ppose f = -4*x + 7*x. Solve 0 - 2*g + 75/4*g**x + 9*g**2 - 85/4*g**4 - 9/2*g**3 = 0 for g.
-2/3, 0, 2/5, 1
Let g be (-12)/8*8/(-6). Factor 3*b**2 + g*b**2 + b**2 - b**3 - 4*b**2.
-b**2*(b - 2)
Let t(q) be the second derivative of q + 0*q**4 + 1/3*q**3 + 1/240*q**6 + 0 - q**2 - 1/40*q**5. Let h(g) be the first derivative of t(g). Factor h(d).
(d - 2)**2*(d + 1)/2
Let z(j) be the second derivative of -j**6/255 - j**5/34 + 35*j. Determine t, given that z(t) = 0.
-5, 0
Let l = -170 - -515/3. Find t such that -l*t - 2/3 + 7/3*t**2 = 0.
-2/7, 1
Let k(j) = -3*j**3 - 29*j**2 + 42*j - 20. Let i(p) = -p**3 - 14*p**2 + 21*p - 10. Let z(h) = -5*i(h) + 2*k(h). Factor z(c).
-(c - 10)*(c - 1)**2
Let h(b) be the first derivative of -b**8/3360 + b**6/720 - 2*b**3/3 - 1. Let w(t) be the third derivative of h(t). Find z, given that w(z) = 0.
-1, 0, 1
Factor -1/3*n + 2/3 - 1/3*n**2.
-(n - 1)*(n + 2)/3
Let o be (1/7)/(36/42). Let p(r) be the first derivative of 1 - 1/2*r - o*r**3 - 1/2*r**2. Determine v so that p(v) = 0.
-1
Let g(s) be the third derivative of 0 + 1/48*s**4 + 1/240*s**6 - 6*s**2 + 0*s + 0*s**3 + 1/60*s**5. Find a such that g(a) = 0.
-1, 0
Let r be (-7 + 7)/(-4 + 1). Let u(h) be the first derivative of 2/5*h**2 + r*h + 2 - 2/15*h**3. What is k in u(k) = 0?
0, 2
Factor -2/5*i**3 + 0*i + 4/5*i**2 + 0.
-2*i**2*(i - 2)/5
Let x(b) be the first derivative of b**4 - 52*b**3/9 + 32*b**2/3 - 16*b/3 - 26. Find r, given that x(r) = 0.
1/3, 2
Let t(h) be the second derivative of 1/6*h**4 - 1/15*h**6 + 0 + 1/21*h**7 + h + 0*h**2 - 1/10*h**5 + 0*h**3. Let t(n) = 0. Calculate n.
-1, 0, 1
Let z = -6 - -11. Let t(v) = -6*v**2 + 3. Let a(s) = -11*s**2 - s + 5. Let i(l) = z*t(l) - 3*a(l). Determine c so that i(c) = 0.
-1, 0
Let w(j) be the second derivative of 32*j**7/21 - 48*j**6/5 + 81*j**5/5 - 28*j**4/3 + 2*j**3 + 6*j. What is i in w(i) = 0?
0, 1/4, 1, 3
Suppose m + 1 + 1 = 0. Let i be (-1 + 3 + -6)/m. What is u in 10 - 10 - 6*u**i - 3*u**3 - 3*u = 0?
-1, 0
Let s(y) = -y**2 + y + 1. Let b be s(2). Let h be b - (3 + -4)*2. Find x, given that h + 3/2*x**2 - 5/2*x = 0.
2/3, 1
Let q = -528 - -3698/7. Factor -2/7*l + 4/7 - q*l**2.
-2*(l - 1)*(l + 2)/7
Let l(f) be the first derivative of -81*f**5/10 - 39*f**4/2 - 40*f**3/3 - 4*f**2 + 2*f - 3. Let x(k) be the first derivative of l(k). Factor x(g).
-2*(g + 1)*(9*g + 2)**2
Solve 8/5*h**2 + 2/5 + 2*h = 0.
-1, -1/4
Factor 3*v + 10*v**3 + 4*v - 6*v**4 + 16*v**2 + 8*v**4 + v.
2*v*(v + 1)*(v + 2)**2
Let u(i) be the first derivative of -3*i**5/5 - 3*i**4/4 + i**3 + 3*i**2/2 + 4. Find m, given that u(m) = 0.
-1, 0, 1
Let k(v) = v**4 + v**3 - v + 1. Let b(h) = -12*h**3 + 6*h**2 + 3*h - 3. Let s(d) = -d + 5. Let q be s(2). Let p(j) = q*k(j) + b(j). Find i such that p(i) = 0.
0, 1, 2
Let j(o) be the first derivative of o**5/10 + o**4/4 - o**2/2 - o/2 + 13. Find s, given that j(s) = 0.
-1, 1
Factor -12*m + 45/2*m**2 + 2 - 25/2*m**3.
