50/9*f**2 + 2/9*f**3.
2*(f + 1)*(f + 12)**2/9
Let g = 190471/8 - 23807. Solve -3/8*h**2 - g + 9/4*h = 0.
1, 5
Let v(h) be the third derivative of h**5/16 - 21*h**4/32 + 2*h**3 + 6*h**2 + 6*h. Solve v(r) = 0 for r.
1, 16/5
Let g = 337/682 + 2/341. Let k(n) be the first derivative of 13 - 1/9*n**3 - g*n**2 - 2/3*n. Factor k(w).
-(w + 1)*(w + 2)/3
Let f = 409 + -409. Let v(u) be the second derivative of 5*u + 1/65*u**5 + f*u**3 + 1/78*u**4 + 1/195*u**6 + 0 + 0*u**2. Solve v(j) = 0.
-1, 0
Factor -22/7*k**2 - 2*k**4 + 0 - 32/7*k**3 - 4/7*k.
-2*k*(k + 1)**2*(7*k + 2)/7
Let g(k) = 29*k**2 + 733*k - 757. Let w(t) = 14*t**2 + 366*t - 378. Let h(a) = 2*g(a) - 5*w(a). Solve h(y) = 0 for y.
-94/3, 1
Let m(p) be the second derivative of p**6/255 - 3*p**5/170 - 3*p**4/34 + 23*p**3/51 - 12*p**2/17 + 35*p. Solve m(l) = 0 for l.
-3, 1, 4
Let f be 4/8*-1*116. Let k = f - -175/3. Find x such that -k + 2/3*x - 1/3*x**2 = 0.
1
Let h(t) be the third derivative of 1/1080*t**6 + 0 + 1/18*t**4 + 0*t - 1/72*t**5 + 7*t**2 - 11/6*t**3. Let s(v) be the first derivative of h(v). Factor s(g).
(g - 4)*(g - 1)/3
Let g(d) be the third derivative of 3*d**6/140 - d**5/210 - 2*d**4/21 + 281*d**2. Factor g(l).
2*l*(l - 1)*(9*l + 8)/7
Let n = 689643/7 - 98362. Let x = 159 - n. Factor 0 + 2*b**3 + x*b**2 + 0*b + 10/7*b**4.
2*b**2*(b + 1)*(5*b + 2)/7
Let d(v) = -v**3 + 28*v**2 + 9*v + 583. Let u be d(29). Factor 98/11*j**u + 16*j + 24/11 + 350/11*j**2.
2*(j + 3)*(7*j + 2)**2/11
Find s, given that 0 - 17/6*s**2 - 4/3*s**3 - 1/6*s**4 - 5/3*s = 0.
-5, -2, -1, 0
Suppose 1/6*a**5 + 0 - 4/3*a + 2/3*a**4 - 1/2*a**3 - 7/3*a**2 = 0. What is a?
-4, -1, 0, 2
Let q(h) be the first derivative of h**5/300 + h**4/40 - h**2 + 7. Let r(u) be the second derivative of q(u). Suppose r(l) = 0. What is l?
-3, 0
Let q(b) be the second derivative of -b**5/135 - b**4/6 - 16*b**3/27 - 8*b**2 - 41*b. Let d(h) be the first derivative of q(h). Factor d(r).
-4*(r + 1)*(r + 8)/9
Let l(x) be the third derivative of -x**7/280 + x**6/120 + x**5/20 + 11*x**3/6 - 14*x**2. Let q(h) be the first derivative of l(h). Factor q(i).
-3*i*(i - 2)*(i + 1)
Let v(l) be the first derivative of l**4/8 - 19*l**3/6 - 5*l**2 + 455. Factor v(a).
a*(a - 20)*(a + 1)/2
Suppose 16 = c + 5*w + 15, c + 4*w - 1 = 0. Let b be c/7 - (-32)/70. Determine j, given that 0*j**2 - b*j**3 + 0 + 0*j = 0.
0
Let i(y) = 4*y**2 - 17. Let q(k) = -2*k**2 + 8. Let c(l) = -6*i(l) - 13*q(l). Factor c(p).
2*(p - 1)*(p + 1)
Let f = 8 + -10. Let j be (1 - f)/(3/2). Factor -3*n**2 - n + 2*n**j - 5*n + 4*n**2.
3*n*(n - 2)
Suppose -2*v - o - 3 = 0, 2*o - 6*o = 2*v + 6. Let q be ((3/(-2))/v - 1) + 0. Factor -1 + q*g**2 + 1/2*g**4 - 3/2*g + 3/2*g**3.
