 - 7/60*t**5 + 5/24*t**4 + 0 + 1/3*t**3 + x*t. Solve z(o) = 0.
-2/7, 1
Determine r so that -4*r**2 + 5*r**2 - 17*r**2 + 0*r**2 + 116*r - 208 = 0.
13/4, 4
Let x be (-10)/(-8) - ((-4765)/(-100) - 48). Factor x*l**3 - 2/5*l + 0 + 6/5*l**2.
2*l*(l + 1)*(4*l - 1)/5
Let r(w) = -9*w**2 + 403*w + 110. Let h(b) = -19*b**2 + 808*b + 225. Let g(l) = -6*h(l) + 11*r(l). Factor g(k).
5*(k - 28)*(3*k + 1)
Factor 3/4*x**2 + 39/4*x + 33/2.
3*(x + 2)*(x + 11)/4
Let j(f) be the third derivative of f**8/1344 - 13*f**7/840 + 23*f**6/240 - f**5/20 - 3*f**4/4 + 2*f**2 - 45. Solve j(g) = 0.
-1, 0, 2, 6
Suppose 28 = -169*s + 183*s. Let p(a) be the third derivative of 0 + 1/80*a**6 + 1/48*a**4 + 0*a**3 + 1/40*a**5 + 0*a + 1/420*a**7 - 8*a**s. Factor p(o).
o*(o + 1)**3/2
Determine z, given that 0 - 6/19*z**2 - 4/19*z - 2/19*z**3 = 0.
-2, -1, 0
Let a(f) be the third derivative of 0*f + 1/90*f**5 - 2*f**2 + 1/9*f**4 + 1/3*f**3 + 0. Factor a(k).
2*(k + 1)*(k + 3)/3
Let y(g) be the third derivative of -g**7/10080 + g**6/576 + g**4/12 - g**3/2 - g**2 + 6. Let n(u) be the second derivative of y(u). Factor n(f).
-f*(f - 5)/4
Let m be (-1012)/132 - (1 + -9). Factor x**2 - m*x + 0 - x**4 + 1/3*x**3.
-x*(x - 1)*(x + 1)*(3*x - 1)/3
Let s be (-8 - 369/(-54))*(-20)/14. Factor s*u**3 - 10/3*u + 0 + 5/3*u**2.
5*u*(u - 1)*(u + 2)/3
Let c(z) be the second derivative of -5*z**8/2016 + z**7/756 + 2*z**6/135 + z**5/45 + 2*z**4/3 + 15*z. Let n(g) be the third derivative of c(g). Factor n(q).
-2*(q - 1)*(5*q + 2)**2/3
Factor 49*j + 112*j**2 + 27*j + 118*j**2 - 232*j**2 + 128*j - 5202.
-2*(j - 51)**2
Let x(g) be the third derivative of g**7/1680 + g**6/960 - g**5/160 - 5*g**4/192 - g**3/24 + 131*g**2. Factor x(t).
(t - 2)*(t + 1)**3/8
Let t = 60 + -15. Let p = t + -40. Factor -1/4*m + 0 - 13/4*m**3 - 3*m**4 - 3/2*m**2 - m**p.
-m*(m + 1)**2*(2*m + 1)**2/4
Let s(w) be the first derivative of 3*w**4 + 2 - 8/3*w**3 - 4*w**2 + 3*w + 7/60*w**6 - w**5. Let g(r) be the first derivative of s(r). Factor g(f).
(f - 2)**3*(7*f + 2)/2
Suppose -146 + 48 + 4*c**2 + 2 - 20*c - 48 = 0. Calculate c.
-4, 9
Let h(y) be the third derivative of 3*y**8/7 - 8*y**7/35 + y**6/30 + 150*y**2 + y. What is d in h(d) = 0?
0, 1/6
Let w(a) be the third derivative of -a**6/24 - 3*a**5/4 - 25*a**4/6 - 10*a**3 - 322*a**2. Solve w(o) = 0 for o.
-6, -2, -1
Let l = -31 + 103. Let b be 18/l + (-11)/(-4). Factor 15*s**b - 14 - 2*s + 7 - 13 - 65*s**2 + 82*s.
5*(s - 2)**2*(3*s - 1)
Let b(g) = 6*g**2 - 60*g + 72. Let r(k) = -3*k**2 + 30*k - 35. Let o(h) = 4*b(h) + 9*r(h). Factor o(f).
-3*(f - 9)*(f - 1)
Let a(b) be the first derivative of 1/9*b**2 - 2/27*b**3 + 0*b + 13. Let a(w) = 0. Calculate w.
0, 1
Let f(i) be the first derivative of -i**6/24 + i**5/4 - 5*i**4/8 + 5*i**3/6 - 5*i**2/8 - 3*i - 5. Let j(h) be the first derivative of f(h). Factor j(t).
