 2)*(k - 1)
Let t(u) be the first derivative of u**4/3 + 4*u**3/3 + 2*u**2 + 6*u + 28. Let c(b) be the first derivative of t(b). Suppose c(l) = 0. What is l?
-1
Let a(q) be the first derivative of q**4/16 + 41*q**3/12 + 79*q**2/8 + 39*q/4 + 155. Factor a(o).
(o + 1)**2*(o + 39)/4
Let f = -315 + 305. Let s be 5/25 + (-28)/f. Factor 2/3*m**2 - 1/3*m**4 + 0*m**s - 1/3 + 0*m.
-(m - 1)**2*(m + 1)**2/3
Solve -17/2*f**2 + 150 - 1/2*f**3 - 20*f = 0.
-10, 3
Find w, given that 24*w - 15*w**4 + w**5 - 2*w**5 - 2*w**5 + 12*w**2 - 18*w**3 + 6*w**5 - 6*w**5 = 0.
-2, 0, 1
Let t be 1/(-2) + 869/22. Let x be t/9 - 5/15. Find o such that 3/2*o**x - 3/2*o**2 + o + o**5 - 2*o**3 + 0 = 0.
-2, -1, 0, 1/2, 1
Let h(p) be the third derivative of p**9/3024 + p**8/448 + p**7/168 + p**6/144 + p**4/24 + 3*p**2. Let j(l) be the second derivative of h(l). Factor j(k).
5*k*(k + 1)**3
Suppose -23*c = -70*c. Factor c*g + g**2 - 1/2*g**3 + 0.
-g**2*(g - 2)/2
Let q(s) be the first derivative of s**8/2520 - s**6/450 + s**4/180 + 3*s**2 + 9. Let u(a) be the second derivative of q(a). Find c such that u(c) = 0.
-1, 0, 1
Factor -9*l + 27*l**2 - 14*l**2 + 5*l**3 - 120 - l + 12*l**2.
5*(l - 2)*(l + 3)*(l + 4)
Suppose 8*g - 9*g + 6 = 0. Find s such that -15*s + 15*s + 4*s**2 + g*s**3 - 2*s**5 = 0.
-1, 0, 2
Let h be (((-27)/(-15))/(9/6))/((-378)/(-840)). Find n such that 2/3*n**5 + 0 + 4*n**3 + h*n**4 + 8/3*n**2 + 2/3*n = 0.
-1, 0
Factor -8/3*b + 2/3*b**3 + 0*b**2 + 0.
2*b*(b - 2)*(b + 2)/3
Let c(y) be the first derivative of -y**6/45 - 4*y**5/75 + 4*y**4/15 + 32*y**3/45 - 16*y**2/15 - 64*y/15 - 313. Factor c(r).
-2*(r - 2)**2*(r + 2)**3/15
Let j(i) be the first derivative of 400/3*i**3 + 44*i**5 + 35/6*i**6 + 40*i**2 + 0*i - 15 + 120*i**4. Solve j(t) = 0.
-2, -2/7, 0
Let k = -1115/3 + 7835/21. Determine b, given that 0 - 6/7*b**2 + 0*b + 2/7*b**5 - 2/7*b**4 - k*b**3 = 0.
-1, 0, 3
Let g(h) be the third derivative of h**7/504 + h**6/36 - 7*h**5/72 - 5*h**3/6 + 30*h**2. Let d(w) be the first derivative of g(w). Find c such that d(c) = 0.
-7, 0, 1
Let x(u) = 3*u**4 + 2*u**3 - 2*u**2 - 2*u. Let o = -4 + 3. Let n(f) = f**4. Suppose -a - 2*m + 3 = 0, 4*m - 2*m = 2. Let z(l) = a*x(l) + o*n(l). Solve z(y) = 0.
-1, 0, 1
Suppose g - 75 = -4*g. Let l be 0/2 - (-1 + 3/g). Suppose -l - 2/5*z**2 + 6/5*z = 0. Calculate z.
1, 2
Let i(l) be the first derivative of l**4/12 - 5*l**3/9 - 13*l**2/6 - 7*l/3 + 99. Find b, given that i(b) = 0.
-1, 7
Let y be 48*(2/15)/((-2)/(-6)). Let j = y + -19. Suppose 0*o - 1/5*o**5 + 0 + 1/5*o**3 + 1/5*o**2 - j*o**4 = 0. Calculate o.
-1, 0, 1
Let h(t) = -3*t**2 + t - 8. Let r(b) = -2*b**2 - 3*b. Let s(g) = -h(g) + 2*r(g). Factor s(y).