(g - 1)*(g + 1)**2*(g + 2)/2
Let s be (15/10)/1 - (-141)/6. Suppose 0 = -5*q + s - 10. Factor 0 - 1/4*r**q + 0*r + 1/2*r**2.
-r**2*(r - 2)/4
Let x be 3*(-10)/45*-3. Factor 16 - 12 - d**3 - d**4 - 4 + 6*d**x.
-d**2*(d - 2)*(d + 3)
Let n(c) be the second derivative of c**6/240 - c**5/10 + c**4 + c**3/3 - 14*c. Let l(u) be the second derivative of n(u). Let l(g) = 0. What is g?
4
What is m in -192/11*m**3 + 0 - 6/11*m**5 + 60/11*m**4 + 228/11*m**2 - 90/11*m = 0?
0, 1, 3, 5
Let a = -66 - -69. Factor 2*d**3 + 0*d**a - 7*d**3 - 3*d**2 + 2*d**2.
-d**2*(5*d + 1)
Let t(b) = -2*b. Let x = 31 - 32. Let h be t(x). Determine p so that -4*p**4 - 6*p - h*p + 20*p**2 - 12*p**3 + 4*p**5 + 0*p**3 = 0.
-2, 0, 1
Let u(g) be the first derivative of 46 + 14/5*g + 2/15*g**3 - 8/5*g**2. Solve u(y) = 0 for y.
1, 7
Suppose -2*x + o + 1 - 2 = 0, 2*o = -4*x + 18. Let b(n) = -n**2 - 1. Let g(z) = z**2 + 2. Let h(y) = x*b(y) + g(y). Let h(t) = 0. What is t?
0
Let p(g) be the first derivative of g**6/1620 + g**5/540 - 7*g**3/3 + 7. Let o(s) be the third derivative of p(s). Factor o(n).
2*n*(n + 1)/9
Let y(h) be the first derivative of -1/60*h**6 - 3/4*h**4 - 7/40*h**5 - h + 2 - 5/3*h**3 - 2*h**2. Let m(p) be the first derivative of y(p). Factor m(s).
-(s + 1)*(s + 2)**3/2
Let p(q) = 2033*q**3 - 1088*q**2 + 160*q. Let i(s) = -1355*s**3 + 725*s**2 - 106*s. Let f(l) = -8*i(l) - 5*p(l). Suppose f(y) = 0. What is y?
0, 4/15
Determine f so that -39/5*f**2 + 3/5*f**4 + 0 + 3*f**3 + 21/5*f = 0.
-7, 0, 1
Let b(k) be the first derivative of k**4/6 + 4*k**3/63 - k**2/3 - 4*k/21 + 13. Factor b(d).
2*(d - 1)*(d + 1)*(7*d + 2)/21
Suppose a**2 - 7*a**2 + 18*a - 67*a**3 - 56 + 65*a**3 + 30*a = 0. Calculate a.
-7, 2
Let i(c) be the third derivative of c**7/840 + c**6/120 - 3*c**5/40 - c**4/24 - 8*c**2. Let n(h) be the second derivative of i(h). Factor n(d).
3*(d - 1)*(d + 3)
Let s(a) = a**2 + 15*a - 321. Let o be s(-27). Let h(m) be the first derivative of 2/3*m**3 + 1/4*m**4 - 2*m**2 - 8*m - o. Suppose h(k) = 0. What is k?
-2, 2
Let s(q) be the third derivative of q**5/75 + q**4/2 - 68*q**3/15 + 187*q**2. Factor s(d).
4*(d - 2)*(d + 17)/5
Let n(m) = 2*m**3 - 20*m**2 - 5. Let j(c) = c**3 - 16*c**2 - 4. Let s(d) = 5*j(d) - 4*n(d). What is l in s(l) = 0?
0
Suppose 5*b - 14 = v, 13*v + 12 = -4*b + 8*v. Let 1/4*p**b - 1/2 - 1/4*p = 0. What is p?
-1, 2
Suppose 3*c - 5*f - 29 = 2*c, 4*c + 4*f - 20 = 0. Suppose c*h - 2 = 8*h. Let -j**2 + 1 - j**2 + j**4 + 5*j**2 - 5*j**h = 0. What is j?
-1, 1
Determine a, given that -1/10 - 1/10*a**2 - 1/5*a = 0.
-1
Let g(z) be the third derivative of -4/5*z**3 - 1/200*z**6 - 3/50*z**5 - 3/10*z**4 + 0*z + 12*z**2 + 0. Factor g(r).
-3*(r + 2)**3/5
Let p = -89 - -95. Let v = p - 11/2. Factor 1/2 + v*c**2 - c.
