2)*(u + 1)*(9*u + 2)
Let r(t) be the first derivative of -t**6/540 + t**5/180 + 2*t**3 + 3. Let d(a) be the third derivative of r(a). Factor d(h).
-2*h*(h - 1)/3
Let s(p) be the third derivative of p**7/630 + p**4/6 - 2*p**2. Let g(c) be the second derivative of s(c). Determine q, given that g(q) = 0.
0
Let j(z) be the first derivative of -5*z**4/8 - 5*z**3/2 - 17. Factor j(u).
-5*u**2*(u + 3)/2
Let r(y) be the first derivative of y**7/210 - y**6/120 - y**5/20 + y**4/24 + y**3/3 + 3*y**2/2 - 2. Let g(l) be the second derivative of r(l). Factor g(n).
(n - 2)*(n - 1)*(n + 1)**2
Factor 0*b**2 + 1/4*b**4 + 0*b + 1/4*b**5 + 0 + 0*b**3.
b**4*(b + 1)/4
Let f be 8 - (4 + 51/15). Factor 2*a + 3/5 + f*a**2.
(a + 3)*(3*a + 1)/5
Let y = -163/30 + 28/5. Let c(u) be the first derivative of 1/15*u**5 - 1/4*u**4 + 1/3*u**3 + 0*u - y*u**2 - 1. Factor c(x).
x*(x - 1)**3/3
Let u(g) = -g + 8. Let o be u(6). Let j(n) be the second derivative of 0*n**o + 0 + 2/3*n**3 + n + 7/6*n**4. Factor j(c).
2*c*(7*c + 2)
Let 1/6*c**3 + 4/3 + 7/3*c**2 - 2/3*c**4 + 1/6*c**5 - 10/3*c = 0. What is c?
-2, 1, 2
Find n such that 2/9*n**3 + 2/3 - 10/9*n + 2/9*n**2 = 0.
-3, 1
Let t(q) = q**2 - 1. Let v(i) = 3*i**2 + 6*i - 6. Let s(h) = -6*t(h) + v(h). Let s(x) = 0. Calculate x.
0, 2
Let w be ((-1)/((-3)/(-15)))/(-1). Let 2*r**4 - 3*r**2 - w*r**3 - 2*r**4 + 3*r**4 + 5*r**2 = 0. Calculate r.
0, 2/3, 1
Let j = -487 + 489. Factor 2/3*d**j - 2*d + 4/3.
2*(d - 2)*(d - 1)/3
Let u(w) = 0 + 0*w**2 + 1 - 2*w**2 - 9*w**2. Let v(d) = -6*d**2. Let c(f) = 3*u(f) - 5*v(f). Suppose c(g) = 0. Calculate g.
-1, 1
Let f(t) be the second derivative of 0 + 2*t + 0*t**2 - 1/12*t**4 + 0*t**3. Solve f(y) = 0 for y.
0
Let n be 57/18 + -1 + -2. Let o(m) be the third derivative of 0*m**3 + 1/15*m**7 + 0*m + 11/30*m**5 + 0 - 2*m**2 + 4/15*m**6 + n*m**4. Factor o(c).
2*c*(c + 1)**2*(7*c + 2)
Suppose 0*m + 0*m**3 + 0 - 2/7*m**2 + 2/7*m**4 = 0. What is m?
-1, 0, 1
Suppose -3*s - 3*s + 6 = 0. Let l be 0 + s - (-3 + 2). Let -4/3*y**l + 1/3 - y = 0. What is y?
-1, 1/4
Let p be (-38)/(-70) + 198/(-495). Factor 0*i + 1/7 - p*i**2.
-(i - 1)*(i + 1)/7
Let y(g) be the second derivative of -g**4/6 + g**2 - 8*g. What is x in y(x) = 0?
-1, 1
Let i(p) = 104*p**3 - 51*p**2 + 4. Let t(v) = -82*v**3 - 34*v**2 - 9 - 125*v**3 + 1 + 137*v**2 + v. Let w(y) = 7*i(y) + 4*t(y). Find o such that w(o) = 0.
-1/4, 2/5
Factor -7*s - 9*s - 3*s**2 + 7*s.
-3*s*(s + 3)
Suppose 2*o + 4 = -4*d, o - 5*o = -4*d + 20. Let b = -2 - o. Suppose 2/3 + 2/3*x**b + 4/3*x = 0. Calculate x.
-1
Factor 68 - 11*f + 99*f**2 - 55*f - 72 - 29*f**2.
2*(f - 1)*(35*f + 2)
Let m = -20 + 8. Let y be (-14)/m - 4/6. Solve 1/2*d**3 + 0 - y*d + 1/2*d**4 - 1/2*d**2 = 0.
-1, 0, 1
Let o(c) be the second derivative of c**7/15 + c**6/30 - 7*c**5/30 - c**4/6 + 3*c**2/2 + 3*c. Let y(k) be the first derivative of o(k). What is i in y(i) = 0?
