*u - 2)/3
Let n = -13 + 8. Let h = 7 + n. Determine j so that -9*j**5 - 6*j**5 + 6*j - 15*j**4 - 6*j**4 + 21*j**h + 9*j**3 = 0.
-1, -2/5, 0, 1
Let c(h) be the first derivative of h**6/180 + h**5/60 - h**3/18 - h**2/12 - 2*h - 1. Let n(a) be the first derivative of c(a). Let n(i) = 0. Calculate i.
-1, 1
Solve -20/13*v - 2/13*v**2 - 50/13 = 0.
-5
Let q(t) be the second derivative of t**7/210 - t**5/60 - 3*t**2/2 + 2*t. Let l(j) be the first derivative of q(j). Factor l(h).
h**2*(h - 1)*(h + 1)
Let a(y) = 5*y**4 + 3*y**3 + 3*y**2 - 5*y. Let d = 5 - -1. Let m(c) = c**4 + c**2 - c. Let t(p) = d*m(p) - a(p). Solve t(o) = 0 for o.
0, 1
Let n = -2 + 4. Factor 6*a**2 - 1 + 3*a**4 + 0*a**3 + n*a - 3 - 2*a**3 - 5*a**4.
-2*(a - 1)**2*(a + 1)*(a + 2)
Let k be 2/5 + 60/75. Factor 3/5*r**3 + 0 + 0*r + k*r**2.
3*r**2*(r + 2)/5
Let w(p) be the third derivative of p**5/20 + 3*p**4/8 + p**3 - 5*p**2. Factor w(n).
3*(n + 1)*(n + 2)
Let l(z) be the second derivative of 3*z**5/140 - 3*z**3/14 - 3*z**2/7 + 43*z. Determine n, given that l(n) = 0.
-1, 2
Let c(i) = i**2. Let w(l) = 1 + 6*l**2 + 1 + 0*l - l**2 + 3*l. Let g(t) = 4*c(t) - w(t). Determine a, given that g(a) = 0.
-2, -1
Let m(o) be the third derivative of 0*o + 0 + 2*o**2 + 1/60*o**5 - 1/350*o**7 - 1/600*o**6 + 1/120*o**4 - 1/15*o**3. Solve m(r) = 0.
-1, 2/3, 1
Let o = 616/129 - -24/43. Factor -o - 24*b - 14/3*b**3 - 20*b**2.
-2*(b + 2)**2*(7*b + 2)/3
Determine c so that -59*c + 3*c**4 + 3*c**4 + 4 + 0*c**3 + 38*c**2 + 37*c - 26*c**3 = 0.
1/3, 1, 2
Let x(t) be the second derivative of 4*t + 1/2*t**2 - 1/12*t**4 + 1/6*t**3 + 0 + 1/80*t**5. Let q(n) be the first derivative of x(n). Find k such that q(k) = 0.
2/3, 2
Let p(m) be the third derivative of m**7/105 - m**5/30 + 2*m**2. Factor p(v).
2*v**2*(v - 1)*(v + 1)
Factor 5*b + 3*b - b**4 - 20*b**2 - 3*b**4 - b**3 + 17*b**3.
-4*b*(b - 2)*(b - 1)**2
Suppose 0 = -5*m - 3 - 2. Let p(z) = z**4 + z - 1. Let c(x) = 3*x**4 - x**3 + 3*x**2 + 6*x - 6. Let w(l) = m*c(l) + 5*p(l). Determine s, given that w(s) = 0.
-1, 1/2, 1
Factor -6*u + 8 + 15*u**2 - 9*u**3 - 8.
-3*u*(u - 1)*(3*u - 2)
Let a(n) be the first derivative of -2/9*n**3 + 0*n + 1/3*n**2 + 5. Factor a(m).
-2*m*(m - 1)/3
Factor 3/2*q**4 + 9*q**3 + 39/2*q**2 + 6 + 18*q.
3*(q + 1)**2*(q + 2)**2/2
Let k be (-318)/14 - 4/14. Let y = 23 + k. Factor 2/7*l + y - 2/7*l**2.
-2*l*(l - 1)/7
Let n(b) be the second derivative of 3*b + 0 - 7/40*b**6 + 11/16*b**4 - 3/2*b**3 + 9/20*b**5 - 3/2*b**2. Solve n(r) = 0.
-1, -2/7, 1, 2
Let v(y) = -y**5 + y**4 + y + 1. Let r(n) = -8*n**5 + 6*n**4 + 7*n + 7. Let g(t) = -4*r(t) + 28*v(t). Determine u, given that g(u) = 0.
-1, 0
Factor 4*q**2 - 4*q**5 + 0*q**5 - 6*q**4 + 4*q**3 + 2*q**4.
