2*(y + 12)**2/2
Let r(a) = 2*a - 11 + 38*a**2 - 30*a**2 + 11*a. Let p(i) = 4*i**2 + 7*i - 5. Let m(b) = -5*p(b) + 3*r(b). Find x such that m(x) = 0.
-2, 1
Let u(g) be the second derivative of -88*g**6/5 + 119*g**5/5 + 82*g**4 + 56*g**3 + 16*g**2 - 216*g. Suppose u(y) = 0. What is y?
-2/3, -1/4, -2/11, 2
Suppose 68*y - 40*y + 5 = 29*y. Solve 0*r - 2/9*r**y + 0 - 2/9*r**2 + 2/9*r**3 + 2/9*r**4 = 0.
-1, 0, 1
Let v(o) be the first derivative of 0*o**5 - 15/8*o**4 + 0*o + 1/4*o**6 + 0*o**3 + 30 + 3*o**2. Determine y so that v(y) = 0.
-2, -1, 0, 1, 2
Let j be 1/(-1) - (-11)/(-33)*-12. Let k(t) be the second derivative of 3*t - t**j - 3/2*t**2 + 0 - 1/4*t**4. Factor k(o).
-3*(o + 1)**2
Let i(z) be the second derivative of -z**5/40 + 11*z**4/24 - 2*z**3 - 9*z**2 - 87*z. Factor i(k).
-(k - 6)**2*(k + 1)/2
Suppose -2*s + 89 = 25. Let x be (-33)/(-36) - 8/s. What is y in x*y - 4/3 + 4/3*y**2 - 2/3*y**3 = 0?
-1, 1, 2
Suppose 0 = 4*z - z - 9. Suppose -2*i = 3*q - 8*q - 14, -z*q - 4 = i. Suppose -14 - 4*d + 8*d - 4*d**3 + 2 + 12*d**i = 0. What is d?
-1, 1, 3
Let j(c) be the second derivative of 0 - 1/6*c**4 - 1/20*c**5 + 1/2*c**3 + c + 0*c**2. Factor j(g).
-g*(g - 1)*(g + 3)
Let d = -1067 - -1071. Suppose 2/5*z**d - 8/5 + 8/5*z**3 + 6/5*z**2 - 8/5*z = 0. What is z?
-2, -1, 1
Let y be 5757/(-45) + (-2)/5. Let m = y - -129. Let -4/3*n**4 + 0 + m*n**3 + 0*n**2 + 2/3*n**5 + 0*n = 0. What is n?
0, 1
Let y(n) be the third derivative of -n**5/15 - 5*n**4/6 - 8*n**3/3 + 12*n**2 + n. Factor y(v).
-4*(v + 1)*(v + 4)
Let a be 1*(0 + (-4)/(-2)). Suppose -2*g + 15 = -3*m, -a*g - 2*g - 4*m = 0. Factor 9*w**2 - g*w + 0*w**3 + 5*w**3 - 3*w**4 - 2*w**3 - 6.
-3*(w - 2)*(w - 1)*(w + 1)**2
Let h be -7 + 1 + -12*18/(-24). Let z(q) be the second derivative of 1/20*q**4 + 0 - 5*q + 3/5*q**2 - 3/10*q**h. Factor z(r).
3*(r - 2)*(r - 1)/5
Let d = -834 - -837. Let f(n) be the third derivative of -7*n**2 - 1/72*n**5 - 1/48*n**4 + 0 + 0*n + 1/18*n**d. Factor f(l).
-(l + 1)*(5*l - 2)/6
Let b be 2*(-3)/24 - (-7)/20. Let r(y) be the second derivative of 0*y**2 + 0*y**4 + 0 + 0*y**3 + b*y**5 - 3*y. Factor r(c).
2*c**3
Let a be -2*((-6)/9 + (-2)/6). Let 13/2*r**a + 4/3*r - 7/6*r**4 - 3/2*r**5 - 2/3 + 29/6*r**3 = 0. What is r?
-1, 2/9, 2
Let b = -3/184 + -36595/1288. Let l = -28 - b. Find c, given that 0 - 3/7*c - l*c**2 = 0.
-1, 0
Let u(j) = j**2 + 76*j + 103. Let i(a) = -3*a**2 - 189*a - 258. Let b(m) = -5*i(m) - 12*u(m). Factor b(t).
3*(t + 2)*(t + 9)
Let x = -145 + 147. Let z(l) be the first derivative of 6/5*l**5 - l**4 - 2*l - 1/3*l**6 - 4/3*l**3 + 10 + 3*l**x. Suppose z(d) = 0. What is d?
-1, 1
Let c(n) = 10*n**2 + 18*n - 56. Let o(l) = 22*l**2 + 37*l - 111. Let f(j) = -9*c(j) + 4*o(j). Solve f(x) = 0.
