 2*r**2. Solve w(h) = 0 for h.
1/6
Factor 10/7*z**2 - 2*z - 2/7*z**3 + 6/7.
-2*(z - 3)*(z - 1)**2/7
Let g(l) = -l**5 - l**3 - l. Let i(t) = -6*t**5 - 20*t**4 - 30*t**3 - 12*t**2 - 2*t. Let h(m) = 2*g(m) - i(m). Solve h(b) = 0.
-3, -1, 0
Let p = -12 - -16. Suppose 6*n**p - 3*n**2 - 3*n**5 + 2*n**2 + 3*n - 5*n**2 = 0. Calculate n.
-1, 0, 1
Let m(i) = 8*i**3 + 8*i**2 + 16*i - 8. Let w(v) = -v**2 - 1. Let y(j) = -m(j) + 12*w(j). Solve y(h) = 0 for h.
-1, -1/2
Let z(w) = -12*w**3 - 164*w**2 - 120*w. Let p(c) = -c**3 - 15*c**2 - 11*c. Let j(f) = -32*p(f) + 3*z(f). Find y such that j(y) = 0.
-2, -1, 0
Let t(z) be the second derivative of z**4/6 - z**3/3 + 5*z. Suppose t(n) = 0. Calculate n.
0, 1
Let z(o) be the third derivative of 2*o**7/105 - 2*o**6/15 + 2*o**5/15 + 2*o**4/3 - 2*o**3 - 12*o**2. What is w in z(w) = 0?
-1, 1, 3
Factor -10/9*a**3 + 2/9*a**5 - 2/3*a**2 + 0 - 2/9*a**4 + 0*a.
2*a**2*(a - 3)*(a + 1)**2/9
Let a = 184 - 717/4. Let l = -17/4 + a. Find i, given that -1/2 - i**2 + i**3 - 3/2*i + l*i**5 + 3/2*i**4 = 0.
-1, 1
Let d(t) be the third derivative of -7/540*t**6 - 1/504*t**8 + 1/135*t**5 + 0*t**4 + 0*t + 0 + 8/945*t**7 + 0*t**3 + 2*t**2. Factor d(y).
-2*y**2*(y - 1)**2*(3*y - 2)/9
Let j(g) be the second derivative of -g**5/150 + g**4/90 + g**3/45 - g**2/15 - 9*g. Suppose j(n) = 0. Calculate n.
-1, 1
Let b(o) be the first derivative of -2/9*o**3 + 0*o + 2/3*o**2 - 2. Factor b(r).
-2*r*(r - 2)/3
Let u be 5*6/150 + 3/(-15). Determine m so that -1/2*m - 3*m**3 + 9/4*m**2 + 5/4*m**4 + u = 0.
0, 2/5, 1
Let p be (13/(65/30))/(-2 + 10). Factor 0*b + 3/4*b**2 - p.
3*(b - 1)*(b + 1)/4
Factor -2*i**4 - 3*i**3 - 2*i**2 - 1/2*i + 0 - 1/2*i**5.
-i*(i + 1)**4/2
Let p(x) be the second derivative of -x**6/150 + x**4/20 - x**3/15 - 33*x. Suppose p(g) = 0. Calculate g.
-2, 0, 1
Let g(q) be the second derivative of 0*q**2 + 3/8*q**6 + 0 + 1/12*q**4 - 2*q + 25/168*q**7 + 0*q**3 + 3/10*q**5. Factor g(f).
f**2*(f + 1)*(5*f + 2)**2/4
Let f(w) = 0*w**2 + 7 - 6*w**2 - 9*w**3 - 3*w**2 - 5*w**4 + 2*w. Let c(a) = 3*a**4 + 5*a**3 + 5*a**2 - a - 4. Let g(i) = -7*c(i) - 4*f(i). Factor g(n).
-n*(n - 1)**2*(n + 1)
Let b be -7*(-4)/98 + (-76)/(-28). Find l, given that 6/7*l**b + 2/7*l**4 + 2/7*l**2 - 4/7 - 6/7*l = 0.
-2, -1, 1
Let c(t) be the third derivative of 19/144*t**6 + 0*t + 13/36*t**4 + 3*t**2 + 5/252*t**7 + 2/9*t**3 + 0 + 19/60*t**5. Determine q so that c(q) = 0.
-2, -1, -2/5
Let d(r) be the third derivative of 0*r**3 + 0*r**4 - 1/90*r**5 + 0 - 4*r**2 - 11/360*r**6 + 0*r. Factor d(y).
-y**2*(11*y + 2)/3
Let w(b) be the third derivative of -b**8/168 + 4*b**7/105 - b**6/15 - 23*b**2. Factor w(d).
-2*d**3*(d - 2)**2
Let k(p) be the first derivative of 2*p**5 - 25*p**4/4 + 20*p**3/3 - 5*p**2/2 + 8. What is a in k(a) = 0?
