+ 129*h - 34*h + 1445 + 5*h**2.
5*(h - 17)**2
Let r(v) be the first derivative of 3 - 6*v + 2*v**3 - 21/4*v**4 + 21/2*v**2. Factor r(t).
-3*(t - 1)*(t + 1)*(7*t - 2)
Determine i so that -i**5 - 35*i**2 + 29*i**2 + i**3 + 6*i**4 - 2*i**5 + 2*i**3 = 0.
-1, 0, 1, 2
Suppose 4*l - 2*l + 38 = 5*s, -3*s + 2*l = -22. Suppose -3*b - 24 = -3*u - s*b, 5*u - 27 = -4*b. Factor 0*t + 0*t**2 - 1/2*t**u + 0 + 2*t**4 - 3/2*t**5.
-t**3*(t - 1)*(3*t - 1)/2
Suppose -26 = 150*k - 626. Let l be -1 - (-1)/(11/19). Determine f, given that -l*f**3 + 6/11*f**k + 0 - 2/11*f**2 + 4/11*f = 0.
-2/3, 0, 1
Suppose -13*j = -10*j - 12. Determine f, given that -f + j + 16*f**3 - 38*f**2 + 22*f**2 - 3 = 0.
-1/4, 1/4, 1
Let r(h) be the first derivative of 12*h**5/5 - 5*h**4 + 4*h**3/3 + 2*h**2 - 5. Suppose r(i) = 0. Calculate i.
-1/3, 0, 1
Let l be (-29)/(((-384)/20)/2) - 3. Let w(g) be the second derivative of l*g**4 + 0 + g - 1/8*g**3 + 1/4*g**2. Factor w(v).
(v - 2)*(v - 1)/4
Suppose 7*u = 2*u + 25. Let m(b) be the first derivative of -27/2*b**4 - 12*b**3 - 27/5*b**5 - u*b**2 - 1 - b. Find d, given that m(d) = 0.
-1, -1/3
Let b(x) be the third derivative of x**7/168 - 17*x**6/480 + 7*x**5/80 - 11*x**4/96 + x**3/12 - 30*x**2. Factor b(g).
(g - 1)**3*(5*g - 2)/4
Let k(v) be the first derivative of -v**6/4 - 3*v**5/5 + v**3 + 3*v**2/4 - 6. Factor k(w).
-3*w*(w - 1)*(w + 1)**3/2
Suppose -24*v = -20*v - 96. Let i be (-4)/(-16) + 2/v. Find x, given that -i + 1/3*x**2 + 1/3*x - 1/3*x**3 = 0.
-1, 1
Let 0*z**4 - z + 2/3 + 4/3*z**3 - 1/3*z**5 - 2/3*z**2 = 0. What is z?
-2, -1, 1
Let n be ((-14)/(-4))/((-2)/(-4)). Suppose 2*j - w = 10 - 2, -j - n = 5*w. Factor v**4 + 0*v**3 + 2*v**2 + 0*v**j + 3*v**3.
v**2*(v + 1)*(v + 2)
Let p(u) = u**2 + 2*u - 5. Let y be p(-4). Let m = 14 + -11. Factor 3 + 9*h**2 - 2 - 3*h**y - 6*h - h**m.
-(h - 1)**2*(4*h - 1)
Let i(x) be the third derivative of x**8/280 - x**7/525 - x**6/100 + x**5/150 - x**2. What is j in i(j) = 0?
-1, 0, 1/3, 1
Factor 0*y - 2/11*y**3 + 0 - 2/11*y**2.
-2*y**2*(y + 1)/11
Factor 3*c**5 + 33/4*c**4 - 3/4*c + 0 + 27/4*c**3 + 3/4*c**2.
3*c*(c + 1)**3*(4*c - 1)/4
Suppose -18*s = -15*s. Let g(t) be the third derivative of 0 + 1/40*t**6 + 1/105*t**7 + 2*t**2 - 1/24*t**4 + 0*t**3 + s*t + 0*t**5. Factor g(k).
k*(k + 1)**2*(2*k - 1)
Let k be ((-27)/6 + 5)*3. Factor -k + 3*n - 3/2*n**2.
-3*(n - 1)**2/2
Suppose -6*k + 5*k + 4 = 0. Factor -56*d**3 + 54*d**3 - d**k - 2*d**4 + 2*d**4 - d**2.
-d**2*(d + 1)**2
Let f(i) be the first derivative of -i**6/15 + 6*i**5/25 - 3*i**4/10 + 2*i**3/15 + 25. Factor f(w).
-2*w**2*(w - 1)**3/5
Let b be 48/(-12)*(2 - (-8)/(-3)). Solve -1/3*r**4 - 4/3*r + 0 - 5/3*r**3 - b*r**2 = 0.