-1, -2/7, 0, 1
Let c(a) be the second derivative of -a**4/72 + a**2/3 - 16*a. Factor c(d).
-(d - 2)*(d + 2)/6
Suppose -n + n = -7*n. Solve 1/3*s**2 + 0 + n*s + 1/6*s**3 = 0.
-2, 0
Factor -3/2*a**3 + 0*a - 3*a**2 + 0.
-3*a**2*(a + 2)/2
Let p be (1088/2700)/((-1)/(-10)) - 4. Let d(o) be the second derivative of -5*o + 0*o**2 + 1/90*o**5 + 0*o**3 + 0*o**4 + 1/63*o**7 + 0 + p*o**6. Factor d(g).
2*g**3*(g + 1)*(3*g + 1)/9
Let w = -70 - -38. Let i = w + 32. Suppose 0 + 0*p - 3/2*p**4 + 1/2*p**3 + i*p**2 = 0. What is p?
0, 1/3
Let v(s) be the second derivative of s**6/5 + s**5/10 - s**4/2 - s**3/3 - 30*s. Determine r so that v(r) = 0.
-1, -1/3, 0, 1
Let n(x) = -9*x**4 - 13*x**3 - 5*x**2 + 13*x - 1. Let g(m) = 8*m**4 + 12*m**3 + 4*m**2 - 12*m. Let d(f) = -5*g(f) - 4*n(f). Factor d(u).
-4*(u - 1)*(u + 1)**3
Let z(l) = -2*l**4 + 2*l**3 - 2*l**2 - 2*l - 2. Let b(n) = -n**3 - n - 1. Let d(x) = -2*b(x) + z(x). What is k in d(k) = 0?
0, 1
Let n = -586 - -590. Let -1/3*u**2 + 0 - 1/3*u**n - 2/3*u**3 + 0*u = 0. Calculate u.
-1, 0
Let g(d) be the first derivative of d**4 + 16*d**3/3 + 8*d**2 - 11. Suppose g(i) = 0. Calculate i.
-2, 0
Let m(n) be the third derivative of n**7/945 - n**6/540 + 13*n**2. Factor m(b).
2*b**3*(b - 1)/9
Let a(p) = -p**3 - 6*p**2 - 4*p - 4. Let x be a(-4). Let s = -16 - x. What is m in 0 - 2/9*m**2 + 2/9*m**s - 2/9*m**3 + 2/9*m = 0?
-1, 0, 1
Suppose 25/4*j + 36*j**3 - 1/2 - 26*j**2 = 0. Calculate j.
2/9, 1/4
Let i(r) be the second derivative of r**4/12 - 4*r**3/3 + 8*r**2 + 5*r. Solve i(o) = 0.
4
Suppose 0 = -3*k + 3, 2*v = 5*k + 3 - 6. Let f be (v/6)/(8/24). Factor 1/2 - j + f*j**2.
(j - 1)**2/2
Let u(j) be the third derivative of j**7/1365 + j**6/780 - j**5/130 - j**4/156 + 2*j**3/39 + 7*j**2. Find s such that u(s) = 0.
-2, -1, 1
Let w = -1 - -2. Let p be (-4)/(-1) - (0 - w). Let -p*f**3 + f**3 + f**2 + 5*f**3 = 0. What is f?
-1, 0
Factor 1/4*v**2 + 3/2*v + 9/4.
(v + 3)**2/4
Suppose 0 = 3*z + 2*z - 90. Let a be (z/21)/((-3)/(-14)). Factor -l**3 - 3/2*l**2 - l - 1/4*l**a - 1/4.
-(l + 1)**4/4
Let 3/5*j + 3/5*j**2 + 1/5*j**3 + 1/5 = 0. Calculate j.
-1
Let z(n) be the first derivative of 2*n**6/15 - 19*n**5/25 + 31*n**4/20 - 19*n**3/15 + n**2/10 + 2*n/5 - 30. Factor z(q).
(q - 2)*(q - 1)**3*(4*q + 1)/5
Find r, given that 0 + 28/5*r**2 + 49/5*r**3 + 4/5*r = 0.
-2/7, 0
Let w = 14 + -8. Solve -2*m**2 - 18*m + w*m - 3 - 6*m**2 - m**2 = 0.
-1, -1/3
Suppose 0 = 2*u + 22 - 12. Let n be (-1 - u/15)*-1. What is g in -10/3*g**2 + 4/9 - n*g + 62/9*g**3 - 10/3*g**4 = 0?
-1/3, 2/5, 1
Let m(h) = -h**3 + 4*h**2 - 2*h - 1. Let f be 6/4 - (-2)/4. Let b be m(f). Let -4/7*v**2 + 4/7*v**4 + 0*v**b + 2/7*v - 2/7*v**5 + 0 = 0. Calculate v.