0, 1/2, 1
Suppose -8/13*o + 20/13*o**3 - 2/13 - 16/13*o**4 + 6/13*o**2 = 0. What is o?
-1/2, -1/4, 1
Suppose -4*l - 1 = -13. Let v = -125/3 - -42. Determine d so that -4*d**2 - 4/3*d**l + 16/3*d**4 + v - 1/3*d = 0.
-1/2, 1/4, 1
Let f = -461/3 + 154. Determine a, given that 0*a + 0 + a**3 + f*a**2 = 0.
-1/3, 0
Let u = -5 + 7. Let l(p) be the first derivative of -2 + 2*p + u*p**2 + 2/3*p**3. Factor l(j).
2*(j + 1)**2
Let z(m) be the third derivative of -m**5/240 - m**4/32 + 11*m**2. Factor z(l).
-l*(l + 3)/4
Let m(x) = -x**3 + 4*x**2 + x - 2. Let a be m(4). Factor 3/5 + 3/5*d**3 - 3/5*d - 3/5*d**a.
3*(d - 1)**2*(d + 1)/5
Let v(a) be the third derivative of -1/210*a**5 + 1/84*a**4 + 0*a**3 + 0 + 0*a - 4*a**2. Factor v(u).
-2*u*(u - 1)/7
Let c = -8 + 11. Let 2*y - 10*y**2 + 7 + 6*y**3 - c - 2 = 0. What is y?
-1/3, 1
Let k(t) = t**4 - 5*t**3 + 9*t**2 - 3*t + 2. Let c(d) = d**4 - 5*d**3 + 9*d**2 - 4*d + 2. Let s(a) = -4*c(a) + 3*k(a). Determine q, given that s(q) = 0.
1, 2
Let c = 183 - 2743/15. Let a(w) be the second derivative of 0 + 1/3*w**4 - c*w**6 + 1/40*w**5 - 1/3*w**3 + 1/28*w**7 + 4*w + 0*w**2. Let a(f) = 0. What is f?
-1, 0, 2/3, 1, 2
Let y(j) = -25*j**2 + 25*j + 60. Let f(i) = i**2 - 1. Let a(z) = 30*f(z) + y(z). Let a(b) = 0. Calculate b.
-3, -2
Suppose -4*x + 12 = 16. Let y be (3 - 0) + 1/x. Factor -18/7*g - 8/7*g**y - 4/7.
-2*(g + 2)*(4*g + 1)/7
Let y(j) = -6*j**4 + 8*j**3 - 2*j**2 - 12*j + 8. Let c(k) = 7*k**4 - 8*k**3 + k**2 + 13*k - 8. Let d(m) = -4*c(m) - 5*y(m). Suppose d(o) = 0. Calculate o.
-1, 1, 2
Let y = -636/7 + 92. Factor 26/7*h**2 + y*h**3 + 6/7*h + 0.
2*h*(h + 3)*(4*h + 1)/7
Let m = 3/68 + 121/340. Let o(s) = 7*s + 150. Let u be o(-21). Factor -1/5*d**4 + 0 - m*d**2 - 3/5*d**u + 0*d.
-d**2*(d + 1)*(d + 2)/5
Suppose 20 = w + 4*w. Let a(k) be the second derivative of k**2 - k + 0 + 1/10*k**5 + 1/2*k**w + k**3. Factor a(r).
2*(r + 1)**3
Let g = -125 + 376/3. Factor 0 + n**2 - g*n + 4/3*n**3.
n*(n + 1)*(4*n - 1)/3
Let w(y) = 3*y**3 - 2*y**2 + 2*y - 2. Let x be w(2). Find f, given that -4*f**4 - 4*f - 6*f**4 + x*f**3 + f**2 - 14*f**5 + 9*f**2 = 0.
-1, 0, 2/7, 1
Let k(v) be the second derivative of v**10/45360 - v**8/3360 - v**7/1890 - v**4/6 - 3*v. Let w(m) be the third derivative of k(m). Factor w(p).
2*p**2*(p - 2)*(p + 1)**2/3
Suppose 127 - 159 = -16*g. Factor -112/3*s**g + 58/3*s - 8/3 + 49/6*s**3.
(s - 4)*(7*s - 2)**2/6
Let g(h) be the second derivative of -5*h**4/12 + 5*h**3/2 + 10*h**2 + 2*h. What is w in g(w) = 0?
-1, 4
Let z(q) = -125*q**2 + 100*q - 20. Let j(y) = 2125*y**2 - 1700*y + 340. Let t(n) = -2*j(n) - 35*z(n). Solve t(a) = 0.
2/5
Suppose -3*k + 12 = -0*k. Suppose -g - 6 = -k*g. Factor 0*c**2 + 2*c**2 - 4*c**2 - g*c**3 + 2 + 2*c.
