u*v**6 + 0*v - 1/108*v**4 + 0 + v**2. What is k in c(k) = 0?
0, 1
Let l(n) = 5*n**5 + 83*n**4 + 76*n**3 - 4*n + 2. Let i(q) = 6*q**5 + 84*q**4 + 75*q**3 - 6*q + 3. Let b(c) = 2*i(c) - 3*l(c). Suppose b(v) = 0. What is v?
-26, -1, 0
Factor 2/5*d**3 + 0 + 72/5*d + 24/5*d**2.
2*d*(d + 6)**2/5
Suppose 0 = j - 2*j + 3. Factor -4*q**2 - 3*q**3 + 11*q**3 - q**j - 3*q**3.
4*q**2*(q - 1)
Let h(y) be the second derivative of -y**5/90 + y**4/36 - 6*y**2 + 7*y. Let i(w) be the first derivative of h(w). Solve i(b) = 0.
0, 1
Let z = 10 - -6. Let -s**2 - 10 + z*s - 10 + 4 - 3*s**2 = 0. Calculate s.
2
Let x be 8/3 + 12/36 + -2. Suppose -3*l + 3*r = 2 + 7, -2*l = -r + x. Factor -1/2*a**l - a - 1/2.
-(a + 1)**2/2
Let v(q) be the third derivative of q**8/4032 - q**7/1008 - 17*q**5/60 + 3*q**2. Let k(l) be the third derivative of v(l). Factor k(d).
5*d*(d - 1)
Suppose -12 = 4*k - 4*f, -6*k + 3*k - 4*f = -26. Factor -u - u + 2*u**2 - u**3 + 0*u**k + 5*u.
-u*(u - 3)*(u + 1)
Let q(g) be the second derivative of g**5/10 + g**4/2 - 8*g**3 - 80*g**2 + 266*g. Factor q(y).
2*(y - 5)*(y + 4)**2
Let f = 1572 - 1569. Suppose 1/3*i**3 + f + 5*i + 7/3*i**2 = 0. Calculate i.
-3, -1
Let h(r) = -r + 4. Let k be h(2). Factor 3*z**k - 12*z**2 + 6*z**2.
-3*z**2
Let z(k) be the second derivative of -k**6/2340 - k**5/78 - 25*k**4/156 - 3*k**3/2 + 6*k. Let u(m) be the second derivative of z(m). Factor u(w).
-2*(w + 5)**2/13
Let f(s) be the first derivative of 4*s**7/21 + s**6/15 - 8*s - 7. Let w(j) be the first derivative of f(j). Factor w(z).
2*z**4*(4*z + 1)
Let w(d) = d. Let q(u) = -u**2 - u. Let r = 25 - 24. Let h(p) = r*q(p) + w(p). Factor h(l).
-l**2
Let u(i) be the first derivative of 0*i + 1/8*i**2 - 7 + 1/32*i**4 - 1/8*i**3. Suppose u(j) = 0. What is j?
0, 1, 2
Let i be (-12)/8*(-10)/(-30)*0. Let k(j) be the third derivative of 2*j**2 + 1/330*j**5 + 0 + i*j - 1/44*j**4 + 0*j**3. Solve k(w) = 0 for w.
0, 3
Let x(z) = -3*z**3 - 12*z**2 - 9. Let n(q) = -q**3 - 6*q**2 - 4. Let p be -27*(-6)/108*-6. Let w(a) = p*n(a) + 4*x(a). Suppose w(i) = 0. Calculate i.
0, 2
Let s(w) = w**2 + 10*w + 8. Let v be s(-8). Let g be v/28 - 176/(-420). Determine n so that -8/15 + 2/5*n + g*n**2 = 0.
-4, 1
Suppose -8*q + 4*q = b - 3, b - 3 = -2*q. Let n(u) be the third derivative of -3/200*u**6 + 0*u + 4/75*u**5 - 6*u**2 - 1/24*u**4 + 0 - 1/15*u**b. Factor n(o).
-(o - 1)**2*(9*o + 2)/5
Suppose -3*d + u = -2 - 0, 12 = 4*d + u. Solve -89*a**3 - 3*a**2 + 84*a**3 - 3*a**4 + a + 2*a**d = 0 for a.
-1, 0, 1/3
Suppose 47 = 5*f - 3. Suppose 5*j = 5*t - f, 0 = -t - 1 + 3. Determine y, given that -2*y**2 + j*y**3 - 3*y + 0*y**3 + y**3 + 4*y = 0.
0, 1
Suppose -28*k = 47 - 131. Let n(d) be the second derivative of 0*d**4 + 0 + 0*d**k + 3/40*d**5 - 2*d + 0*d**2. What is r in n(r) = 0?