-1, 0, 1
Let k(y) = 6*y**2 + 8*y + 4. Let c(s) = -7*s**2 - 9*s - 5. Let n(v) = 2*c(v) + 3*k(v). Factor n(t).
2*(t + 1)*(2*t + 1)
Suppose -6 = k - 4*s, 4*k - 5*s = -0*s - 2. Suppose -k*b - 30 = -5*b. Factor -5*g**2 + 23*g**2 + 9 - b*g**3 + 3*g**4 - 14*g - g**4 - 5.
2*(g - 2)*(g - 1)**3
Let p(d) be the first derivative of -d**6/14 + 6*d**5/35 - 3*d**4/28 + 22. Let p(k) = 0. Calculate k.
0, 1
Let h(u) = -30*u**4 - 21*u**3 + 30*u**2 - u - 11. Let t(i) = -15*i**4 - 11*i**3 + 15*i**2 - i - 6. Let f(z) = 6*h(z) - 11*t(z). Suppose f(s) = 0. Calculate s.
-1, -1/3, 0, 1
Let k = -83 - -83. Let 1/5*a**2 + 2/5*a**3 + 0 + k*a = 0. What is a?
-1/2, 0
Let a = 9 - 3. Let d(i) be the first derivative of 1/15*i**5 + 0*i**3 - 1/18*i**a + 0*i**4 + 0*i - 2 + 0*i**2. Factor d(f).
-f**4*(f - 1)/3
Solve -10*v**3 - 6*v**3 - v**4 - 3*v**4 - 20*v**2 - 8*v = 0 for v.
-2, -1, 0
Determine t so that 33/2*t**2 - 6 - 6*t + 9*t**3 - 27/2*t**4 = 0.
-2/3, 1
Find w, given that -6*w**2 - 10*w**5 + 420*w**3 - 5*w + 6*w**4 + w - 406*w**3 = 0.
-1, -2/5, 0, 1
Let t be 2 - -2*(-1)/(-2). Let a(u) = u**2 - 5*u + 7. Let y be a(3). Factor 1/2*l**t - 1/2*l - y + l**2.
(l - 1)*(l + 1)*(l + 2)/2
Let s(z) be the second derivative of z**6/180 - z**5/15 + z**4/3 - z**3/3 - 2*z. Let y(x) be the second derivative of s(x). Solve y(u) = 0.
2
Let r = 83/2 - 407/10. Factor -r - 1/5*j**2 - 4/5*j.
-(j + 2)**2/5
Let h(p) = -2. Let y(w) = -5. Let z(t) = 8*h(t) - 3*y(t). Let u(g) = g**2 - 2*g - 2. Let v(l) = -u(l) + 2*z(l). Factor v(q).
-q*(q - 2)
Suppose 2*l + 2*y + 12 = 3*l, 0 = l + y. Solve -3*j**5 + 2 - 8*j**2 + l*j**3 + 2*j**4 + 4*j**4 + j**5 - 2*j**5 = 0 for j.
-1, -1/2, 1
Let p(v) be the second derivative of v**6/300 + v**5/150 - v**4/30 + 3*v**2 - 3*v. Let u(l) be the first derivative of p(l). Factor u(g).
2*g*(g - 1)*(g + 2)/5
Let c(s) = s**2 - s. Let t(z) = -1. Let a(w) = c(w) - t(w). Let o = 0 + -2. Let n(y) = y - 2. Let j(b) = o*a(b) - 2*n(b). Determine g, given that j(g) = 0.
-1, 1
Let x be (-4)/15*505/2. Let y = 68 + x. Solve -4/3*m**4 + 0*m**3 + 0 + 4/3*m**2 + 2/3*m**5 - y*m = 0 for m.
-1, 0, 1
Let r = 13/28 - 3/14. Suppose -28*i = -32*i + 12. Solve 0 - 1/4*f**4 + r*f**i + 1/4*f**2 - 1/4*f = 0.
-1, 0, 1
Let s(o) be the third derivative of 0 + 0*o**5 - 1/336*o**8 + 0*o - 6*o**2 - 1/24*o**4 + 1/60*o**6 + 0*o**7 + 0*o**3. Solve s(d) = 0 for d.
-1, 0, 1
Let n(f) be the first derivative of -f**5 + 15*f**4/4 + 5*f**3/3 - 15*f**2/2 + 2. Factor n(u).
-5*u*(u - 3)*(u - 1)*(u + 1)
Let b = 3 - 1. Suppose 3*y = b*y + 2. Determine d so that d - 2*d + 2*d - d**y = 0.
0, 1
Let i(h) be the second derivative of 2*h**7/21 - 13*h**6/30 + 3*h**5/4 - 7*h**4/12 + h**3/6 + 2*h. Factor i(f).
f*