-4*q**2*(q - 1)*(q + 1)**2
Let o(f) be the second derivative of 1/9*f**4 - 4*f + 5/18*f**3 + 1/60*f**5 + 1/3*f**2 + 0. Determine w, given that o(w) = 0.
-2, -1
Find j such that -10*j + 17/2*j**3 + 4 - 5/2*j**4 - 3*j**2 = 0.
-1, 2/5, 2
Let w(o) be the second derivative of -o**4/12 + o**3/6 + o**2 - 19*o. Factor w(j).
-(j - 2)*(j + 1)
Let m(n) be the third derivative of n**8/560 + 2*n**7/175 - 3*n**6/100 - n**5/25 + n**4/8 + 21*n**2. What is j in m(j) = 0?
-5, -1, 0, 1
Let v(z) be the first derivative of -z**4/12 + 4*z**3/9 + 2*z**2/3 - 16*z/3 + 73. Factor v(t).
-(t - 4)*(t - 2)*(t + 2)/3
Let j(r) = 5*r**2 + 24*r - 3. Let d be j(-5). Let -4/5*o**d + 0 - 2/5*o**3 - 2/5*o = 0. Calculate o.
-1, 0
Suppose -9*w + 4*w = 0. Let o(a) be the first derivative of w*a**5 - a**2 + a**4 + 0*a - 2 - 1/3*a**6 + 0*a**3. Solve o(k) = 0 for k.
-1, 0, 1
Factor 920/9*b**3 - 608/9*b**4 - 482/9*b**2 - 8/9 + 104/9*b + 128/9*b**5.
2*(b - 2)**2*(4*b - 1)**3/9
Factor -1/6*k**4 + 0*k**3 + 0 + 0*k + 1/6*k**2.
-k**2*(k - 1)*(k + 1)/6
Let q = 4/9 + 1/18. Let 0 + 1/2*m**2 - q*m = 0. What is m?
0, 1
Let c(p) be the second derivative of -p**6/75 + 2*p**5/25 - p**4/6 + 2*p**3/15 - 32*p. Factor c(l).
-2*l*(l - 2)*(l - 1)**2/5
Determine b so that -2*b + 6*b + 8*b - 6*b**2 + b**3 - 8 = 0.
2
Determine d, given that 6/11*d + 2/11*d**2 + 4/11 = 0.
-2, -1
Let g be (2 + -1)/((-6)/30). Let n be (-4)/g*(-105)/(-42). Suppose 46/11*m**3 + 26/11*m + 14/11*m**4 + 54/11*m**n + 4/11 = 0. Calculate m.
-1, -2/7
Let j be ((-15)/50)/(36/(-10)). Let s(u) be the first derivative of -1 + 1/4*u + 1/8*u**2 - j*u**3 - 1/16*u**4. Factor s(h).
-(h - 1)*(h + 1)**2/4
Let b be (-2)/17 + -4*2/(-68). Solve 1/4*k**3 - 1/4*k + b + 0*k**2 = 0 for k.
-1, 0, 1
Suppose -36 = -4*t - 4*n, 2*t - n - 9 = 6. Factor -3*h**2 - 7*h + 2 - t - 2*h + 0*h**2.
-3*(h + 1)*(h + 2)
Let m = -6 - -8. Determine s so that -4*s - 8 - s**3 + 2*s**3 + m*s**2 - 8*s**2 + 16*s = 0.
2
Let n(w) = -3 + 1 + w - w**2 + 2. Let d(c) = -4*c**2 + 7*c. Let k(o) = -d(o) + 5*n(o). Find s such that k(s) = 0.
-2, 0
What is i in 2/5*i - 3/5 + 1/5*i**2 = 0?
-3, 1
Let b be 3*(0 - (-8)/6). Solve 3*j**b - 2*j**4 + 4*j**3 + 6*j**2 - 2*j + 6*j + 1 = 0 for j.
-1
Let u(i) be the first derivative of i**6/24 + 3*i**5/10 + 9*i**4/16 - 1. Factor u(c).
c**3*(c + 3)**2/4
Let i(r) be the third derivative of 0*r + 1/8*r**3 - 3/64*r**4 + 0 + 1/160*r**5 + 6*r**2. Factor i(b).
3*(b - 2)*(b - 1)/8
Let w = 172 + -2063/12. Let l(r) be the first derivative of 1/4*r**2 - 1/4*r - 1 - w*r**3. Let l(k) = 0. Calculate k.
1
Factor -8*p**2 + 2*p**3 + 13*p**3 - 11*p**3 - 12*p.
4*p*(p - 3)*(p + 1)
Let a = 41 - 31. Suppose 11*x - a = 6*x. Suppose -4/7 - 2/7*s + 6/7*s**x = 0. What is s?
-2/3, 1
Suppose -3*x**3 - 3*x**5 - 3*x**4 + 9*x**4 - x**2 + x**2 = 0. Calculate x.