-5*(t - 1)**4/4
Let c = 322 - 962/3. Solve -c*n**3 - 4/3*n**2 + 0*n + 0 = 0.
-1, 0
Suppose -6 + 1/4*s**2 - 5/4*s = 0. What is s?
-3, 8
Let r(w) be the first derivative of -w**6/720 + 19*w**5/720 - w**4/24 + w**3/3 + 13. Let u(t) be the third derivative of r(t). Factor u(a).
-(a - 6)*(3*a - 1)/6
Let u be ((-8)/(-14))/(32/112). Let r be 7/(2205/(-56)) + u/5. Factor 0*d**3 + 0 - 2/9*d**4 + 0*d + r*d**2.
-2*d**2*(d - 1)*(d + 1)/9
Let k be -2*(-2)/16 + (-70)/(-40). Factor 20*t**4 - 6*t + 4 + 26*t + t**2 + 39*t**k + 40*t**3 + 0*t**5 + 4*t**5.
4*(t + 1)**5
Let o(a) = a**2 - 108*a - 6684. Let k be o(-44). What is i in 1/3*i**2 + 5/3*i - 1/3*i**k + 0 - 5/3*i**3 = 0?
-5, -1, 0, 1
Suppose -11*y + 7*y + 3*s = 7, 2*s = y + 8. Let a(l) be the first derivative of 0*l + y*l**2 - 2 + 2/3*l**3. Find q, given that a(q) = 0.
-2, 0
Let h(f) be the second derivative of -f**4/18 - 17*f**3/9 - 22*f**2 - f - 136. Factor h(p).
-2*(p + 6)*(p + 11)/3
Let z(v) = 57*v**3 + 135*v**2 + 225*v - 351. Let n(k) = -7*k**3 - 17*k**2 - 28*k + 44. Let t(m) = -33*n(m) - 4*z(m). Factor t(s).
3*(s - 1)*(s + 4)**2
Let y = 38 + -38. Let q(a) be the first derivative of 0*a**2 + y*a + 5 - 1/22*a**4 + 2/33*a**3 + 1/33*a**6 - 2/55*a**5. Suppose q(d) = 0. What is d?
-1, 0, 1
Let y(g) be the third derivative of -g**6/200 + 17*g**5/50 - 63*g**4/10 - 324*g**3/5 + 6*g**2 - 24. Factor y(h).
-3*(h - 18)**2*(h + 2)/5
Let x(z) = -9*z**2 - 92*z + 289. Let v(c) = 10*c**2 + 95*c - 290. Let i(t) = 4*v(t) + 5*x(t). Suppose i(f) = 0. What is f?
-19, 3
Let n**4 + 122 + 176*n**2 - 192*n - 134 - 5*n**4 - 32*n**3 + 12 = 0. Calculate n.
-12, 0, 2
Let z(n) be the third derivative of -n**6/60 + 4*n**5/45 + n**4/12 + 4*n**2 - 2*n. Factor z(d).
-2*d*(d - 3)*(3*d + 1)/3
Let d be 3/((2/(-20))/(38/(-285))). Suppose -2*b = 3*s + s + 4, -5*b + d*s = -32. Determine l so that -16/3 + 8*l - b*l**2 + 2/3*l**3 = 0.
2
Let c(w) be the first derivative of w**7/210 + w**6/18 - 11*w**3/3 - 23. Let o(d) be the third derivative of c(d). Factor o(g).
4*g**2*(g + 5)
Let i(k) be the third derivative of k**5/300 + k**4/10 + 149*k**2. Suppose i(c) = 0. Calculate c.
-12, 0
Suppose 0 = 15*i + 304 - 165 - 184. Factor -1/4 - 5/4*p**4 - 5/2*p**2 - 5/2*p**i - 1/4*p**5 - 5/4*p.
-(p + 1)**5/4
Suppose -4 = 2*z - 3*k - 1, 4*z - 5*k + 3 = 0. Find g, given that 19*g**2 - 4*g**3 - z - 3 + 4*g - 11*g**2 - 2*g**4 + 0*g = 0.
-3, -1, 1
Let a(i) be the first derivative of 0*i**3 + 0*i + 5/6*i**6 - 11 + 0*i**2 - i**5 - 5/2*i**4. Factor a(u).
5*u**3*(u - 2)*(u + 1)
Suppose 0 = 3*t - 24*t + 105. Suppose -44 + 54 = t*k. Factor -16/3*h**5 + 0 + 0*h + 8*h**4 + 1/3*h**k - 3*h**3.
-h**2*(h - 1)*(4*h - 1)**2/3
Let h(q) be the third derivative of -q**6/40 + 29*q**5/20 - 39*q**4/4 - 16*q**2. Suppose h(s) = 0. What is s?
