 x, given that r(x) = 0.
-1, 0, 1
Let m(s) be the second derivative of -10*s**2 + 5/4*s**4 + 27*s + 0*s**3 + 0 - 1/4*s**5. Determine i so that m(i) = 0.
-1, 2
Let w = 3 + -1. Factor -16*o**2 + 4*o**4 + 35*o**3 - o**w - 31*o**3 - 7*o**2.
4*o**2*(o - 2)*(o + 3)
Let a(n) be the first derivative of -43/18*n**4 - 4/9*n**2 + 16/9*n**3 + 4/3*n**5 - 46 - 7/27*n**6 + 0*n. Solve a(k) = 0.
0, 2/7, 1, 2
Let m be 412/28 - 4/(-14). Let o be (-3)/m*(-4)/6*5. Suppose -4/9 - o*z - 2/9*z**2 = 0. What is z?
-2, -1
Let x = 11 + -9. Factor 3 - 2*a**2 - 9*a**4 + 3*a**5 - 14*a + 6*a**2 + 6*a**3 + x*a**2 + 5*a.
3*(a - 1)**4*(a + 1)
Let h(f) be the third derivative of -14*f**5/15 - f**4/3 - f**3/21 - 7*f**2 + 15*f. Solve h(j) = 0.
-1/14
Suppose -1/4*l**4 + 7/6*l**3 - 7/6*l + 0 + 1/4*l**2 = 0. What is l?
-1, 0, 1, 14/3
Let p be (-9 - -13)*3*(-77)/(-396). Factor -p*y + 0 + 1/3*y**2.
y*(y - 7)/3
Let k = -1421 + 1425. Let x(t) be the third derivative of 8*t**2 + 1/210*t**6 - 2/105*t**5 + 0 + 4/21*t**3 - 1/42*t**k + 0*t. Determine g so that x(g) = 0.
-1, 1, 2
Let w = 6 + -8. Let t be (5 - 3) + w - -3. Find s, given that s**3 - 8*s**3 - 4*s**5 + 8*s**4 + 0*s**5 + t*s**3 = 0.
0, 1
Let u be (-2)/(-4)*(-66)/(-55). Let s = 242 - 240. Factor 12/5*f**s - 3*f + u.
3*(f - 1)*(4*f - 1)/5
Let d(u) = -u**3 + 2*u**2 + 3*u + 4. Let i be d(3). Let q = 71 + -42. What is z in -5*z**2 + z**i + q + z**3 + 3*z - 29 = 0?
-3, 0, 1
Factor 23*o**3 - 26*o**3 - 2*o**5 + 2*o**5 - 4*o**5 + 7*o**3.
-4*o**3*(o - 1)*(o + 1)
Factor 54*r**3 + r**2 - 8*r**4 - 13*r**2 - 121*r**3 + 62*r**3 - r**5 + 14*r**4.
-r**2*(r - 4)*(r - 3)*(r + 1)
Let p(k) be the first derivative of -k**5/15 - k**4/2 + 20*k**3/3 - k**2 + 3*k + 18. Let c(n) be the second derivative of p(n). Factor c(i).
-4*(i - 2)*(i + 5)
Let x = 205/978 + -7/163. Factor x*t**4 + 0 + 0*t + 0*t**2 - 1/6*t**3.
t**3*(t - 1)/6
Suppose -2*c - j + 3*j - 4 = 0, 26 = 2*c + 4*j. Let o be (-53363)/(-2924) - (-18)/(-1). Factor o*l**4 + 0*l**2 - 1/2*l**c + 0 + 0*l.
l**3*(l - 2)/4
Suppose a - 23 - 62 = 0. Let m = a + -58. Let -8 + 11*t + 10*t**2 - 225*t**2 - m*t**2 - 99*t = 0. Calculate t.
-2/11
Let o(h) = -4*h**4 - 4*h**3 + 8*h**2 + 4*h. Let c(i) = -i**5 + 4*i**4 + 4*i**3 - 7*i**2 - 3*i. Let a(v) = 4*c(v) + 3*o(v). Let a(d) = 0. What is d?
-1, 0, 1
Suppose 0 = x + 2*z + 12, z = 2*x + 6*z + 28. Let m be (-6 - x)*(-6)/3. Let 3*d**4 - 4*d**4 + 8*d**2 - 7*d**m + 2*d - 2*d**3 = 0. What is d?
-1, -1/4, 0, 1
Let m(x) be the second derivative of -x**6/60 + 7*x**5/20 - x**4/2 - 7*x**3/6 + 13*x**2/4 + 245*x. Factor m(o).
-(o - 13)*(o - 1)**2*(o + 1)/2
Let a = -774 - -778. Determine c, given that -4/11*c**3 + 5/11*c - 1/11*c**5 + 2/11 + 2/11*c**2 - 4/11*c**a = 0.
