c**6 + 0*c**2 + 1/3*c**3 + 2. Let m(r) be the first derivative of b(r). Factor m(z).
z*(z - 1)*(z + 2)*(7*z - 2)/2
Suppose 3*t - 9*c + 25 = -4*c, 0 = -5*c + 25. Let k(r) be the first derivative of t*r - 2/45*r**3 - 8 - 1/15*r**2. Suppose k(j) = 0. Calculate j.
-1, 0
Let o = -149 + 153. Let u(b) be the first derivative of 1 - 21/4*b**o + 24*b - 30*b**2 + 3/5*b**5 + 18*b**3. What is p in u(p) = 0?
1, 2
Let z be ((-2680)/(-180) + -15)*(-2)/(-2)*-6. Factor 1/3*h**2 + h + z.
(h + 1)*(h + 2)/3
Let a(b) be the second derivative of 0*b**2 - 30*b + 0*b**4 + 1/4*b**5 + 0 + 0*b**3. Find c such that a(c) = 0.
0
Let l(v) be the first derivative of -2/57*v**3 - 23 - 1/19*v**2 + 4/19*v. Suppose l(k) = 0. Calculate k.
-2, 1
Let t be 13/3 - ((-1067)/(-33) + -32). What is i in 8/7 + 6/7*i**5 + 40/7*i + 74/7*i**3 + 34/7*i**t + 78/7*i**2 = 0?
-2, -1, -2/3
Factor -24/5*n**2 + 20*n - 16/5.
-4*(n - 4)*(6*n - 1)/5
Let m be 159/33 + -5 - (-46)/132. Let l(v) be the second derivative of m*v**4 + 0 - 1/3*v**3 + 8*v - 2*v**2. Find d such that l(d) = 0.
-1, 2
Let u be (-289)/255 - 28/(-12). Factor 0 + u*f + 3*f**3 + 21/5*f**2.
3*f*(f + 1)*(5*f + 2)/5
Let h(d) = 8*d + 56. Let f be h(-6). What is o in -o - 2*o**2 + 22 - 11*o - f*o = 0?
-11, 1
Let m be (14 + 1 - -1) + (-15 - -11). Factor 11 + 4*d**2 + 10 + m*d - 13.
4*(d + 1)*(d + 2)
Let j(y) = 29*y**2 - 40*y. Let f(m) = -7*m**2 + 10*m. Let s be 7/(7/(-2))*(-9)/2. Let a(i) = s*f(i) + 2*j(i). Factor a(x).
-5*x*(x - 2)
Suppose -225 = 2*u + 7*u. Let v be (5/u)/(3/(-24)). Factor 8/5*n**2 + v*n + 2/5*n**3 + 0.
2*n*(n + 2)**2/5
Let m be (-34)/(-8) + 5/(-20). Suppose -2*g - 4*k + 16 = 2*g, -3*g - m = -5*k. Factor 5*q**2 - 5*q**g + 2*q - 2 - 2*q**3 - 2*q**2 + 4*q**2.
-2*(q - 1)**2*(q + 1)
Suppose -3*p - 15 = -f, 9*p = -5*f + 11*p + 10. Let o(i) be the first derivative of -1/6*i**4 + 0*i - 2 + 0*i**2 + f*i**3. Factor o(k).
-2*k**3/3
Let u(k) be the third derivative of -k**5/15 + k**4/3 - 2*k**3/3 - 303*k**2. Let u(i) = 0. What is i?
1
Let d(p) = p**5 + p**4 + p**3 + p**2 + p - 1. Let c(m) = -11*m**5 - 17*m**4 - 5*m**3 + m**2 - 2*m + 2. Let w(l) = c(l) + 2*d(l). Factor w(j).
-3*j**2*(j + 1)**2*(3*j - 1)
Let y = 26821/15 - 1788. Let h(i) be the second derivative of -1/135*i**6 - y*i**5 + 0 - 1/3*i**2 - 2/9*i**4 - 10/27*i**3 - 3*i. Suppose h(q) = 0. Calculate q.
-3, -1
Solve y**3 + 24*y**2 - 2*y**4 + 3*y**3 + 3*y - 10 + 25*y + 20 = 0 for y.
-1, 5
Let h(u) be the third derivative of u**8/3024 + 4*u**7/315 + 47*u**6/360 - 7*u**5/54 - 16*u**4/9 + 16*u**3/3 + 75*u**2. Let h(s) = 0. What is s?
-12, -2, 1
Let r = 8 + 1. Let b be (-1 - -1) + r/3. Find c such that -b + 4*c - 2*c + 3 - 2*c**3 = 0.
-1, 0, 1
Let v(k) be the first derivative of -k**3/6 + 9*k**2/4 - 9*k - 224. Determine c, given that v(c) = 0.
