4*h**3.
2*h**2*(h + 1)**2
Let g(x) be the second derivative of -x**8/6720 + x**6/240 - x**5/60 - 7*x**4/12 - 8*x. Let v(y) be the third derivative of g(y). Factor v(m).
-(m - 1)**2*(m + 2)
Suppose -f = -5*u + 2 + 38, -2*f + 4*u = 86. Let i be 6/(-10) - 42/f. Factor 4/3*s + i*s**2 + 4/3.
(s + 2)**2/3
Let b = 2 - -1. Let r(q) = 21*q**2 - 33*q + 21. Let w(l) = l**3 + 22*l**2 - 32*l + 20. Let k(h) = b*w(h) - 4*r(h). Find v such that k(v) = 0.
2
Let r(x) be the third derivative of 23/8*x**4 - 7/20*x**5 + 0*x + x**2 - 3*x**3 + 0. Solve r(f) = 0.
2/7, 3
Let p be 64/20 + 4/(-20). Let d(x) be the first derivative of 1/4*x**4 + 6*x**2 - 5 + 8*x + 2*x**p. Find u, given that d(u) = 0.
-2
Let z = 7/310 + -20791/930. Let f = -463/21 - z. Factor 0 - 2/7*y**2 - f*y.
-2*y*(y + 1)/7
Let m(r) be the third derivative of r**7/525 - 7*r**6/150 + 2*r**5/5 - 5*r**4/6 - 25*r**3/3 + 4*r**2. Factor m(v).
2*(v - 5)**3*(v + 1)/5
Suppose -5*o + y = -2*o - 12, 4*o = 5*y + 16. Factor 0 - 1/3*j**2 + 1/3*j + 1/3*j**o - 1/3*j**3.
j*(j - 1)**2*(j + 1)/3
Factor -4/3*h**3 - 8/9*h**4 - 2/9*h - 2/9*h**5 - 8/9*h**2 + 0.
-2*h*(h + 1)**4/9
Factor 15/2*h**3 + 3*h**2 + 0*h - 24*h**4 + 27/2*h**5 + 0.
3*h**2*(h - 1)**2*(9*h + 2)/2
Let w = -2724 - -30002/11. Factor w*x**3 + 32/11*x + 50/11*x**2 + 2/11*x**5 + 14/11*x**4 + 8/11.
2*(x + 1)**3*(x + 2)**2/11
Let v(y) = 5*y**2 + y. Let m be v(-1). Let b(k) be the third derivative of 0*k - 1/60*k**6 + 0*k**3 + 0*k**5 - k**2 + 0 + 0*k**m. Let b(t) = 0. What is t?
0
Suppose 2*s**4 - 13*s**3 - 4*s**4 - 10*s**2 - 4*s + 5*s**3 = 0. What is s?
-2, -1, 0
Let x(t) be the first derivative of t**6/540 - t**3/3 + t + 2. Let p(m) be the first derivative of x(m). Let c(g) be the second derivative of p(g). Factor c(k).
2*k**2/3
Let w be 16/3 + 4/(-12). Find t, given that 0 - 22/13*t**2 + 10/13*t**w + 42/13*t**3 - 34/13*t**4 + 4/13*t = 0.
0, 2/5, 1
Let h = 9/272 + -809/28560. Let v(i) be the third derivative of 4/21*i**3 + 0 + h*i**5 + i**2 - 1/21*i**4 + 0*i. Solve v(q) = 0.
2
Let n(s) = s**2 - 6*s + 3. Let k be n(8). Let q = 21 - k. Suppose 2*l**q - 4*l + 8/3 - 1/3*l**3 = 0. What is l?
2
Let v(f) = -30*f + 14*f + 3 + f**2 + 14*f. Let r be v(2). Let 3 + 21*w**r + 3/2*w - 51/2*w**2 = 0. What is w?
-2/7, 1/2, 1
Let o(b) = -b**3 - 4*b**2 - 2*b. Let x(l) = 9*l**3 + 33*l**2 + 17*l. Let g(a) = -51*o(a) - 6*x(a). Factor g(s).
-3*s**2*(s - 2)
Let 1/3*h**4 - 5/3*h**3 + 8/3*h**2 + 0 - 4/3*h = 0. What is h?
0, 1, 2
Determine t so that -2*t**3 - 9*t - 6 + 4*t**2 - 7*t - 26 + 10*t**2 = 0.
-1, 4
Let j = -1 - -5. Solve -1/4*t**2 - 1/4*t**j + 0 + 1/2*t**3 + 0*t = 0 for t.
0, 1
Let j be (-15)/(-3)*-1 - -1. Let n be (5/4)/(-1)*j. Solve -2*y + 5*y**2 - 2*y**2 - n*y**2 = 0.
-1, 0
Let o(k) be the third derivative of -k**5/240 + k**4/32 + k**3/6 + 10*k**2. Let o(i) = 0. What is i?