-2, -1, 1
Let w(v) be the third derivative of -59*v**2 + 0 + 0*v**4 + 0*v**3 + 0*v + 0*v**5 - 1/1155*v**7 + 1/660*v**6. Factor w(a).
-2*a**3*(a - 1)/11
Suppose -5*m + f + 6 = 0, -5*m = f - 5*f + 6. Suppose -3*k + 14 = m. Factor 377*u**3 + 264*u + 475*u**2 + 18*u**k - 161*u**2 + 72 - 245*u**3.
2*(u + 3)**2*(3*u + 2)**2
Let x = -1429/21 - 284/3. Let s = x + 163. Solve -1/7*k**3 + s + 1/7*k - 3/7*k**2 + 1/7*k**4 = 0.
-1, 1, 2
Let d(s) be the third derivative of s**5/210 - 5*s**4/42 + 54*s**2. Solve d(u) = 0 for u.
0, 10
Let p(w) = w**2 - 2*w + 4. Let v be p(7). What is d in d + 42*d**2 - 3*d**2 + 16*d**2 + 15*d**3 - 20 + v*d = 0?
-2, 1/3
Let h = -12304 - -86370/7. Factor h*n - 44/7*n**2 + 0 + 2/7*n**3.
2*n*(n - 11)**2/7
Let s(q) = -8*q + 24. Let j be s(-8). Let d be (2 + j/(-50))*(-3 - -8). Find w such that -d*w**2 - 4/5*w + 0 + 0*w**3 + 2/5*w**4 = 0.
-1, 0, 2
Let v(l) = -l**5 + l**4 - 1. Let i be -2 + (7*-5 - -1). Let h(b) = 38 - 80 - 28*b**4 + 32*b**5 - 4*b**3 + 60. Let j(w) = i*v(w) - 2*h(w). Factor j(t).
-4*t**3*(t - 1)*(7*t + 2)
Let n = -26801 + 26804. Solve -6*b**n + 3/2*b**5 + 9/2*b + 0 - 3*b**2 + 3*b**4 = 0.
-3, -1, 0, 1
Let z(a) be the first derivative of -a**4/6 + 5*a**3/3 + 6*a**2 + 19*a - 1. Let c(q) be the first derivative of z(q). Factor c(y).
-2*(y - 6)*(y + 1)
Factor r**5 + 31 + 30 - 3*r**3 + 8*r**4 - 6*r**4 - 61.
r**3*(r - 1)*(r + 3)
Let u(d) = -36*d**2 + 96*d + 448. Let x(v) = 7*v**2 - 19*v - 87. Let z(m) = -3*u(m) - 16*x(m). Solve z(g) = 0 for g.
-2, 6
Let g(o) be the first derivative of -5*o**4/48 - 5*o**3/12 - 10*o + 8. Let k(w) be the first derivative of g(w). Factor k(q).
-5*q*(q + 2)/4
Suppose -20 = -707*q + 697*q. Let s(j) be the first derivative of 11/4*j**q - j + 7/8*j**4 - 8/3*j**3 - 1. Solve s(t) = 0 for t.
2/7, 1
Factor -3*x - 15*x**2 + 3*x**3 - 15*x**2 + 21*x**2 + 3 + 6.
3*(x - 3)*(x - 1)*(x + 1)
Let y(g) = 2 - 6 + g - 6 - 2. Let m be y(14). Factor 1 + 2 - 5 - m - 2*q**3 + 6*q.
-2*(q - 1)**2*(q + 2)
Let m(g) be the third derivative of -1/30*g**5 + 0*g**3 + 0*g - 5*g**2 + 1/6*g**4 - 1/60*g**6 + 0. Factor m(c).
-2*c*(c - 1)*(c + 2)
Let q(j) be the third derivative of 1/90*j**6 + 13*j**2 + 0*j**4 + 0 + 0*j**5 - 1/45*j**7 + 0*j**3 + 0*j - 1/126*j**8. Factor q(r).
-2*r**3*(r + 2)*(4*r - 1)/3
What is d in -4/3*d**4 - 2*d**2 + 1/3*d**5 + 0 - 11/3*d**3 + 0*d = 0?
-1, 0, 6
Let q(z) be the third derivative of -1/120*z**5 + 7*z**2 + 0*z**3 + 1/240*z**6 + 0*z - 1/24*z**4 + 0. Find v, given that q(v) = 0.
-1, 0, 2
Suppose 2*j - 14 = 5*z, -85 = 3*z - 5*j - 50. Factor z*g + 3/5*g**3 - 2/5*g**4 + 0 + 0*g**2 - 1/5*g**5.
-g**3*(g - 1)*(g + 3)/5
Let g = 82/135 + -11/27. Let r(i) be the first derivative of 4/5*i - g*i**4 - 3 - 2/3*i**3 - 1/5*i**2. Factor r(f).