3, 6
Let c(k) be the second derivative of 1/14*k**4 - 3/70*k**5 - 3*k + 0*k**2 + 1/105*k**6 + 0 - 1/21*k**3. Factor c(o).
2*o*(o - 1)**3/7
Suppose 5*w = 30, -4*o + 93 + 49 = 5*w. Suppose o*a - 4/3 - 147*a**2 = 0. Calculate a.
2/21
Determine r, given that -36*r**2 + 122*r**3 - 258*r**3 + 133*r**3 - 90 + 129*r = 0.
-15, 1, 2
Let q(b) = -b**3 - b - 1. Let h(g) = -18*g**4 - 68*g**3 - 14*g**2 + 48*g + 2. Let s(y) = 2*h(y) + 20*q(y). Let s(f) = 0. Calculate f.
-4, -1, 1/3
Let b be 3/(-4) - (-1)/(-4). Let r be (b - (0 - -1)) + (-320)/(-144). Solve r - 2/9*y**3 - 2/3*y + 2/3*y**2 = 0.
1
Let x(l) be the second derivative of -l**5/5 + 8*l**3/3 + 310*l. Find k such that x(k) = 0.
-2, 0, 2
Let w(f) = 3*f**4 - 26*f**3 + 18*f**2 + 91*f - 101. Let q(l) = l**3 + l + 1. Let z(v) = -5*q(v) - w(v). Suppose z(m) = 0. Calculate m.
-2, 1, 4
Let i(j) be the third derivative of -j**8/70560 + j**6/2520 + 11*j**5/60 + 2*j**2. Let o(q) be the third derivative of i(q). Determine x, given that o(x) = 0.
-1, 1
What is i in 124*i - 9/2*i**3 - 177/2*i**2 - 42 = 0?
-21, 2/3
Let b = -863 - -4316/5. Let w(j) be the first derivative of -1 + 0*j**2 - b*j**5 + 1/3*j**3 + 0*j - 1/4*j**4 + 1/6*j**6. Solve w(x) = 0.
-1, 0, 1
Let y = 86 - 81. Let q(h) be the first derivative of 243/5*h**y + 81*h**4 + 18*h**2 + 3*h - 8 + 54*h**3. Factor q(v).
3*(3*v + 1)**4
Let u be (-2 - -1)*(-20)/14400. Let k(x) be the third derivative of 1/144*x**4 - u*x**6 - 5*x**2 + 1/1260*x**7 + 0*x - 1/360*x**5 + 0 + 0*x**3. Factor k(a).
a*(a - 1)**2*(a + 1)/6
Suppose 16 = 2*q - 3*s - 2*s, -3*s - 2 = -5*q. Let b be ((-16)/(-48))/(q/(-48)). Solve b*j**2 - j**2 - 3 - 12*j + 15*j**2 - 7*j**2 = 0 for j.
-1/5, 1
Let y(z) be the second derivative of -z**5/3 + 2*z**4/3 + 2*z**3/3 - 3*z**2/2 - 6*z. Let o(h) be the first derivative of y(h). Suppose o(i) = 0. What is i?
-1/5, 1
Let a = 11 + -2. Suppose -5*o - 12 = -a*o. What is z in -z**4 + 6*z**4 - 8*z**4 + o*z**2 = 0?
-1, 0, 1
Let q(t) = 6*t**4 - 91*t**3 - 660*t**2 - 973*t. Let i(o) = -20*o**4 + 272*o**3 + 1980*o**2 + 2920*o. Let p(j) = 5*i(j) + 16*q(j). Factor p(a).
-4*a*(a + 2)*(a + 11)**2
Let h(s) = -2*s**2. Let v(z) = 3*z**2. Suppose 0 = -2*j - 0*r + 4*r - 10, 4*r = -3*j - 15. Let i(k) = j*h(k) - 3*v(k). Find g such that i(g) = 0.
0
Let h(t) be the second derivative of 2*t + 0 + 2/15*t**3 + 1/30*t**4 + 0*t**2. Factor h(d).
2*d*(d + 2)/5
Let w(u) = -6*u**4 - 28*u**3 + 2*u + 2. Let s(y) = 7*y**4 + 28*y**3 - 3*y - 3. Let h(r) = -2*s(r) - 3*w(r). Determine i, given that h(i) = 0.
-7, 0
Suppose 0*g - 3*b = 2*g - 2, -4*g - 3*b + 10 = 0. Let t be ((-1)/((-1)/g))/2. Suppose -f**2 - 4*f**t + 2*f**2 - 2*f**3 - f**4 + 2*f**2 = 0. What is f?
-1, 0
Let -16/9*x**3 + 2/9*x**4 + 0 + 8/3*x**2 + 0*x = 0. What is x?