-(y - 1)*(y + 8)
Let m(g) = g**4 + g**2 + g. Let x(w) = -2*w**5 - 6*w**4 + 26*w**3 - 30*w**2 - 6*w. Let s(o) = -6*m(o) - x(o). What is z in s(z) = 0?
-4, 0, 1, 3
Let g(o) be the second derivative of -31/108*o**4 - 1/90*o**5 + 1 - 7*o + 0*o**2 + 8/27*o**3. Factor g(k).
-k*(k + 16)*(2*k - 1)/9
Let r = 8 - 6. Let x(c) = c - 3. Let z be x(13). Let -u - z*u**r + 4 - 2*u**3 + 0*u**3 + 6*u**4 - u + 4*u**3 = 0. Calculate u.
-1, 2/3, 1
Let i(m) be the first derivative of 0*m + m**4 + 4/3*m**3 - 6 + 0*m**2. Factor i(z).
4*z**2*(z + 1)
Let w(n) be the third derivative of -n**6/900 + 3*n**5/50 - 27*n**4/20 + 9*n**3/2 + 21*n**2. Let r(l) be the first derivative of w(l). Factor r(o).
-2*(o - 9)**2/5
Let m(b) be the first derivative of 16/21*b**3 + 8/7*b**2 + 0*b + 1/7*b**4 + 3. Solve m(t) = 0 for t.
-2, 0
Suppose 2*s = -2*i - 32, 3*s - 6*s - 43 = 4*i. Let h be (-12)/21*s/6. Factor -2/3*a**3 + 4/9 - 14/9*a + 16/9*a**h.
-2*(a - 1)**2*(3*a - 2)/9
Let o(a) be the second derivative of a**6/1800 - a**5/120 + a**4/30 - 3*a**3/2 - a. Let x(j) be the second derivative of o(j). Let x(b) = 0. What is b?
1, 4
Let l(z) be the third derivative of 13*z**2 - 1/70*z**7 + 0*z**6 + 0*z**3 + 1/20*z**5 + 0*z**4 + 0*z + 0. Determine n so that l(n) = 0.
-1, 0, 1
Factor -9/7*y + 9/7*y**2 - 1/7*y**4 + 0 + 1/7*y**3.
-y*(y - 3)*(y - 1)*(y + 3)/7
Let p(h) be the second derivative of h**5/100 - 13*h**4/30 + 169*h**3/30 + 137*h + 1. Suppose p(f) = 0. What is f?
0, 13
Let 0 + 38/3*m + 2/9*m**2 = 0. Calculate m.
-57, 0
Let a be (((-44)/16)/(-11))/(-4 - (-556)/128). Determine y so that 8/11 - 8/11*y - 2/11*y**4 - 6/11*y**2 + a*y**3 = 0.
-1, 1, 2
Suppose -22 = i - 12*i. Let o be (1/3)/(4/6). Let -o*j**i + 0 + 0*j = 0. What is j?
0
Suppose 5*d = -0*g + 5*g - 25, 2*g = 3*d + 9. Factor g*u - 4*u**2 - 16*u**3 + 0*u - 9*u**3 + 23*u**3.
-2*u*(u - 1)*(u + 3)
Let x = 96627/11 - 8783. Find z, given that x*z**2 + 2/11*z**3 + 16/11*z - 32/11 = 0.
-4, 1
Suppose -14 + 2 = 4*s, -s - 3 = 3*i. Suppose -16*l = -i*l - 48. Suppose 4/7 - 1/7*c**l + 5/7*c**2 - 8/7*c = 0. Calculate c.
1, 2
Suppose -18*y - 37 + 40 = -51. Factor -3/5*h**y + 18/5 - 6/5*h**2 + 3*h.
-3*(h - 2)*(h + 1)*(h + 3)/5
Let w(y) = -y**3 + 11*y**2 - 19*y - 1. Let q(d) = 5*d**2 - 10*d - 1. Let v(p) = -10*q(p) + 6*w(p). Factor v(s).
-2*(s - 1)**2*(3*s - 2)
Let l(h) be the second derivative of -2*h - 23/2*h**3 - 21/4*h**4 - 3*h**2 + 2. Let l(g) = 0. What is g?
-1, -2/21
Let 4/17*b**2 - 16/17 - 2/17*b**3 + 8/17*b = 0. What is b?
-2, 2
Let u = 31708 + -95123/3. Solve -u*x**2 + 10/3*x - 3 = 0.
1, 9
Suppose 6*h - h - 85 = 5*j, 4*h = -j + 43. Factor 30*s**3 - h*s**3 + 4*s**4 - 14*s**3 - 4*s**5 - 4*s**2.