-10, 3
Suppose 441 = 10*o - 639. Let w = -322/3 + o. Find i, given that -2/3*i**2 - 2/9*i + 0 - w*i**3 - 2/9*i**4 = 0.
-1, 0
Let c(u) be the second derivative of -8*u**6/105 - 8*u**5/7 + 3*u**4/2 - 16*u**3/21 - 49*u**2/2 - 2*u. Let g(l) be the first derivative of c(l). Factor g(m).
-4*(m + 8)*(4*m - 1)**2/7
Let j = 1567 + -7789/5. Let l = j - 169/20. Factor 3/4 - 3*x + l*x**4 - 3*x**3 + 9/2*x**2.
3*(x - 1)**4/4
Suppose -2*h - 2*h + 12 = 0. Factor 8*a**3 - 5*a**3 - 2*a**4 + a**2 - h*a**2 + a**4.
-a**2*(a - 2)*(a - 1)
Let m(p) be the second derivative of -p**5/12 + p**4/8 + p**3/3 + 8*p**2 + 4*p. Let a(f) be the first derivative of m(f). Factor a(u).
-(u - 1)*(5*u + 2)
Suppose -524 - 82 + 620*c**2 + 1018*c + 1047*c + 45*c**3 + 116 = 0. Calculate c.
-7, 2/9
Let q = -111 - -116. Let f(t) be the first derivative of 3/2*t**4 - 3*t**2 - 3*t + 3/5*t**5 + q + 0*t**3. Factor f(m).
3*(m - 1)*(m + 1)**3
Let z(k) be the third derivative of -2*k**7/105 - 7*k**6/30 + k**5/15 + 7*k**4/6 - 196*k**2. Determine l, given that z(l) = 0.
-7, -1, 0, 1
Let p be (4 + (-27)/6)*0. Let g = 3 - p. Find z such that 6*z + 3 - 3*z**g + 3*z - 3*z**2 - 12*z + 6*z = 0.
-1, 1
Let d(x) = x**3 - 8*x**2 - x - 13. Let a be d(8). Let l = -21 - a. Factor l + 16/7*p + 2*p**4 + 2/7*p**5 + 36/7*p**3 + 40/7*p**2.
2*p*(p + 1)*(p + 2)**3/7
Let l = 204 - 204. Let s be (l + 4)*(-1 - 9/(-4)). Find c, given that 0*c**4 + 2/3*c**3 - 2/3*c**s + 0 + 0*c**2 + 0*c = 0.
-1, 0, 1
Let y(g) be the third derivative of -g**6/780 + 4*g**5/195 - 4*g**4/39 - 3*g**2 + 2*g. Factor y(c).
-2*c*(c - 4)**2/13
Let q be ((3 - 8/(-14)) + -3)*7. Let r be (q + -3)/(-2) + 9/12. Factor -r*i**3 + 2 - 3*i + 3/2*i**2.
-(i - 2)**3/4
Let z(c) = -3*c**5 - c**4 + 4*c**3 + 7*c**2. Let d(m) = -m**5 - m**4 + 2*m**3 + 3*m**2. Let t(v) = -7*d(v) + 3*z(v). Factor t(b).
-2*b**3*(b - 1)**2
Let x be (-7 - (-259)/35)/((-2)/(-4)). Let x*h + 8/5*h**4 - 2*h**3 - 14/5*h**2 + 0 = 0. Calculate h.
-1, 0, 1/4, 2
Let v(m) be the first derivative of m**5/20 - 5*m**4/8 - 35*m**2/2 + 25. Let d(b) be the second derivative of v(b). Factor d(x).
3*x*(x - 5)
Let v(m) be the first derivative of -5*m**4/4 - 35*m**3 - 260*m**2 - 770. Find t, given that v(t) = 0.
-13, -8, 0
Let t(w) be the third derivative of -3/4*w**5 + 0 + 1/14*w**7 - 10/3*w**3 + 18*w**2 - 1/12*w**6 + 5/2*w**4 + 0*w. Determine d, given that t(d) = 0.
-2, 2/3, 1
Let n(a) = 22*a**2 - 10*a - 8. Let h(x) be the first derivative of 23*x**3/3 - 9*x**2/2 - 9*x + 6. Let d(f) = -4*h(f) + 5*n(f). Solve d(r) = 0.
-2/9, 1
Let t(x) be the second derivative of x**6/50 + 27*x**5/100 + 23*x**4/20 + 3*x**3/10 - 54*x**2/5 - 22*x. Factor t(u).
3*(u - 1)*(u + 3)**2*(u + 4)/5
Let b be 380/100 - (-4)/20. Let -6*x - 2/3*x**5 - 4/3 - 28/3*x**3 - 4*x**b - 32/3*x**2 = 0. Calculate x.