0
Let w(l) = 4*l - 1. Let s(p) = p**3 - 117*p**2 - 229*p - 121. Let k(o) = -3*s(o) + 6*w(o). Factor k(i).
-3*(i - 119)*(i + 1)**2
Factor -18*d**2 + 206 - 131 - 87*d + 51.
-3*(d + 6)*(6*d - 7)
Factor 8/5*f**4 - 32/5*f**2 + 8/5*f**3 - 8/5 - 4/5*f**5 + 28/5*f.
-4*(f - 1)**4*(f + 2)/5
Let o(k) = -k**4 + k**3 - 2*k**2 + k. Let r(m) = -m**4 + 21*m**3 + 133*m**2 - 629*m. Let y(b) = 4*o(b) + r(b). What is p in y(p) = 0?
-5, 0, 5
Let x be 8*3/(-6)*-1. Suppose 14 = x*a - 2. Find p, given that -p**3 + 3*p**3 - a*p + p - p**5 + 2*p = 0.
-1, 0, 1
Let y(w) be the second derivative of -w**5/90 - w**4/9 + 31*w**2/2 - 3*w. Let c(p) be the first derivative of y(p). Factor c(a).
-2*a*(a + 4)/3
Let y(w) be the first derivative of -w**5/70 + 3*w**4/14 - 8*w**3/7 + 16*w**2/7 + 22*w - 22. Let f(v) be the first derivative of y(v). Factor f(s).
-2*(s - 4)**2*(s - 1)/7
Suppose -9*k = -12 - 33. Suppose k*q**3 + 5*q**2 - 6*q + 23*q**4 + q - 28*q**4 = 0. What is q?
-1, 0, 1
Find u such that -2/5*u**2 + 1/5*u**5 - 4/5*u**3 + 2/5*u**4 + 3/5*u + 0 = 0.
-3, -1, 0, 1
Let p be (-12 - -8) + 4/1. Let t(a) be the third derivative of 0 + 5*a**2 + 1/420*a**6 - 1/84*a**4 + 1/735*a**7 - 1/210*a**5 + 0*a**3 + p*a. Factor t(r).
2*r*(r - 1)*(r + 1)**2/7
Find t such that 2/7 + 2*t**3 + 4/7*t**4 + 10/7*t + 18/7*t**2 = 0.
-1, -1/2
Let l(y) be the second derivative of -1/10*y**5 - 5/3*y**3 - 10*y + 0 - 2/3*y**4 - 2*y**2. Determine w, given that l(w) = 0.
-2, -1
Let w(u) be the first derivative of 11*u**4/6 - 34*u**3/9 - 41*u**2/12 + u/3 - 34. Let w(m) = 0. Calculate m.
-1/2, 1/22, 2
Let t(y) be the third derivative of y**7/210 - 3*y**6/8 + 21*y**5/10 + y**4/6 - 28*y**3 - 2*y**2 + 71. Factor t(k).
(k - 42)*(k - 2)**2*(k + 1)
Let h(u) = -2*u**2 + 18*u + 6. Let c(r) = -4*r**2 + 38*r + 13. Let x(y) = -6*c(y) + 13*h(y). Factor x(p).
-2*p*(p - 3)
Suppose -3*w - 7 = 4*f, -3*w = -4*f - 23 - 2. Let 78*i**3 + 2*i - 41*i**w - 42*i**3 + 3*i**4 - i - 3*i**2 + 4*i**5 = 0. Calculate i.
-1, 0, 1/4, 1
Let h(r) be the third derivative of r**5/420 - 163*r**4/84 + 26569*r**3/42 + 375*r**2. Factor h(l).
(l - 163)**2/7
Let m(b) be the first derivative of -b**7/1680 + b**6/720 + b**5/40 - 6*b**3 - 40. Let n(k) be the third derivative of m(k). Factor n(u).
-u*(u - 3)*(u + 2)/2
Let c(n) be the second derivative of -n**5/15 + 2*n**4 - 24*n**3 + 39*n**2/2 - 32*n. Let o(s) be the first derivative of c(s). Factor o(j).
-4*(j - 6)**2
Suppose -15*c = 7*c - 24*c. Let s(n) be the second derivative of 0 + 0*n**6 + 0*n**2 + 2*n + 1/105*n**7 + 0*n**3 + 0*n**5 + c*n**4. Factor s(w).
2*w**5/5
Suppose 0 - 1/3*h + 1/3*h**2 = 0. What is h?
0, 1
Factor 4*o**2 + 18 + 18 - 12*o**2 + 96*o - 108*o.