-4*s**2*(s - 1)**2*(s + 1)
Let h be (16/96)/(-1*(-6)/27). Let v(f) be the second derivative of 0*f**2 + f**3 + 0*f**5 + 2*f + 1/10*f**6 - h*f**4 + 0. Factor v(x).
3*x*(x - 1)**2*(x + 2)
Let o(i) be the second derivative of 0*i**4 + 0 + 0*i**2 - 1/112*i**7 - 1/16*i**3 + 3/80*i**5 + 0*i**6 + 24*i. Solve o(u) = 0.
-1, 0, 1
Let k(i) be the second derivative of i**4/12 + i. Let s = 9 - 15. Let m(u) = 4*u**2 - 4*u - 2. Let q(j) = s*k(j) + m(j). Suppose q(l) = 0. Calculate l.
-1
Let h(a) be the second derivative of -1/3*a**3 + 0 + 1/8*a**4 - 1/60*a**5 - 5*a - 2*a**2. Let o(q) be the first derivative of h(q). Factor o(l).
-(l - 2)*(l - 1)
Let x(g) be the third derivative of -g**8/13440 + g**7/1680 - g**6/480 + g**5/240 - 31*g**4/24 - 2*g**2. Let z(n) be the second derivative of x(n). Factor z(w).
-(w - 1)**3/2
Factor -4*a**3 + 3*a**3 + 10345*a**2 - 17*a - 10327*a**2.
-a*(a - 17)*(a - 1)
Determine p, given that -24*p**3 - 72*p**2 - 41*p - 7*p**4 - p**4 - 23*p + 6*p**4 = 0.
-8, -2, 0
Solve 40*b**4 + 8*b**4 - 566*b**3 - 850*b**3 + 3243*b + 2067*b + 675 + 10083*b**2 = 0.
-1/4, 15
Let q(w) be the second derivative of w**4/108 - 43*w**3/27 + 1849*w**2/18 + 9*w + 6. Factor q(i).
(i - 43)**2/9
Let g(h) be the third derivative of h**6/48 + 11*h**5/24 + 95*h**4/48 + 15*h**3/4 - 11*h**2 - 12. Factor g(x).
5*(x + 1)**2*(x + 9)/2
Let y(f) be the first derivative of 1/10*f**5 - 6 + 0*f + 1/2*f**3 + 3/8*f**4 + 1/4*f**2. Determine a so that y(a) = 0.
-1, 0
Let a(g) be the third derivative of g**5/105 - 2*g**4/7 + 22*g**3/21 + 20*g**2 - g. Solve a(p) = 0 for p.
1, 11
Let s(h) be the third derivative of -2*h**7/105 + h**6/15 + h**5/15 - h**4/3 - 256*h**2. Let s(z) = 0. What is z?
-1, 0, 1, 2
What is c in 0*c + 12 - 1/3*c**2 = 0?
-6, 6
Let n(i) be the third derivative of i**5/390 - 2*i**4/39 + 16*i**3/39 + 219*i**2. Suppose n(r) = 0. Calculate r.
4
Let a(q) be the first derivative of -4*q**5/5 + 38*q**4 - 480*q**3 - 76*q**2 + 1444*q - 227. Determine x, given that a(x) = 0.
-1, 1, 19
Let n(p) be the second derivative of -p**4/36 + 10*p**3/9 - 19*p**2/6 - 7*p - 7. Factor n(z).
-(z - 19)*(z - 1)/3
Let q(u) be the third derivative of -u**6/960 - 13*u**5/480 - 55*u**4/192 - 25*u**3/16 - 2*u**2 - 240*u. Find v such that q(v) = 0.
-5, -3
Let t(w) = -w**3 - 8*w**2. Suppose -49*a = -59*a - 80. Let v be t(a). Determine m so that 1/2*m**4 + 1/6*m**2 + 1/2*m**3 + v + 0*m + 1/6*m**5 = 0.
-1, 0
Let f = 866 + -6058/7. Find j, given that 0 + 2/7*j**3 + 0*j - 2/7*j**5 + f*j**2 - 4/7*j**4 = 0.
-2, -1, 0, 1
Let m be (5/(-2)*2)/1. Let s = 7 + m. Factor w**2 + 1 - 3*w - w**3 + s*w**2 + 0*w**2.
-(w - 1)**3
Let h = 136 - 133. Suppose 0 = -r - 0*r. Suppose -1/4*k + r + k**2 - k**h = 0. What is k?
0, 1/2
Let c be (((-16)/(-6))/8)/((-6)/(9 + -45)). Suppose -1/3*v**3 + 0 - 2/3*v**c + 1/3*v**4 + 0*v = 0. What is v?
-1, 0, 2
Suppose -3*w**2 + 9 - 87*w - 124 + 31 = 0. Calculate w.
-28, -1
Suppose -642