-1, 4
Let c = -2627/312 - -110/13. Let k(o) be the second derivative of -1/168*o**7 + 0 - 1/8*o**2 - c*o**3 + o + 1/24*o**4 - 1/120*o**6 + 1/40*o**5. Factor k(p).
-(p - 1)**2*(p + 1)**3/4
Suppose 0 - 8 = 4*a. Let j be (a - (0 + 4))/(-2). Factor 2*c**2 - 3*c**j - 3*c**5 - 2*c**4 + c**5 + 5*c**3.
-2*c**2*(c - 1)*(c + 1)**2
Let t(b) = 2*b**2 + 15*b + 7. Let x(p) = -p**2 - 1. Let a(h) = -t(h) + 3*x(h). Factor a(l).
-5*(l + 1)*(l + 2)
Let w(o) = -91*o**3 + 53*o**2 + 60*o - 5. Let s(l) = -30*l**3 + 18*l**2 + 20*l - 2. Let a(c) = 17*s(c) - 6*w(c). Suppose a(r) = 0. What is r?
-1/3, 1
Determine x so that 1/2*x**3 + 1/4*x + 0 - 5/8*x**2 - 1/8*x**4 = 0.
0, 1, 2
Suppose 10/3 + 5/6*r**4 + 0*r - 25/6*r**2 + 0*r**3 = 0. What is r?
-2, -1, 1, 2
Let c(p) be the third derivative of -p**5/100 + p**4/40 - 30*p**2. Solve c(n) = 0 for n.
0, 1
Factor -16*j - 15*j**2 - 50*j**3 - 42*j**3 - 16*j**4 - 65*j**2 - 12*j**4.
-4*j*(j + 1)*(j + 2)*(7*j + 2)
Let m(g) = -2*g**3 - g. Let z be m(-1). Suppose 2/3*l + 1/3*l**2 - 1/3*l**4 - 2/3*l**z + 0 = 0. What is l?
-2, -1, 0, 1
Factor -4/15 - 14/15*w + 6/5*w**2.
2*(w - 1)*(9*w + 2)/15
Suppose 2/9*v**4 - 14/9*v**2 - 8/9*v - 4/9*v**3 + 0 = 0. Calculate v.
-1, 0, 4
Suppose 3*r + 32 = h, -5*h + 29 = 4. Let b = 14 + r. Factor -b*v**3 - 2*v**2 + 2*v**3 + 2*v - v.
-v*(v + 1)*(3*v - 1)
Let r(y) be the third derivative of 2/3*y**3 + 0 + 0*y + 11/12*y**4 - 2*y**2 + 8/15*y**5 + 7/60*y**6. Factor r(t).
2*(t + 1)**2*(7*t + 2)
Factor 0*v**2 + 0*v - 1/4*v**3 + 1/4*v**4 + 0.
v**3*(v - 1)/4
Let q be (-5 + 76/16)/(1/(-2)). Find u, given that 1/4*u - 1/4*u**3 + 1/2*u**2 - q = 0.
-1, 1, 2
Let m(d) be the first derivative of -d**4/22 - 2*d**3/11 - 2*d**2/11 - 7. Let m(s) = 0. What is s?
-2, -1, 0
Let g(o) = 3*o + 10. Let s be g(-3). Suppose -s + 3 = d. Factor 0 + 1/4*n**4 - 1/4*n**d - 1/4*n**5 + 0*n + 1/4*n**3.
-n**2*(n - 1)**2*(n + 1)/4
Determine k, given that 24/19 + 350/19*k**2 - 98/19*k**3 - 176/19*k = 0.
2/7, 3
Determine f so that 0 - 4/13*f**2 - 6/13*f + 2/13*f**3 = 0.
-1, 0, 3
Let i = -42 + 45. Let k(t) be the first derivative of 2/3*t**3 - i - 2*t - t**2 + 1/2*t**4. Factor k(d).
2*(d - 1)*(d + 1)**2
Let v be 16/6*3/2. Suppose -z + 3 - 1 = 2*n, -15 = -v*z - n. Factor 2*s**z - 9*s + 9*s - 2*s**3.
2*s**3*(s - 1)
Let l(j) = 4*j**2 - 8*j + 4. Let p(n) = -2*n**2 + 4*n - 2. Let u(k) = 2*l(k) + 5*p(k). Factor u(y).
-2*(y - 1)**2
Let w = 2 - 4. Let q be (w - -5)*(4 + -3). Determine s, given that -s + 0*s + 3*s**2 + 3*s**q - 6*s**3 + s**4 = 0.
0, 1
Let h(g) be the first derivative of -6 + 0*g - g**2 - 2/3*g**3 + 1/2*g**4 + 2/5*g**5. Find l such that h(l) = 0.