-2, -1, 0
Let s be (-12)/20*(-2 - (0 + -1)). Let q be 24/10 + (-2)/5. Find y such that -9/5*y**3 + 0*y - 12/5*y**4 + 0 + s*y**q = 0.
-1, 0, 1/4
Let h(m) be the third derivative of m**5/240 - m**4/24 + m**3/6 + 4*m**2. Determine w, given that h(w) = 0.
2
Suppose 6 = 2*y + 2. Let m be (-1 - y) + 116/28. What is k in 2/7*k**5 + 0 - 8/7*k**4 - m*k**2 + 2/7*k + 12/7*k**3 = 0?
0, 1
Let p(x) be the third derivative of -5*x**2 + 1/270*x**5 + 1/54*x**4 + 0*x + 0*x**3 + 0. Solve p(i) = 0 for i.
-2, 0
Let c be 2/(-5) + 168/20. Let n(k) = 5*k**4 - 2*k**3 + 9*k**2 - 12*k - 12. Let a(z) = 3*z**4 - z**3 + 6*z**2 - 8*z - 8. Let b(d) = c*a(d) - 5*n(d). Factor b(v).
-(v - 2)**2*(v + 1)**2
Let w be -3 + 0 + (1 - (-28)/12). Find s such that -2/3*s + s**2 - w = 0.
-1/3, 1
Let g(h) be the second derivative of -h**6/1800 - h**5/150 - h**4/30 + h**3/2 - 2*h. Let j(m) be the second derivative of g(m). Factor j(k).
-(k + 2)**2/5
Factor -2/9*r**2 + 0*r + 0 + 0*r**3 + 2/9*r**4.
2*r**2*(r - 1)*(r + 1)/9
Let o(w) = w**3 + w**2 - 1. Let n(p) = 19*p**3 - 5*p**2 + 2*p - 8. Let k(a) = -5*n(a) + 40*o(a). Suppose k(r) = 0. What is r?
0, 2/11, 1
Let s be 12/36 - 2/8. Let d(z) be the second derivative of 0*z**2 - 3*z + 0*z**5 - 1/16*z**4 + s*z**3 + 1/120*z**6 + 0. Solve d(w) = 0.
-2, 0, 1
Find l, given that -2 - 2 + 45*l**3 + 15*l**4 + 83*l**3 + 72*l**2 + 45*l**4 = 0.
-1, -1/3, 1/5
Let x(w) be the first derivative of w**8/840 - w**6/180 - 2*w**3/3 - 4. Let d(b) be the third derivative of x(b). Solve d(r) = 0.
-1, 0, 1
Let u(y) be the second derivative of 3*y + 1/6*y**3 - y**2 + 0 + 1/12*y**4. What is x in u(x) = 0?
-2, 1
Let w(g) be the third derivative of g**2 + 1/1080*g**6 + 1/6*g**3 + 0*g + 1/18*g**4 - 1/90*g**5 + 0. Let s(u) be the first derivative of w(u). Factor s(b).
(b - 2)**2/3
Let g(v) be the third derivative of -v**8/6720 + v**7/420 - v**6/80 - v**5/6 - 10*v**2. Let b(i) be the third derivative of g(i). Factor b(a).
-3*(a - 3)*(a - 1)
Let y(n) be the second derivative of 1/6*n**4 + 0*n**3 - n**2 - n + 0. What is t in y(t) = 0?
-1, 1
Let -8*l**2 + 0 - l - 11/4*l**5 - 63/4*l**3 - 23/2*l**4 = 0. Calculate l.
-2, -1, -2/11, 0
Let b(t) = 3*t**5 - 6*t**4 - 6*t**3 - 9*t - 6. Let w(x) = -x**3 - x**2 - x - 1. Let d(u) = b(u) - 6*w(u). Let d(j) = 0. What is j?
-1, 0, 1
Let i be 0 - -1 - (0 - 1). Let u = 10 + -5. Let 5*d**5 - 3*d**5 + 5*d**3 + i*d - u*d**3 - 4*d**3 = 0. Calculate d.
-1, 0, 1
Suppose 4*r - 2*u + 4*u - 388 = 0, -289 = -3*r - 2*u. Let b be 117/r + (-2 - -1). Solve 4/11*h**3 - 4/11*h**2 + 2/11 - b*h**5 + 2/11*h**4 - 2/11*h = 0 for h.
-1, 1
Let p(b) be the first derivative of b**8/120 - b**7/210 - 7*b**6/180 + b**5/30 - b**3/3 + 4. Let r(u) be the third derivative of p(u). Factor r(y).
2*y*(y - 1)*(y + 1)*(7*y - 2)
Let z(g) = -g**3 - 3*g**2 + 2*g - 5. Let m be z(-4). Factor -9*i**2 + 3*i**3 + 7*i**3 + 0*i**3 + 3*i**4 - 4*i**m.