-(m - 1)*(5*m - 2)**2/2
Let p(s) be the third derivative of 3*s**2 + 1/12*s**4 + 0 + 1/10*s**5 + 1/20*s**6 + 1/105*s**7 + 0*s + 0*s**3. Suppose p(b) = 0. What is b?
-1, 0
Let m(a) be the third derivative of -1/2*a**3 - 1/40*a**6 + 0*a - 3/8*a**4 - 3/20*a**5 - 3*a**2 + 0. Factor m(c).
-3*(c + 1)**3
Let p be (-6)/(-4)*(-4)/(-3). Let o = -6 + 9. Factor -1 + x**p - x**4 - 7*x**2 + 4*x**o + 6*x - 2*x.
-(x - 1)**4
Let t = 0 + -4. Let f be 32/(-3)*1/t. Factor -f - 2/3*w**2 + 8/3*w.
-2*(w - 2)**2/3
Let u be ((-175)/(-10))/(1/(-2)). Let g be (100/u)/(12/(-70)). Factor -125/3*c**3 - 8/3 + 20/3*c + g*c**2.
-(5*c - 2)**2*(5*c + 2)/3
Let o be ((-8)/(-6))/((-8)/60). Let k be 3 + -5 + o/(-4). Find b, given that 0 - 1/2*b**3 + 1/2*b**2 + 1/2*b**5 - k*b**4 + 0*b = 0.
-1, 0, 1
Let u(y) = -5*y**2 + 4*y - 5. Let k(f) = 1 - 3*f + 6*f**2 - 1 + 4 + 2. Let d(t) = 2*k(t) + 3*u(t). Solve d(h) = 0 for h.
1
Suppose -7*u + 3*u = 2*u. Let o(n) be the second derivative of 0*n**4 + 0 - 4*n + 0*n**2 - 1/6*n**3 + 1/10*n**5 - 1/42*n**7 + u*n**6. Factor o(c).
-c*(c - 1)**2*(c + 1)**2
Let h(l) be the second derivative of -l**4/60 + 4*l**3/5 - 72*l**2/5 - 26*l. Factor h(f).
-(f - 12)**2/5
Suppose -6 = 2*b + b. Let r = b - -2. Factor -2/3*t**2 + r*t + 2/3.
-2*(t - 1)*(t + 1)/3
Let w(n) = 2*n. Suppose -4*x + 18 = 3*s + 4, -s = -2. Let q be w(x). Find b such that -3*b**2 - q*b - 4 + b**3 - 3*b**3 + 10*b**2 = 0.
-1/2, 2
Let m be (-3 + 0)/((-12)/8). Suppose -12 + m = -5*g. Find o, given that 13*o**g - 5*o**3 - 2 + o - 12*o**4 + 4*o + o**2 = 0.
-1, -2/3, 1/4, 1
Let v(o) be the first derivative of -19/14*o**4 - 2 - 1/21*o**6 - 16/7*o**2 + 2/5*o**5 + 50/21*o**3 + 8/7*o. Find b such that v(b) = 0.
1, 2
Let u(s) = 15*s**5 + 16*s**4 - 7*s**3 - 23*s**2 - 8*s + 7. Let y(t) = 7*t**5 + 8*t**4 - 3*t**3 - 11*t**2 - 4*t + 3. Let d(q) = 3*u(q) - 7*y(q). Factor d(r).
-4*r*(r - 1)*(r + 1)**3
Suppose 4*p = -r + 6, 3*r + 7*p - 11 = 2*p. Factor 2/9*i**r - 8/9*i + 8/9.
2*(i - 2)**2/9
Factor 0*i + 1/4*i**4 - 1/2*i**3 + 0 + 1/4*i**2.
i**2*(i - 1)**2/4
Let j = -104/33 - -42/11. Factor j*t**3 - 2/3*t**5 + 0 + 0*t - 2/3*t**2 + 2/3*t**4.
-2*t**2*(t - 1)**2*(t + 1)/3
Let u = 33832/63 + -537. Let b(z) be the second derivative of -2*z + 0 + 0*z**6 + 0*z**4 - 1/15*z**5 + 1/9*z**3 + 0*z**2 + u*z**7. Factor b(s).
2*s*(s - 1)**2*(s + 1)**2/3
Let s be 1 + (-4 - (4 - 9)). Let f(h) be the third derivative of 0*h - 1/15*h**3 + 0 - 2*h**s + 1/525*h**7 - 1/150*h**6 + 0*h**5 + 1/30*h**4. Factor f(y).
2*(y - 1)**3*(y + 1)/5
Let f(i) = 12*i**2 - 32*i - 33. Let r(p) = p**2 - p + 1. Let l(c) = -f(c) - 3*r(c). Solve l(d) = 0 for d.