-1, 0, 1
Let t(n) be the first derivative of -1 - 2/27*n**3 + 0*n - 2/9*n**2. Factor t(w).
-2*w*(w + 2)/9
Let v(h) = -h**2 + 2. Let a be v(0). Let m be ((-2)/24)/((-3)/8). Find l, given that -2/9 + 4/9*l - m*l**a = 0.
1
Let k(r) = -9*r**3 - 12*r**2 + 15*r - 11. Let b(i) = 3*i**3 + 4*i**2 - 5*i + 4. Let w(g) = 17*b(g) + 6*k(g). Factor w(x).
-(x - 1)*(x + 2)*(3*x + 1)
Let q be (-54)/75*(1 - 6). Factor 22/5*h**3 + 2/5*h - 2/5 + 8/5*h**4 + q*h**2.
2*(h + 1)**3*(4*h - 1)/5
Suppose -o - 4*o + 45 = 0. Let s be (-38)/(-10) - (-6 + o). Factor -s*k - 2/5 - 2/5*k**2.
-2*(k + 1)**2/5
Suppose -k + 4 = -l, 2*k - 5*l - 6 - 8 = 0. Let k*o**2 + o + 3*o**2 - 4 - o**2 + 6*o**3 - 7*o = 0. What is o?
-1, -2/3, 1
Find p, given that 9/2*p**2 + 3/2*p**3 + 0 + 3*p = 0.
-2, -1, 0
Let p(b) be the first derivative of b**3 + 0*b**2 + 1/36*b**5 - 1/36*b**4 - 1 + 0*b - 1/135*b**6. Let t(v) be the third derivative of p(v). Factor t(r).
-2*(r - 1)*(4*r - 1)/3
Let y(m) = -3*m**3 + 36*m**2 - 144*m + 192. Let v(q) = 3*q**3 - 36*q**2 + 144*q - 192. Let b(n) = -2*v(n) - 3*y(n). Factor b(s).
3*(s - 4)**3
Let r = 328 + -4256/13. Suppose 0 - 2/13*s**4 + 0*s - r*s**5 + 2/13*s**2 + 8/13*s**3 = 0. What is s?
-1, -1/4, 0, 1
Suppose -5*h - 2 = -0*l + 2*l, -l + 6 = -h. Find w such that 2 - 554*w**2 + 112*w - 10 - 158*w**l - 1568*w**5 + 1006*w**3 + 270*w**4 = 0.
-1, 1/4, 2/7
Let l(f) be the second derivative of -f**7/8820 + f**6/1260 - f**5/420 - f**4/6 - 2*f. Let q(w) be the third derivative of l(w). Let q(u) = 0. Calculate u.
1
Let n(h) be the first derivative of 0*h**3 - 1 - 1/16*h**4 + 1/2*h**2 - 1/40*h**5 + 0*h. Let v(k) be the second derivative of n(k). What is m in v(m) = 0?
-1, 0
Factor -7/2*t - 3/2*t**2 - 1.
-(t + 2)*(3*t + 1)/2
Let y = 89 - 87. Solve 2*o + 2/3*o**y + 4/3 = 0.
-2, -1
Suppose 0*x = -3*x - 12. Let s be ((-9)/(-3))/((-6)/x). Determine p so that 0 - 1/3*p**s + 0*p + 1/3*p**4 + 1/3*p**5 - 1/3*p**3 = 0.
-1, 0, 1
Let r(i) = -i**2 + 6. Let b be r(2). Let z(a) be the first derivative of 0*a - 2 - 1/9*a**3 + 0*a**b. Suppose z(d) = 0. Calculate d.
0
Let h(p) be the third derivative of 0 + 0*p + 0*p**3 + 3/32*p**4 - 1/80*p**5 - 7*p**2. Factor h(s).
-3*s*(s - 3)/4
Let j(b) be the third derivative of b**7/630 - b**6/360 - 5*b**2. Let j(n) = 0. What is n?
0, 1
Solve 1368*v - 5*v**4 + 5*v**3 + 10*v**2 - 1368*v = 0 for v.
-1, 0, 2
Let u(h) be the first derivative of -27*h**5/5 + 27*h**4 - 35*h**3 - 6*h**2 + 12*h - 9. Let u(z) = 0. What is z?
-1/3, 1/3, 2
Suppose -29*l + 16*l + 15*l = 0. Find y such that 0*y**4 - 2/15*y**5 + 2/15*y**3 + 0 + l*y + 0*y**2 = 0.
-1, 0, 1
Let p(m) = m**3 + 3*m**2 + m + 2. Suppose -3*n = -4*t - 0*n - 5, -2*n = -3*t - 4. Let q be p(t). Determine z so that 2*z**3 + 0*z**3 - 3*z**4 + 2*z**q = 0.
0, 2
Let j(i) be the second derivative of 1/60*i**5 + 1/8*i**4 - 1/2*i**2 +