(c - 1)**2/2
Let u(m) be the third derivative of 0*m**6 + 1/630*m**7 + 1/18*m**3 + 0*m + 0*m**4 + 2*m**2 + 0 - 1/90*m**5. Factor u(v).
(v - 1)**2*(v + 1)**2/3
Suppose -6 = -2*g - 0. Let m(i) be the first derivative of 4*i**3 - 1 + g - i**4 - 12*i - 4*i - 1. Factor m(w).
-4*(w - 2)**2*(w + 1)
Suppose -49 - 5*y**2 + 3*y + 6*y**2 + 49 = 0. What is y?
-3, 0
Let d = 422 + -598. Let a = -173 - d. Find l, given that 24/7 + 3*l**a + 3/7*l**4 + 60/7*l + 54/7*l**2 = 0.
-2, -1
Determine f so that -358/3*f**2 - 12*f**3 - 1/3*f**4 - 289/3 - 204*f = 0.
-17, -1
Suppose 0 = -3*b - 12, 5*b - 5 = -5*c - 0. Let q(d) be the third derivative of 1/9*d**3 + 0 + 0*d**4 - 1/90*d**c + 3*d**2 + 0*d. Suppose q(k) = 0. What is k?
-1, 1
Let m(b) be the third derivative of 1/105*b**7 - 1/4*b**4 + 0 - 2/3*b**3 + 0*b + 11*b**2 + 1/20*b**6 + 1/30*b**5. Determine n so that m(n) = 0.
-2, -1, 1
Let n(u) be the first derivative of -3 - 32*u + 8*u**2 - 2/3*u**3. Factor n(o).
-2*(o - 4)**2
Let h(v) = -6*v**3 + 8*v**2 - 51 + 55 + 5*v**3. Let r be h(8). Factor 0*u + 2/7*u**5 - 2/7*u**3 + 2/7*u**r - 2/7*u**2 + 0.
2*u**2*(u - 1)*(u + 1)**2/7
Let k(c) = 8*c**5 + 8*c**4 + 16*c**3 - 8*c**2 - 14*c - 10. Let u(g) = g**5 + g**4 + g**3 - g**2 - g - 1. Let x(n) = -k(n) + 10*u(n). Let x(v) = 0. What is v?
-2, -1, 0, 1
Let r(s) be the second derivative of 2*s**7/105 - s**6/30 - s**5/20 + s**4/6 - s**3/6 + s**2/2 - 4*s. Let m(d) be the first derivative of r(d). Factor m(a).
(a - 1)*(a + 1)*(2*a - 1)**2
Let x(a) = -23*a - 45. Let n be x(-11). Let q be (n/273)/((-2)/(-3)). Determine k so that -q*k + 16/7 + 1/7*k**2 = 0.
4
Suppose 0 = 4*u + 2*h - 20, 2*u + 2*h - 12 = -2. Suppose -u*i + 3*i = -10. Determine z so that 2*z**2 - 9*z**3 + i*z**3 + 5*z**3 + 0*z**2 = 0.
-2, 0
Suppose 99*n = 91*n + 24. Let y(h) be the third derivative of 0*h**n + 9*h**2 + 1/20*h**5 + 0*h + 0 + 0*h**4. Let y(s) = 0. Calculate s.
0
Factor -8694*v**3 + 70*v - 48*v**2 + 17374*v**3 - 8685*v**3 - 17*v**2.
-5*v*(v - 1)*(v + 14)
Solve 0 + 40/7*i**2 + 200/7*i + 2/7*i**3 = 0 for i.
-10, 0
Let p(a) be the first derivative of a**6/2520 + a**5/168 + a**4/42 + 5*a**3 - 11. Let i(r) be the third derivative of p(r). Find s, given that i(s) = 0.
-4, -1
Let n(t) = -t**2 - t + 1. Let z(o) = -8*o**2 + 84*o - 82. Let l(u) = -6*n(u) + z(u). Let l(f) = 0. What is f?
1, 44
Let c(v) be the second derivative of v**4/4 + 53*v**3 - 108*v + 1. Factor c(s).
3*s*(s + 106)
Let c(s) = 15*s**3 + 113*s**2 - 136*s. Let y(l) = -5*l**3 - 38*l**2 + 46*l. Let a(b) = -3*c(b) - 8*y(b). Solve a(z) = 0 for z.
-8, 0, 1
Let d(i) be the second derivative of -5*i**7/42 + i**6/2 + 13*i**5 + 200*i**4/3 + 160*i**3 + 200*i**2 - 3*i + 30. Factor d(g).
-5*(g - 10)*(g + 1)*(g + 2)**3
Suppose l - 4*r = -7 + 1, 3*l - 2*r - 22 = 0. Determine z, given that -15*z**2 + l*z + 2