4*k**3. Factor u(i).
(i - 1)*(3*i - 1)/4
Suppose 0 = -v + 2*x - 4, 5 = 2*x - 1. Let d(u) be the first derivative of -u**3 - 3/2*u**2 - v + 0*u. Factor d(f).
-3*f*(f + 1)
Let b(v) be the third derivative of v**6/90 + 13*v**5/270 + v**4/12 + 2*v**3/27 - 12*v**2. Determine q so that b(q) = 0.
-1, -2/3, -1/2
Let o = 4 + 1. Suppose -3*b = -b + 14. Let m(r) = 7*r**2 + 9*r - 3. Let h(j) = 10*j**2 + 13*j - 4. Let w(q) = b*m(q) + o*h(q). Factor w(f).
(f + 1)**2
Let f = 3 + 1. Let l = -367 - -2573/7. Solve -l + 10/7*k**5 + 10/7*k - 20/7*k**3 - 4/7*k**f + 8/7*k**2 = 0 for k.
-1, 2/5, 1
Let w(g) be the first derivative of -2 + g**2 + 2/3*g**3 - 4*g. Solve w(r) = 0 for r.
-2, 1
Suppose 0*c + 2*c = 8. Let i(x) be the third derivative of -1/30*x**5 - 1/6*x**c + 0*x - 2*x**2 + 0 - 1/3*x**3. Suppose i(a) = 0. Calculate a.
-1
Determine n so that -9*n - 4*n**2 - 6 + 3*n**2 - 2*n**2 + 0*n**2 = 0.
-2, -1
Let v(q) be the second derivative of q**6/20 - 3*q**5/10 + 3*q**4/4 - q**3 + 3*q**2/4 - 10*q. Factor v(y).
3*(y - 1)**4/2
Let u(p) be the second derivative of p + 7/108*p**4 - 2/27*p**3 + 1/135*p**5 + 0 - 7/540*p**6 - 3/2*p**2. Let x(a) be the first derivative of u(a). Factor x(l).
-2*(l - 1)*(l + 1)*(7*l - 2)/9
Let v(a) be the first derivative of a**7/210 + a**6/360 - a**3/3 + 3. Let s(f) be the third derivative of v(f). Suppose s(x) = 0. What is x?
-1/4, 0
Let p(a) be the first derivative of a**7/630 - a**6/180 - a**5/180 + a**4/36 + 3*a**2/2 - 3. Let b(v) be the second derivative of p(v). Let b(q) = 0. What is q?
-1, 0, 1, 2
Let z be -3*3/(-9) + (-28)/(-21). Let o = 1582/291 + -10/97. Factor -19/3*s**3 - 1/3*s**5 + z*s**4 + 25/3*s**2 + 4/3 - o*s.
-(s - 2)**2*(s - 1)**3/3
Let c(v) be the third derivative of v**5/300 - v**4/60 + v**3/30 - 6*v**2. Suppose c(w) = 0. What is w?
1
Let s(k) = -k + 33. Let i(f) = 2*f - 50. Let r(a) = 5*i(a) + 8*s(a). Let h be r(-6). Factor 1/2*t**h + 1/2*t**3 - 1/4*t**5 - 1/4 - 1/4*t - 1/4*t**4.
-(t - 1)**2*(t + 1)**3/4
Let 0*a + 2/5*a**2 + 0 = 0. What is a?
0
Let f(x) be the third derivative of -x**7/840 - x**6/160 - x**5/80 - x**4/96 - 12*x**2. Solve f(p) = 0.
-1, 0
Let y(x) be the first derivative of -x**5/10 - 3*x**4/8 + x**3/6 + 3*x**2/4 + 10. Factor y(s).
-s*(s - 1)*(s + 1)*(s + 3)/2
Let t(f) be the third derivative of f**7/42 - 15*f**2. Factor t(i).
5*i**4
Determine a so that 3*a**2 - 128 + 128 + 12*a = 0.
-4, 0
Let b = -46 + 50. Let y(h) be the second derivative of 0*h**2 + 0 + 0*h**3 + 0*h**5 - 1/45*h**6 + 1/18*h**b + 2*h. Factor y(o).