0, 3, 26
What is r in 17*r**2 + 85*r + 10 + 148*r**2 - 107*r**4 - 93*r**3 + 8*r**3 - 68*r**4 = 0?
-1, -2/7, -1/5, 1
Let t(f) = -f**3 + f**2 - f - 1. Let z(p) = 6*p**3 - 27*p**2 + 12*p + 15. Let u(k) = -15*t(k) - z(k). Determine o so that u(o) = 0.
-1, -1/3, 0
Let o = 382 - 378. Let i(n) be the second derivative of -3*n + 3/2*n**2 + 0 + 0*n**3 - 1/4*n**o. Factor i(g).
-3*(g - 1)*(g + 1)
Suppose -7 = -3*s + 2. Let l(x) = -x**2 + 9*x + 22. Let d be l(10). Suppose 2*p**3 - 3*p**s - d*p**4 + 6*p + 27*p**2 + 10*p**3 = 0. What is p?
-1, -1/4, 0, 2
Let y be (-12)/(-2) + 39/(-13). Factor 42*x**2 - 3*x**4 - x**y - 42*x**2 - 2*x**3.
-3*x**3*(x + 1)
Let s(n) = n**2 - n. Let o(q) = 4*q**2 + 270*q + 9248. Let i(x) = -o(x) + 2*s(x). Factor i(d).
-2*(d + 68)**2
Let n = -3866 + 3868. Let -1/4*d**5 + 0*d**3 + 0*d + 0*d**n + 1/4*d**4 + 0 = 0. What is d?
0, 1
Suppose -2/3*s + 0 - 1/3*s**2 = 0. Calculate s.
-2, 0
Let v = 61 - 58. Let i(n) = n**3 - 2*n**2 - 3*n. Let f be i(v). Suppose 10/3*z**4 - 16/3*z**3 + 0*z + f - 8/3*z**2 = 0. Calculate z.
-2/5, 0, 2
Let b(l) be the second derivative of -1/2*l**3 + 3*l**2 + 25*l + 0 + 1/32*l**4. Factor b(u).
3*(u - 4)**2/8
Suppose 2/5*m**5 + 12/5*m**2 + 18/5*m**4 + 44/5*m**3 - 6 - 46/5*m = 0. Calculate m.
-5, -3, -1, 1
Suppose -5*a - 7 = 3. Let x be 1 - 2 - a - -4. Factor 5*p - 6*p**x + 2*p**3 - 5*p + 4*p**4.
-2*p**3*(p - 1)*(3*p + 1)
Suppose -4*c + 15 = -5. What is g in 7*g**3 - 2*g**3 - c + 0*g**2 + 5*g**2 - 5*g = 0?
-1, 1
Suppose -2/21*j + 2/7 - 2/7*j**2 + 2/21*j**3 = 0. Calculate j.
-1, 1, 3
Let u = 7575 - 37851/5. Factor -u + 98/5*q**3 + 176/5*q - 70*q**2.
2*(q - 3)*(7*q - 2)**2/5
Let k(m) be the second derivative of 0 + 0*m**2 + 3*m + 2/3*m**4 + 1/6*m**3. Factor k(y).
y*(8*y + 1)
Let s be (0 + 4)*(-1)/(-10). Let y = 2943 + -2939. Find d such that 2*d - 2*d**4 + y*d**3 - 2/5 + s*d**5 - 4*d**2 = 0.
1
Let w(g) be the second derivative of -g**8/4480 - g**7/1680 + 17*g**4/6 + 28*g. Let h(j) be the third derivative of w(j). Factor h(c).
-3*c**2*(c + 1)/2
Let n(u) be the third derivative of -u**5/12 + 170*u**4/3 - 46240*u**3/3 - 278*u**2 + 2*u. Factor n(f).
-5*(f - 136)**2
Factor -3*b**5 - 15*b**3 + 6*b**2 + 12*b**4 + 5375*b - 5375*b.
-3*b**2*(b - 2)*(b - 1)**2
Suppose 0 = i - 6*i + 15. Suppose -26 = -i*j - 14. Solve -11*u**3 + 10 + 5*u**j + 20*u**2 - 14*u**3 + 25*u**2 - 35*u = 0.
1, 2
Let l = 106 + -104. Suppose 13*z**2 - 12*z - 13*z**2 - 3 + 15*z**2 + 0*z**l = 0. Calculate z.
-1/5, 1
Suppose -3 + 9 = 3*q. Suppose -4*i + 10 - q = 0. Factor 2*x - 4 + 5*x - i*x**3 - 5*x + 0*x + 4*x**2.
-2*(x - 2)*(x - 1)*(x + 1)
Let j(z) be the first derivative of -z**3/12 + 5*z**2 + 41*z/4