-2, -1
Let h(q) be the third derivative of -q**8/40320 + q**7/10080 + q**5/10 - 7*q**2. Let z(n) be the third derivative of h(n). Factor z(d).
-d*(d - 1)/2
Let h(s) be the third derivative of 0 - 1/36*s**4 - 1/2016*s**8 + 1/30*s**5 + 23*s**2 + 1/210*s**7 - 13/720*s**6 + 0*s**3 + 0*s. Factor h(g).
-g*(g - 2)**2*(g - 1)**2/6
Let k = 181 + -127. Let c = -161/3 + k. Solve -1/6*x**4 - 1/6*x**5 + c*x**2 + 1/3*x**3 - 1/6 - 1/6*x = 0 for x.
-1, 1
Let t(s) be the third derivative of -5*s**9/3024 - s**8/168 + s**6/36 + s**5/24 - 4*s**3/3 - 4*s**2. Let j(d) be the first derivative of t(d). Factor j(n).
-5*n*(n - 1)*(n + 1)**3
Let i(c) = -9*c**2 + 74*c - 242. Let k(y) = 12*y**2 - 75*y + 243. Let w(m) = 3*i(m) + 2*k(m). Determine t so that w(t) = 0.
4, 20
Find k, given that -12/7*k**5 + 30/7*k**3 - 22/7*k**4 + 12/7 + 90/7*k**2 + 62/7*k = 0.
-3/2, -1, -1/3, 2
Let h(a) = 9*a + 191. Let i be h(-21). Factor 4/15 - 2/15*f - 2/15*f**i.
-2*(f - 1)*(f + 2)/15
Let l(m) = -m**3 - m. Let k be (4/12)/(4/12). Let o(v) = v**5 + v**4 + 3*v**3 - v**2 + 4*v. Let r(a) = k*o(a) + 4*l(a). Factor r(y).
y**2*(y - 1)*(y + 1)**2
Suppose 2*b + 0*a + 5*a = 99, -236 = -5*b - a. Let v = 47 - b. Suppose v + 3/2*w + 3/4*w**4 - 15/4*w**2 - 3/4*w**5 + 9/4*w**3 = 0. What is w?
-2, 0, 1
Let x(k) be the first derivative of 1/18*k**3 + 1/18*k**4 - 7 + 5*k + 1/60*k**5 + 0*k**2. Let p(z) be the first derivative of x(z). Suppose p(n) = 0. What is n?
-1, 0
Solve -2/5*f - 2/5*f**2 + 4/5 = 0 for f.
-2, 1
Suppose 5*q + 2*c - 11 = -2*c, 2*q - 3*c = 9. Suppose -q = -2*g + 5. Factor -1/4*l - 3/4*l**3 - 3/4*l**2 - 1/4*l**g + 0.
-l*(l + 1)**3/4
Solve -80/9 - 28/9*o**2 + 88/9*o + 2/9*o**3 = 0.
2, 10
Let y(x) be the first derivative of -x**4/12 + 5*x**3/3 - 23*x**2/6 - 13*x - 524. Factor y(c).
-(c - 13)*(c - 3)*(c + 1)/3
Let q(c) be the third derivative of 0*c**5 + 0 + 0*c + 2*c**2 - 1/84*c**4 + 1/420*c**6 + 0*c**3. Find n, given that q(n) = 0.
-1, 0, 1
Let t = 517 - 514. Let i(n) be the third derivative of -3/8*n**4 - 1/70*n**7 + 0 + n**3 - 1/20*n**5 + 3/40*n**6 + 0*n - t*n**2. Factor i(j).
-3*(j - 2)*(j - 1)**2*(j + 1)
Let o(g) be the first derivative of -g**4/4 + 4*g**3 - 24*g**2 - 15*g + 1. Let z(q) be the first derivative of o(q). Factor z(p).
-3*(p - 4)**2
Let r(j) be the third derivative of j**8/504 - 37*j**7/105 + 11*j**6/18 - 645*j**2. Factor r(h).
2*h**3*(h - 110)*(h - 1)/3
Let d(h) be the second derivative of -h**5/30 + 76*h**4/9 - 1975*h**3/3 + 3750*h**2 - 124*h. Factor d(p).
-2*(p - 75)**2*(p - 2)/3
Find u such that -15/7*u**3 + 3*u**2 - 3/7*u**4 + 15/7*u - 18/7 = 0.
-6, -1, 1
Suppose 80 = 21*n - 5*n. Suppose 11*m**3 + 9*m**5 - 6*m**3 - 10*m**4 - 4*m**n = 0. What is m?
0, 1
Let u(g) be the second derivative of -g**7/21 + 