-4*(o + 3)*(2*o - 3)
Let g(j) be the second derivative of -j**6/120 + j**5/40 + j**4/4 + 7*j**3/12 + 5*j**2/8 + 13*j + 1. Suppose g(h) = 0. Calculate h.
-1, 5
Factor 6*w**2 - 12 + 104 + 15*w**2 + 426*w + 28.
3*(w + 20)*(7*w + 2)
Let n(z) be the second derivative of -z**5/240 - z**4/96 + z**3/12 - 5*z**2/2 - 24*z. Let c(r) be the first derivative of n(r). Let c(s) = 0. Calculate s.
-2, 1
Determine r, given that -1782*r - 214/3*r**3 + 8/3*r**4 - 486 + 630*r**2 = 0.
-1/4, 9
Suppose 0 = -5*q - z - 4, -14 - 6 = 5*q + 5*z. Find w, given that -3/4*w**2 + 3*w + q = 0.
0, 4
Suppose -4*d + 4*n - 112 = 0, 0 = -5*d - 9*n + 7*n - 119. Let w be ((-2)/(-8))/(d/(-200)). Suppose 14/9*v + 10/9*v**w + 2/3 + 2/9*v**3 = 0. What is v?
-3, -1
Let t(h) be the first derivative of h**6/72 - h**5/8 + 2*h**3/3 - 18. Let n(r) be the third derivative of t(r). Factor n(m).
5*m*(m - 3)
Let x(g) = 2*g**4 + 2*g**3 + 6*g**2 + 12*g + 6. Let q(n) = -n**3 + 2*n + 1. Let r(o) = -12*q(o) + 2*x(o). Factor r(u).
4*u**2*(u + 1)*(u + 3)
Suppose 0 = -2*n - 3*n - 150. Let g(t) = t**4 - t + 1. Let f(r) = 35*r**4 - 5*r**3 - 15*r**2 - 5*r + 20. Let b(p) = n*g(p) + f(p). Find j such that b(j) = 0.
-2, 1
Let t(q) be the second derivative of -q**7/42 - q**6/15 + 171*q. Suppose t(y) = 0. Calculate y.
-2, 0
Let k(h) = h**5 + h**4 + h. Let i(g) = 7*g**5 + 11*g**4 - 4*g**3 - 8*g**2 + 3*g. Let p(t) = i(t) - 3*k(t). Let p(o) = 0. Calculate o.
-2, -1, 0, 1
Let d(j) = 22*j**2 - 488*j + 936. Let a(k) = 14*k**2 - 325*k + 624. Let v(m) = -8*a(m) + 5*d(m). Find p, given that v(p) = 0.
2, 78
Let i = 4890 + -14666/3. Factor 0*q**2 + 0*q - 2*q**5 - 2/3*q**4 + 0 + i*q**3.
-2*q**3*(q + 1)*(3*q - 2)/3
Let m(l) be the third derivative of -l**8/8064 + l**7/1512 + l**6/864 - l**5/72 + 29*l**4/24 - 15*l**2. Let a(j) be the second derivative of m(j). Factor a(h).
-5*(h - 2)*(h - 1)*(h + 1)/6
Suppose -4*x + 4*n = -28, 3*n + 7 = -5*x + 2*n. Factor 0*p**2 + x - 1/8*p**3 + 1/8*p.
-p*(p - 1)*(p + 1)/8
Suppose -7*w = 3*w + 1680. Let t be (48/w)/((-5)/7). Factor -2/5*l + t + 2/5*l**3 - 2/5*l**2.
2*(l - 1)**2*(l + 1)/5
Factor 2/13*i**4 + 2/13*i**5 + 16/13*i - 2/13*i**2 - 10/13*i**3 - 8/13.
2*(i - 1)**3*(i + 2)**2/13
Factor -4/3*v**3 + 14 + 10*v**2 - 68/3*v.
-2*(v - 3)*(v - 1)*(2*v - 7)/3
Let t = 62/99 + -2/11. Let l(k) be the first derivative of 1/18*k**4 + 2/9*k**3 - t*k + 4 - 2/45*k**5 - 1/9*k**2. Suppose l(a) = 0. Calculate a.
-1, 1, 2
Let d(p) be the first derivative of p**6/6 + 18*p**5/5 - 43*p**4/4 - 56*p**3/3 + 42*p**2 + 80*p - 237. Let d(k) = 0. What is k?
-20, -1, 2
Let w(o) = -5*o - 137. Let s be w(-28). Let k(l) be the second derivative of -1/3*l**4 - l**5 + 0 + 0*l**s + 13*l - 8/15*l**6 + 0*l**2. Factor k(a).
-4*a**2*(a + 1)*(4*a + 1)
Let u(i) = -28*i**2 - 1012*i - 1792. Let z(q) = -4*q**2 - 145*q 