0, 1
Let k(h) be the second derivative of -4*h - 1/30*h**6 + 0*h**5 - 1/2*h**2 + 0 + 1/6*h**4 + 0*h**3. Factor k(x).
-(x - 1)**2*(x + 1)**2
Let w(x) be the second derivative of -x**4/8 - x**3/2 + 6*x**2 - 11*x. Factor w(m).
-3*(m - 2)*(m + 4)/2
Suppose -4 = -5*t - 24. Let f be t/(-7) - 6/21. Solve -2/7*i**2 - f*i**4 + 0 + 0*i + 4/7*i**3 = 0 for i.
0, 1
Let l = -21286/19 + 1120. Let b = 94/57 + l. Factor -7/3*f**2 + 0 - 13/3*f**4 - 1/3*f - b*f**5 - 5*f**3.
-f*(f + 1)**3*(4*f + 1)/3
Let q be (-139)/(-90) - (0 + 1). Let j = -2/45 + q. Determine t, given that 1/4*t**2 - 1/4*t - j = 0.
-1, 2
Let u be 3 + 1 - (5/(-2))/(-1). Factor 1/4*p**2 - u*p + 9/4.
(p - 3)**2/4
Let q(s) = s**3 + 7*s**2 + 3*s - 2. Let n be q(-6). Solve -4*h**2 - 26*h + 10*h - n + 0 = 0.
-2
Let u(s) be the first derivative of -s**3/15 + s**2/10 + 2*s/5 + 5. Factor u(k).
-(k - 2)*(k + 1)/5
Let i(l) be the second derivative of l**4/4 - 3*l**3 + 15*l**2/2 - 23*l. Factor i(x).
3*(x - 5)*(x - 1)
Let s(n) = -n**3 + 18*n**2 - n + 18. Let p be s(18). Let k(z) be the first derivative of 0*z + 1/6*z**4 + 3 + 0*z**2 + p*z**3. Solve k(w) = 0.
0
Let t be (-2 - (3 - 5)) + 3. Suppose 2*j - t*j = -2. Let 8/3 - 2*d**j - 40/3*d + 98/3*d**4 + 140/3*d**3 = 0. What is d?
-1, 2/7
Let h(g) be the second derivative of -7/100*g**5 + 0*g**2 - 3*g + 0 - 1/12*g**4 + 1/15*g**3. Factor h(x).
-x*(x + 1)*(7*x - 2)/5
Solve 2/11*u**2 + 0 + 2/11*u = 0 for u.
-1, 0
Find f such that -2/3*f + 1/3*f**4 + 0*f**2 - 1/3 + 2/3*f**3 = 0.
-1, 1
Let j(h) be the first derivative of 3*h**4/20 - 3*h**2/10 + 10. Solve j(p) = 0 for p.
-1, 0, 1
Let t(k) = k + 3. Let s be t(0). Suppose -5*g = -q + 4*q - 40, -5 = -4*q + s*g. Factor 2*u**4 + 4*u**4 - q*u**4 - 4 - 2*u**2 + 5.
(u - 1)**2*(u + 1)**2
Let p(v) be the first derivative of -2*v**5/85 - 5*v**4/34 - 6*v**3/17 - 7*v**2/17 - 4*v/17 - 18. Factor p(z).
-2*(z + 1)**3*(z + 2)/17
Let l(d) be the third derivative of -d**5/170 - 5*d**4/204 - 2*d**3/51 - d**2. Factor l(y).
-2*(y + 1)*(3*y + 2)/17
Let o(h) be the first derivative of -2*h**3/15 - h**2/5 + 8. Determine r, given that o(r) = 0.
-1, 0
What is i in 5*i**4 - 24*i**3 - 70*i**5 + i**4 - 12 + 6*i**2 + 73*i**5 + 21*i = 0?
-4, -1, 1
Let y = -1/1279 + 10239/8953. Let c(t) be the first derivative of -y*t - 2/21*t**3 - 4/7*t**2 + 2. Factor c(x).
-2*(x + 2)**2/7
Let n(h) = h**3 - h**2 + h + 1. Let q be n(2). Let f = q + -3. Factor -3*b**2 + 4*b**f - 2*b**5 - b**2 + 16*b - 14*b.
-2*b*(b - 1)**3*(b + 1)
Let g(z) = 4*z**3 + 6*z**2 + 6*z + 4. Let n(h) = h + 3*h**3 + 5*h**2 + 2*h - 4*h + 4 + 7*h. Let s(f) = -5*g(f) + 6*n(f). Factor s(w).
-2*(w - 2)*(w + 1)**2
Let h(v) be the first derivative of 2*v**3/9 + 3*v**2/2 - 5*v/3 + 12. Suppose h(m) = 0. Calculate m.
-5, 1/2
Let z(s) = 9*s**