0, 2, 6
Let o(y) = 7*y. Let c(n) = 48*n. Let f(v) = -4*c(v) + 27*o(v). Let m be f(-1). Factor h**3 - 2*h**3 - 4*h**5 + 2*h**4 + m*h**5.
-h**3*(h - 1)**2
Let x = -91 + 4461/49. Let y = x + 45/98. Determine v so that 1/2*v + v**2 + y*v**3 + 0 = 0.
-1, 0
Let o be 75/(-45)*1/(-5). Let t(w) be the second derivative of o*w**3 - 7/12*w**4 + 0*w**2 + 0 + w. Factor t(x).
-x*(7*x - 2)
Let p(r) = 4*r**3 - 30*r**2 + 78*r - 37. Let w(c) = 15*c**3 - 105*c**2 + 273*c - 129. Let a(o) = -18*p(o) + 5*w(o). Factor a(z).
3*(z - 1)**2*(z + 7)
Let a(t) = 0 + 5 + 2 - 2 - 6*t + 5*t**2. Let r(z) = -21*z**2 + 24*z - 21. Suppose 2*m - 13 = 5. Let g(c) = m*a(c) + 2*r(c). Factor g(q).
3*(q - 1)**2
Let y(n) be the second derivative of -n**8/336 - n**7/105 - n**6/120 - 17*n**2/2 + 46*n. Let s(p) be the first derivative of y(p). Factor s(x).
-x**3*(x + 1)**2
Let m = -77072/5 + 15424. What is o in m*o + 32/5 + 18/5*o**2 + 2/5*o**3 = 0?
-4, -1
Let q be ((-4)/(-8))/((-215)/20). Let w = 104/387 + q. Factor -w*b**3 - 8/9 + 0*b + 2/3*b**2.
-2*(b - 2)**2*(b + 1)/9
Let l = 6/209 - -340/2717. Determine x so that -2/13*x**3 + 2/13*x + l*x**2 - 2/13*x**4 + 0 = 0.
-1, 0, 1
Let a be 3/(-18) + (-3)/36*-62. Let p be -10 + 9 + 51/a. Find d, given that p*d**2 + 8/5*d**5 - 26/5*d + 4/5 - 22/5*d**3 - 2*d**4 = 0.
-2, 1/4, 1
Let r(j) = 15*j**2 - 318*j - 333. Let g(c) = -6*c**2 + 127*c + 133. Let s(l) = 12*g(l) + 5*r(l). Factor s(d).
3*(d - 23)*(d + 1)
Let k(v) = 22*v**2 + 22*v + 4. Let z(m) = 22*m**2 + 23*m + 4. Let r(p) = 3*k(p) - 4*z(p). Factor r(w).
-2*(w + 1)*(11*w + 2)
Suppose w - 34 = -5*y, -2*w + w - 3*y + 26 = 0. Determine f so that -20*f**2 - 12*f**3 - 3*f**4 + 16*f**5 + w*f**4 + 9*f**4 - 4*f = 0.
-1, -1/4, 0, 1
Let s(i) = i**3 + 4*i**2 - i. Let n be s(-4). Suppose -60*f - 28*f**5 + 68*f - 16*f**n + 36*f**2 - 20*f**4 + 20*f**3 = 0. What is f?
-1, -2/7, 0, 1
Let n be (-301)/774*4/(-21). Let a(h) be the first derivative of 1/36*h**4 - 5 + 1/18*h**2 + 0*h + n*h**3. Factor a(i).
i*(i + 1)**2/9
Let t(n) be the third derivative of 1/270*n**5 + 1/27*n**3 + 0*n + 0 - 1/54*n**4 - 21*n**2. Factor t(z).
2*(z - 1)**2/9
Let y(n) = -188*n**2 + n**3 + 210*n**2 + 1 + 2. Let f be y(-22). Find w, given that -6 - 6 + 4*w + 23*w - 9*w**2 - f*w = 0.
2/3, 2
Suppose -16*z - 35*z = z. Let t(x) be the second derivative of 7*x + 1/16*x**4 + z + 0*x**2 + 1/40*x**5 - 1/12*x**3 - 1/40*x**6. Find a, given that t(a) = 0.
-1, 0, 2/3, 1
Solve -3 + 3/7*v**5 - 3*v**4 - 6/7*v**3 + 3/7*v + 6*v**2 = 0 for v.
-1, 1, 7
Let y be 3*20/3 + -2. Let j = y - 17. Let -3*f - 3*f + f**2 - j + 4*f + 2 = 0. What is f?
1
Let s(g) be the second derivative of 6*g + 4/15*g**3 - 8/5*g**2 + 0 + 1/15*g**4 - 1/50*g**5. Factor s(k).
-2*(k - 2)**2*(k + 2)/5
Let m be 7 + (