3*i**2*(i - 1)*(i + 3)
Let c(w) = 32*w**4 - 46*w**3 - 122*w**2 - 66*w - 10. Let z(k) = 64*k**4 - 91*k**3 - 245*k**2 - 131*k - 19. Let d(t) = 5*c(t) - 2*z(t). Factor d(v).
4*(v - 3)*(2*v + 1)**3
Let q(a) be the third derivative of a**9/54432 + a**8/45360 + a**5/60 - a**2. Let w(h) be the third derivative of q(h). Find l, given that w(l) = 0.
-2/5, 0
Let r be 18/(-4)*(-4)/6. Factor -26/9*x**2 - 8/9*x**r - 22/9*x - 4/9.
-2*(x + 1)*(x + 2)*(4*x + 1)/9
Let w(f) be the second derivative of -4*f - 1/4*f**4 - 27/2*f**2 - 3*f**3 + 0. Factor w(r).
-3*(r + 3)**2
Let c(g) = g**3 + g**2 + 3*g + 1. Let x be 2/4*1*6. Let r(t) = -t**2 - 2 - 4*t + 4*t**3 - 5*t**x + 0*t**3 - t**3. Let i(h) = 3*c(h) + 2*r(h). Factor i(n).
-(n - 1)**2*(n + 1)
Let n = 5/258 - -341/9030. Let y(a) be the first derivative of -n*a**5 - 2 - 12/7*a**3 + 4/7*a**4 + 0*a**2 + 54/7*a. Determine g so that y(g) = 0.
-1, 3
Factor 5*l**3 + 134*l**2 - 9*l + 3*l - 129*l**2 - 4*l**3.
l*(l - 1)*(l + 6)
Let x(j) = -j**2 + 10*j - 20. Let h be x(6). Let c(n) be the second derivative of 0 - 1/70*n**5 + 1/21*n**3 + n + 1/42*n**h - 1/105*n**6 + 0*n**2. Factor c(l).
-2*l*(l - 1)*(l + 1)**2/7
Let q(x) be the first derivative of 2*x**3/9 + 2*x**2 + 10*x/3 - 8. Factor q(w).
2*(w + 1)*(w + 5)/3
Let n(i) be the third derivative of -i**10/50400 + i**9/6720 - i**8/2240 + i**7/1680 + i**5/60 + 5*i**2. Let p(m) be the third derivative of n(m). Factor p(v).
-3*v*(v - 1)**3
Let s = 31 + -27. Let x(v) be the second derivative of 1/21*v**s + 0 + 0*v**2 - 2*v - 3/70*v**5 + 0*v**3. Find z such that x(z) = 0.
0, 2/3
Let t(l) = 2*l + 1. Let c be t(6). Factor -2 + c*w**4 - 6*w**4 - 5*w**2 + 9*w - 4*w**3 - 5*w**3.
(w - 1)**2*(w + 1)*(7*w - 2)
Let n be (-24)/10*30/(-9). Let -n*t + 2 + 2*t**2 + 2 + 2*t = 0. What is t?
1, 2
Suppose -8*f + 4*f = -8. Let c(d) be the second derivative of 0 + 1/12*d**4 - 7/40*d**5 + 7/12*d**3 - 1/2*d**f + 2*d. Determine z so that c(z) = 0.
-1, 2/7, 1
Let v(o) = -1 - o - 6*o + 6*o. Let u(a) = -a**2 - 3. Let w = 1 - 0. Let n(t) = w*u(t) - 2*v(t). Suppose n(b) = 0. Calculate b.
1
Let h = 68006/19831 + -2/2833. Factor -h*o**2 - 4/7 - 22/7*o.
-2*(3*o + 2)*(4*o + 1)/7
Let f(w) = -114*w**3 - 161*w**2 + 191*w - 51. Let r(p) = 23*p**3 + 32*p**2 - 38*p + 10. Let i(o) = 2*f(o) + 11*r(o). Let i(c) = 0. What is c?
-2, 2/5
Let l(b) = -9*b**5 + 12*b**4 - 7*b**3 - b**2 + 5*b + 5. Let t(h) = h**5 - h**3 + h**2 - h - 1. Let g(z) = -l(z) - 5*t(z). Find d, given that g(d) = 0.
0, 1
Let w(b) be the third derivative of -b**9/23520 + b**8/5880 - b**7/4410 - b**5/20 + 3*b**2. Let y(c) be the third derivative of w(c). Let y(k) = 0. What is k?
0, 2/3
Factor -t**3 - 4*t**5 - 40*t**2 - 12*t - 18*t**3 - 24*t**4 - 29*t*