-2*(f + 1)*(f + 2)*(2*f - 1)/5
Let f(i) = i**2 + 13*i + 3. Let j be f(-13). Suppose -j*w - 2*w - 4*m + 23 = 0, 0 = -w + 5*m - 7. Suppose 6*t**2 - 12*t + 3*t + 6*t - w*t**3 = 0. What is t?
0, 1
Let p(q) be the first derivative of -q**4/48 - 5*q**3/24 - q**2/2 + q - 12. Let o(b) be the first derivative of p(b). Determine d, given that o(d) = 0.
-4, -1
Let v(n) = 14*n**2 - 20*n - 85. Let h(w) = -5*w**2 + 6*w + 28. Let a(d) = -11*h(d) - 4*v(d). Find q such that a(q) = 0.
-2, 16
Let j(t) be the third derivative of -t**5/20 + 9*t**4/8 + 5*t**3 - 2*t**2 - 20*t. Factor j(h).
-3*(h - 10)*(h + 1)
Let z(v) = 4*v - 10. Let i(p) = 9*p - 20. Let r(h) = -2*i(h) + 5*z(h). Let j be r(7). What is a in 3*a**4 - a**5 - j*a**2 + 0*a**5 + 2*a**2 + a - a**4 = 0?
-1, 0, 1
Let w = 10407/2 + -20813/4. Factor w*m**2 - 1 - 3/4*m.
(m - 4)*(m + 1)/4
Let j = 623/5 + -3733/30. Let d(q) be the first derivative of 0*q - 1/12*q**4 - j*q**2 + 2/9*q**3 - 5. Factor d(m).
-m*(m - 1)**2/3
Suppose 38*i = 35*i + m + 7, -i - 3*m = -19. Let u(d) be the first derivative of 0*d**2 - 12/5*d - 4 + 3/5*d**3 + 3/20*d**i. Solve u(v) = 0.
-2, 1
Determine k so that -72/7 + 75/7*k - 3/7*k**2 = 0.
1, 24
Let r be 18/27 + (-1 - 14/(-24)). Let a(k) be the third derivative of 0 + 0*k**3 + r*k**4 + 0*k - 6*k**2 + 1/8*k**6 - 7/20*k**5. Factor a(v).
3*v*(v - 1)*(5*v - 2)
Let f(q) = 2*q + 27. Let j be f(-11). Factor -107*s**2 + 4 - j - 22*s - 14*s**2.
-(11*s + 1)**2
Let r be (1 - 14/20)*(231/(-42) + 13). Find t such that -r*t + 3/2 + 3/4*t**2 = 0.
1, 2
Let u(c) be the second derivative of -c**5/10 - 2*c**4/3 - 2*c + 47. Find y, given that u(y) = 0.
-4, 0
Let q be -5 - (11 + -13 + -3) - 0. Factor 10/21*l**3 + 0*l - 4/21*l**2 + q.
2*l**2*(5*l - 2)/21
Suppose -3*y = -2*k + 386, y + 137 = 4*k + 15. Let o be 8/2 - y/(-39). Find l such that -o*l**3 + 0*l + 0 - 2/3*l**2 = 0.
-1, 0
Factor 22/9*j**3 + 14/3*j + 2 - 82/9*j**2.
2*(j - 3)*(j - 1)*(11*j + 3)/9
Let i(o) be the third derivative of -o**7/840 - o**6/480 + o**5/240 + o**4/96 + o**2 + o. Factor i(k).
-k*(k - 1)*(k + 1)**2/4
Let a(r) = -3*r - 9. Let l be a(-8). Determine x, given that 4*x**2 - l - 24*x**2 - 85*x - 5 = 0.
-4, -1/4
Suppose 2*p = 9*p - 35. Let u be p/(-2)*(-6)/(-2 + 8). Find o, given that -u*o**5 - 7/2*o**2 + 0 + 7/2*o**4 + o + 3/2*o**3 = 0.
-1, 0, 2/5, 1
Suppose 2/5*r**3 + 164/5*r**2 + 0 + 3362/5*r = 0. What is r?
-41, 0
Let r = -41/5 - -25/3. Let b(f) be the first derivative of -r*f**3 - 18/5*f + 6/5*f**2 + 3. Let b(w) = 0. What is w?
3
Let s(c) be the third derivative of c**6/720 - c**4/144 + 94*c**2. Let s(a) = 0. What is a?
-1, 0, 1
Let f(k) = 121*k. Let y be f(0). Factor y*g**2 - 1/4*g**3 - 1/2*g**4 - 1/4*g**5 + 0 + 0*g.
-g**3*(g + 1)**2/4
Let y(f) = 2*f**3 - 9*f**2 - 8*f + 25. Let q be y(5). Let p(g) be the first derivative of -q + 3/7*g**2 - 