-2/3, 3
Factor 0 - 5/3*f**3 - 7/3*f**4 - 4/3*f + 16/3*f**2.
-f*(f - 1)*(f + 2)*(7*f - 2)/3
Let r(j) = -j**3 - 4*j**2 + 2*j + 3. Let k be r(-3). Let c be k/(-8)*8/6. Factor -4*a**5 - 8*a**4 - 1 + a**4 + 2*a + 4*a**2 + 2*a**3 + 4*a**c.
-(a - 1)*(a + 1)**3*(4*a - 1)
Let o(f) be the second derivative of f**6/6 - 2*f**5 + 10*f**4 - 80*f**3/3 + 40*f**2 - 38*f. Suppose o(x) = 0. What is x?
2
Let g(y) be the first derivative of y**7/14 + 3*y**6/10 + 3*y**5/20 - 3*y**4/4 - y**3 - y + 1. Let v(z) be the first derivative of g(z). Factor v(f).
3*f*(f - 1)*(f + 1)**2*(f + 2)
Find p such that -5*p - 5/3*p**4 - 5/3*p**3 + 25/3*p**2 + 0 = 0.
-3, 0, 1
Let c(q) be the third derivative of -q**9/52920 + q**8/11760 - q**7/8820 - q**4/4 - 4*q**2. Let m(g) be the second derivative of c(g). Factor m(a).
-2*a**2*(a - 1)**2/7
Let 6/13 + 2/13*a**2 - 8/13*a = 0. Calculate a.
1, 3
Let q(n) be the first derivative of -n**7/420 - n**6/180 + n**5/30 + n**3/3 + 7. Let b(c) be the third derivative of q(c). Factor b(z).
-2*z*(z - 1)*(z + 2)
Let t = 4/89 - -81/178. Factor 0*z + 1/2*z**2 - t.
(z - 1)*(z + 1)/2
Suppose v - 6*v + 20 = 0. Suppose v*h = -h. Factor 0*f**2 + h*f - 2/3*f**3 + 0.
-2*f**3/3
Solve -4*c**2 + 3*c - 4*c + 2*c - 5*c = 0.
-1, 0
Let v(j) = 4*j**4 + 8*j**3 - 3*j**2 + j + 5. Let d(x) = -x**4 - x**3 - 1. Let i(t) = -5*d(t) - v(t). Factor i(u).
u*(u - 1)**3
Factor 2*c**3 + 0 + 0*c - 4/5*c**2 - 8/5*c**4 + 2/5*c**5.
2*c**2*(c - 2)*(c - 1)**2/5
Suppose -v + 13 = 2*o, 2*v - 2 = 4*o - 16. Factor 8*j**2 + o - 5 - 6*j**3 - 42*j**4 - 10*j**3.
-2*j**2*(3*j + 2)*(7*j - 2)
Let g(o) be the first derivative of -o**3/3 - 5*o**2 - 25*o - 35. What is x in g(x) = 0?
-5
What is w in -5*w**3 + 0 + 7/3*w**4 + 3*w**2 - 1/3*w**5 + 0*w = 0?
0, 1, 3
Factor -21*s**2 + s + 4*s + 5*s**3 + 31*s**2.
5*s*(s + 1)**2
Factor -1/4*c**2 - 1/4 + 1/2*c.
-(c - 1)**2/4
Let d = 2 - 3. Let p(n) = -n**3 - n. Let j(b) = 4*b**3 - 18*b**2 - 18*b. Let g(a) = j(a) - 10*p(a). Let l(s) = -s. Let y(o) = d*g(o) + 12*l(o). Factor y(x).
-2*x*(x - 1)*(7*x - 2)
Let v(o) be the second derivative of -o**6/10 + 2*o**5/5 - 7*o**4/12 + o**3/3 + 15*o. Factor v(j).
-j*(j - 1)**2*(3*j - 2)
Let a(j) = -j**3 + 10*j**2 + 5*j - 12. Let m(f) = -12*f**3 + 129*f**2 + 66*f - 156. Let n(v) = 27*a(v) - 2*m(v). Factor n(t).
-3*(t - 4)*(t - 1)*(t + 1)
Let -3*z - 6*z + 13 - 1 - 2*z**2 + 11*z = 0. What is z?
-2, 3
Let p be 4/(-14) + (-38)/14. Let v be ((-30)/20)/(p/4). Factor 1/3*u - 2/3*u**v + 1/3.
-(u - 1)*(2*u + 1)/3
Let f = -121 + 123. Let m(x) be the first derivative of 0*x**3 + x - x**f - 1/5*x**5 + 1/2*x**4 + 2. Factor m(l).
-(l - 1)**3*(l + 1)
Let q(y) = -62*y**3 + 89*y**2 - 32*y + 3. Let j(g) = 125*g**3 - 179*g**2 + 65*g - 6. Let p(u) = 2*j(u) + 5*q