-2*(c - 1)*(c + 1)**2
Let z = 61/24 + -15/8. Let t be (2/12)/((-2)/(-8)). Find k, given that -4/3*k - z*k**2 - t = 0.
-1
Let f(t) be the first derivative of t**6/15 - 2*t**5/25 - t**4/10 + 2*t**3/15 - 19. Factor f(y).
2*y**2*(y - 1)**2*(y + 1)/5
Let v(y) = 3*y**2 - 1. Let w = 3 + -4. Let l be v(w). Factor 3*q**2 - 5*q**l + 2*q**3 + 2*q + 2*q**4 - 4*q**3.
2*q*(q - 1)**2*(q + 1)
Let z = 65 + -62. Let g(j) be the first derivative of -1 + z*j - 9/4*j**2 + 1/2*j**3. Factor g(v).
3*(v - 2)*(v - 1)/2
Let f(s) be the first derivative of s**9/1008 - s**7/140 + s**5/40 + 2*s**3/3 + 6. Let i(t) be the third derivative of f(t). Factor i(b).
3*b*(b - 1)**2*(b + 1)**2
Determine c so that -c + 1 + 1/4*c**4 - 3/4*c**2 + 1/2*c**3 = 0.
-2, 1
Let y(k) be the first derivative of -k**4/9 + k**3/18 + 6*k + 3. Let s(u) be the first derivative of y(u). Solve s(a) = 0.
0, 1/4
Let a(i) be the third derivative of -i**6/200 + 3*i**5/100 - 3*i**4/40 + i**3/10 + 2*i**2. Find p, given that a(p) = 0.
1
Let r(n) be the second derivative of 1/21*n**7 + 0*n**4 + 0*n**6 + 0*n**2 - 1/10*n**5 + 2*n + 0 + 0*n**3. Let r(d) = 0. Calculate d.
-1, 0, 1
Let x(o) = -o**3 + 7*o**2 - 6*o - 5. Let d be (-2)/11 + 46/11. Let h(n) = -n**3 + 6*n**2 - 5*n - 4. Let a(m) = d*x(m) - 5*h(m). What is z in a(z) = 0?
0, 1
Let f(m) be the third derivative of 3*m**2 + 0*m**3 + 0 + 1/840*m**7 + 1/96*m**4 + 1/80*m**5 + 1/160*m**6 + 0*m. Determine w so that f(w) = 0.
-1, 0
Suppose -2*u = 2*b, 0 = 2*b + u + 2*u + 3. Factor -6*z**2 - 5 + 48*z - 12*z**b + 37 + 3*z**2 - 5*z**2.
-4*(z - 2)*(z + 2)*(3*z + 2)
Suppose 0 = 7*s - 3*s - h - 14, -2*s + 2*h = -10. Factor 5*c**s + 8*c**2 - 10*c**2 - c**3 - 2*c**4.
-2*c**2*(c - 1)**2
Let b(m) be the third derivative of -1/2*m**3 + 0*m + 0*m**4 - 3*m**2 + 0 - 1/150*m**5 + 1/180*m**6. Let v(x) be the first derivative of b(x). Factor v(g).
2*g*(5*g - 2)/5
Let d = 622/5 - 124. Suppose -2*n = 3*n. Solve n*z + d*z**2 - 2/5 = 0 for z.
-1, 1
Let g be (2/4)/(2/8). Find s such that -s**2 - 3*s**4 + 3*s**4 + g*s**4 - s**4 = 0.
-1, 0, 1
Suppose -3*k - 24 = -4*u - 5*k, 5*k = 5*u. Factor 4*q**u - q**4 + 2 + 0*q**2 - 4*q**2 - q**4.
2*(q - 1)**2*(q + 1)**2
Let r(d) be the second derivative of d**4/42 - d**2/7 + 20*d. Suppose r(j) = 0. What is j?
-1, 1
Let h(d) = -d**3 - 4*d**2 + 4*d - 1. Let c be h(-5). Factor 15*j**3 - 39*j**c + 3*j + 24*j**2 + 42*j**4 + 9*j.
3*j*(j + 1)*(j + 2)**2
Let n(l) be the first derivative of l**5/10 - 2*l**4/3 + 5*l**3/3 - 2*l**2 + 2*l - 2. Let b(o) be the first derivative of n(o). Factor b(f).
2*(f - 2)*(f - 1)**2
Let 0 + 0*c + 60/7*c**3 - 33/7*c**4 - 15*c**5 - 12/7*c**2 = 0. Calculate c.
-1, 0, 2/7, 2/5
Let t(m) be the third derivative of 5*m**8/672 + m**7/30 + m**6/30 - m**5/12 - 13*m**4/48 - m**3/3