-2*o**2*(o - 1)*(o + 1)/3
Let k(i) be the second derivative of -i**7/189 - i**6/45 - i**5/90 + i**4/18 + 2*i**3/27 + 31*i. Find p, given that k(p) = 0.
-2, -1, 0, 1
Let q(s) be the second derivative of 2*s**6/45 + s**5/4 - 4*s**4/3 + 35*s**3/18 - s**2 + 18*s. Factor q(o).
(o - 1)**2*(o + 6)*(4*o - 1)/3
Let o(a) = -a**5 - a**4 - 1. Let m(p) = -8*p**5 - 26*p**4 + 3*p**3 + 21*p**2 - 5. Let q(z) = -m(z) + 5*o(z). Factor q(g).
3*g**2*(g - 1)*(g + 1)*(g + 7)
Let j(c) be the third derivative of -c**8/5040 + c**7/630 + 2*c**5/15 - 8*c**2. Let h(x) be the third derivative of j(x). Solve h(r) = 0.
0, 2
Let j(y) be the third derivative of -y**8/336 + y**7/210 + y**6/120 - y**5/60 - 4*y**2. Suppose j(m) = 0. Calculate m.
-1, 0, 1
Suppose 9*q - 4*q - 5 = 0. Suppose -g - g + 0*g**2 - g**2 - q + 4*g = 0. What is g?
1
Let j be (12/18)/(2/15). Let c(y) be the third derivative of 4*y**2 + 1/360*y**j + 0*y + 0 + 1/18*y**3 + 1/48*y**4. Factor c(m).
(m + 1)*(m + 2)/6
Let m(a) be the second derivative of a**7/105 + a**6/360 - a**5/60 + a**4/6 + a. Let j(h) be the third derivative of m(h). Factor j(c).
2*(3*c + 1)*(4*c - 1)
Factor 5/2*z**2 - 4*z - 1/2*z**3 + 2.
-(z - 2)**2*(z - 1)/2
Let v be -4*(1 + 4 + -4). Let z be (2/v)/(2/(-20)). What is b in 2/3 + 22*b**4 + 20*b**2 + 6*b**z + 6*b + 92/3*b**3 = 0?
-1, -1/3
Let m(v) = -v + 1. Let z be m(1). Let b = 17/12 + -43/36. Factor -b*n**4 + 0 + 0*n**3 + 2/9*n**2 + z*n.
-2*n**2*(n - 1)*(n + 1)/9
Let p(m) be the second derivative of -1/12*m**4 + 0*m**2 + 0 - 1/20*m**5 + 3*m + 0*m**3. Let p(j) = 0. What is j?
-1, 0
Let k = 1 - -3. Let x(f) = -f + 4. Let h be x(k). Suppose 11*j**2 - 19*j**3 + 17*j**4 + h*j**5 - 2*j**3 - 5*j**5 - 2*j = 0. What is j?
0, 2/5, 1
Solve -3/4*l**2 + 3/4*l**4 + 0 + 3/4*l**3 - 3/4*l = 0.
-1, 0, 1
Let g(l) = -19*l**2 - 25*l + 13. Let o(b) = -3*b**2 - 4*b + 2. Let i(r) = 6*g(r) - 39*o(r). Factor i(x).
3*x*(x + 2)
Let 0*z**2 - 2/7*z**3 + 0 + 0*z = 0. Calculate z.
0
Let q(d) = -7*d**2 + d. Let p(c) = -6*c**2 + c. Let j(u) = -6*p(u) + 5*q(u). What is g in j(g) = 0?
0, 1
Let o(w) = w**2 - 11*w + 12. Let q be o(10). Suppose -8 + 12 = q*l. Suppose 12*m**3 - 12*m + 21/4*m**4 + 3/4*m**5 - 12 + 6*m**l = 0. Calculate m.
-2, 1
Factor -1/4*o**2 + 5/4*o + 3/2.
-(o - 6)*(o + 1)/4
Let v(n) be the third derivative of n**8/336 - n**7/126 - 7*n**6/360 + n**5/20 + n**4/18 - 2*n**3/9 + 3*n**2. Let v(k) = 0. What is k?
-1, 2/3, 1, 2
Let i(x) be the first derivative of x**6/1620 - x**4/27 + 2*x**3/3 + 5. Let l(t) be the third derivative of i(t). Factor l(u).
2*(u - 2)*(u + 2)/9
Let f(t) = 13*t**4 - 35*t**3 + 11*t**2 + 6*t + 5. Let y(j) = 45*j**4 - 123*j**3 + 39*j**2 + 21*j + 18. Let g(w) = -18*f(w) + 5*y(w). Let g(c) = 0. What is c?
-1/3, 0, 1
Let j(a) be the first derivative of a**4/6 + a**3 + 2*a**2 + 3*a - 3. Let x(d) be the first derivative of j(d). Find n such that x(n) = 0.
-2, -1
Let y(p) = -p**3 + 4*p**2 + p - 1. Let h be y(4). Factor -2*q**2 - q**3 + q**h - q**3 + q**2.
-q**2*(q + 1)
Factor -2/9*o**5 + 2/9*o**4 + 2/9 + 4/9*o**3 - 2/9*o - 4/9*o**2.
-2*(o - 1)**3*(o + 1)**2/9
Let h(n) = n**2 - n - 2. Let k(y) = -y**2 - 3*y - 2. Let m be k(-3). Let i be h(m). Factor 6*s**3 + 2*s**2 - 4*s - 2*s**i + 5*s**3 - 7*s**3.
-2*s*(s - 2)*(s - 1)*(s + 1)
Let g = -1097 + 1099. Find n, given that 0 - 2/13*n**g - 2/13*n**3 + 2/13*n**4 + 2/13*n**5 + 0*n = 0.
-1, 0, 1
Let g(p) be the second derivative of p**6/1440 - p**5/80 + 3*p**4/32 + 7*p**3/6 + 8*p. Let d(b) be the second derivative of g(b). Solve d(q) = 0.
3
Let x(g) = 9*g**3 + 17*g**2 + 5*g + 13. Let m be (-3 + 2)/((-3)/18). Let j(k) = -5*k**3 - 9*k**2 - 3*k - 7. Let z(o) = m*x(o) + 11*j(o). Solve z(i) = 0.
1
Let n(g) be the third derivative of -2*g**7/315 - g**6/90 + 2*g**5/45 - 21*g**2. Suppose n(r) = 0. What is r?
-2, 0, 1
Determine y, given that 0*y**2 - 2*y**2 - 6 - 1 - 1 - 8*y = 0.
-2
Let y(v) be the third derivative of -v**6/60 - v**5/10 + 6*v**2. Factor y(c).
-2*c**2*(c + 3)
Suppose -2*h = -6 + 2. Let c be (-48)/16 + 6/h. Suppose 1/5*l**2 + 0*l + c - 1/5*l**3 = 0. Calculate l.
0, 1
Let g(t) = -t**2 - 7*t - 8. Let f be g(-5). Factor -8/5*k**3 - 4/5*k**f - 3/5*k**4 + 0*k + 0.
-k**2*(k + 2)*(3*k + 2)/5
Let s(x) be the third derivative of x**7/210 - x**6/60 + x**4/12 - x**3/6 + 7*x**2 + 3. Determine n, given that s(n) = 0.
-1, 1
Let v be -3*20/48*4. Let k(g) = g**2 + 4*g - 3. Let u be k(v). Solve -4/5*f - 2/5*f**3 + 0 + 6/5*f**u = 0 for f.
0, 1, 2
Determine p so that 30*p - 10*p**3 - 2*p**2 + 5*p**5 + 2*p**2 - 25*p = 0.
-1, 0, 1
Let 6*m**2 + 9*m**5 + 9*m + 9*m**5 - 6 - 12*m**3 - 15*m**5 = 0. Calculate m.
-2, -1, 1
Let l(r) be the second derivative of -r**5/90 + r**3/9 - r**2/2 - 4*r. Let g(d) be the first derivative of l(d). Factor g(a).
-2*(a - 1)*(a + 1)/3
Let i = 40 - 37. Let j(w) be the third derivative of 0*w**4 + 0 - 1/120*w**6 - 1/180*w**5 - 1/210*w**7 + 0*w - 1/1008*w**8 - 3*w**2 + 0*w**i. Factor j(q).
-q**2*(q + 1)**3/3
Let o(k) = -20*k**3 + 25*k**2 - 11*k. Let y(r) = 4*r**3 - 5*r**2 + 2*r. Let p(j) = -4*o(j) -