n**2 + n. Let z(d) be the first derivative of r(d). Factor z(c).
-2*c*(c - 1)**3*(c + 1)/9
Let p(m) = -1 + 21*m - 22*m + 4. Let w be p(3). Factor 0 + 0*t**3 + w*t**2 - 3/2*t**5 + 0*t + 1/2*t**4.
-t**4*(3*t - 1)/2
Let p(x) be the first derivative of -x**3 + 30*x**2 - 300*x + 17. Factor p(l).
-3*(l - 10)**2
Find x such that -2/9*x**3 + 10/9*x**2 - 10/9 + 2/9*x = 0.
-1, 1, 5
Let j = 1390/519 - 2/173. Suppose 0 = 2*w - 0 - 4. Solve -j + 8/3*n - 2/3*n**w = 0 for n.
2
Let c(z) = 9*z**3 - 2*z**2 - 7*z. Let r(x) = -4*x**3 + x**2 + 3*x. Let s(q) = -q**2 + 7*q - 7. Let n be s(5). Let y(v) = n*c(v) + 7*r(v). Factor y(i).
-i**2*(i - 1)
Let u = -4 + 4. Factor 0 + 2/5*k**2 - 2/5*k**3 - 2/5*k**4 + u*k + 2/5*k**5.
2*k**2*(k - 1)**2*(k + 1)/5
Let o(q) = -16*q - 108. Let u be o(-7). Factor -1/2*s**u - 1/2*s**3 + 1/2*s + 1/2*s**2 + 0.
-s*(s - 1)*(s + 1)**2/2
Determine j so that 0*j + 0 + 1/4*j**4 - 1/2*j**2 - 1/4*j**3 = 0.
-1, 0, 2
Let f = 83/126 + -3/14. What is h in -2/9*h**2 - 2/9 - f*h = 0?
-1
Let s(a) be the second derivative of -1/150*a**6 + 0*a**2 + 0*a**3 + 2*a + 0 - 1/100*a**5 + 0*a**4. Solve s(x) = 0.
-1, 0
Suppose 0 = 2*r - 4*f - 7 + 3, -10 = -2*r - 2*f. What is i in 5*i**4 - 2*i**r - 4*i**4 = 0?
0
Let z(j) be the first derivative of -77*j**6/9 - 108*j**5/5 - 89*j**4/6 + 4*j**2/3 - 7. Solve z(g) = 0 for g.
-1, -2/7, 0, 2/11
Let u = 367/1611 - 1/179. Factor -4/3*r**3 + 0 - 2/9*r**2 + u*r.
-2*r*(2*r + 1)*(3*r - 1)/9
Let v(r) be the second derivative of r**5/60 + r**4/4 + 4*r**3/3 + 8*r**2/3 - 25*r. Factor v(y).
(y + 1)*(y + 4)**2/3
Let k(n) be the second derivative of -5*n**4/24 - 17*n**3/12 - 3*n**2/2 + 2*n. Factor k(t).
-(t + 3)*(5*t + 2)/2
Let o(m) be the third derivative of m**7/490 - m**6/56 + 9*m**5/140 - m**4/8 + m**3/7 + 7*m**2. Find u, given that o(u) = 0.
1, 2
Let v(c) = -c**3 + 2*c**2 + 2. Let i be v(2). Find u such that 1/2*u + 1/2*u**i + 0 = 0.
-1, 0
Let c(d) = -d + 2. Let t be c(-5). Let j = t + -3. Solve -1 - 1 + 2*i + 6*i**2 - 6*i**3 - 4*i**4 + j*i**3 = 0 for i.
-1, 1/2, 1
Let f be (3 - 4/(-10)) + (-2)/5. Let q(h) be the third derivative of 7/300*h**6 + 1/75*h**5 + 0*h**f + 0 + 0*h**4 + h**2 + 1/105*h**7 + 0*h. Factor q(s).
2*s**2*(s + 1)*(5*s + 2)/5
Factor 2/3*f**5 + 0 + 0*f + 2/3*f**2 + 2*f**3 + 2*f**4.
2*f**2*(f + 1)**3/3
Let f(t) be the second derivative of -t**7/56 + t**6/20 - 3*t**5/80 + 18*t. Factor f(v).
-3*v**3*(v - 1)**2/4
Let x = 361/6 - 7219/120. Let g(t) be the third derivative of -1/12*t**3 - t**2 + 0 + 0*t + x*t**5 + 0*t**4. Factor g(n).
(n - 1)*(n + 1)/2
Let b(k) be the first derivative of -5*k**3/12 - k**2/4 - 1. Let b(v) = 0. What is v?
-2/5, 0
Let y(w) be the third derivative of 0*w**5 + 0*w**4 - 1/40*w**6 + 0*w**3 - 1/35*w**7 + 3/112*w**8 + 0*w + 2*w**2 + 0. Find d, given that y(d) = 0.
-1/3, 0, 1
Let v = -310/11 - -2280/77. Let r = 956/7 + -136. Factor 4/7 + v*k + r*k**2.
2*(k + 2)*(2*k + 1)/7
Let w = 28 + -28. Let l(n) be the third derivative of -3*n**2 - 1/600*n**6 + 1/30*n**3 + w + 1/100*n**5 + 0*n - 1/40*n**4. Determine q so that l(q) = 0.
1
Let k(m) be the second derivative of 3*m**5/50 + 12*m**4/5 + 192*m**3/5 + 1536*m**2/5 + 37*m. Factor k(i).
6*(i + 8)**3/5
Let x(q) be the second derivative of -q**5/4 + 25*q**4/12 - 5*q**3/2 - 45*q**2/2 + 5*q + 2. Factor x(k).
-5*(k - 3)**2*(k + 1)
Suppose 3*z = -q + 9, 17*q - 18*q = -2*z + 1. Suppose 0*x**q - 1/5*x**4 + 2/5*x + 0 + 3/5*x**2 = 0. What is x?
-1, 0, 2
Let c(d) be the third derivative of -2*d**7/105 - d**6/30 + d**2. Factor c(w).
-4*w**3*(w + 1)
Let s(r) = -r**2 + 13*r - 19. Let q(p) = -4*p**2 + 40*p - 56. Let k = -10 - -18. Let d(a) = k*s(a) - 3*q(a). Factor d(o).
4*(o - 2)**2
Suppose -g + 2 = 5*p - 0*p, 2*p + 2 = g. Let b = p + 3. Let z**2 - b*z**2 - z**3 + 0*z**3 - z = 0. What is z?
-1, 0
Find y such that 2/5*y**2 - 1/5*y + 1/5*y**5 - 2/5*y**4 + 0*y**3 + 0 = 0.
-1, 0, 1
Let s be (-1)/(-4) + 3/36. Let i = 5/12 + -1/12. What is l in 0 + i*l**2 + s*l = 0?
-1, 0
Solve 4/7*x**3 - 2/7 - 6/7*x + 6/7*x**4 - 4/7*x**2 + 2/7*x**5 = 0.
-1, 1
Let l(c) be the first derivative of -c**8/1008 + c**7/630 + c**6/360 - c**5/180 - 2*c**2 - 1. Let m(g) be the second derivative of l(g). Factor m(p).
-p**2*(p - 1)**2*(p + 1)/3
Suppose 2 = -4*b + 2*o - o, 4*o = -2*b + 8. Let g = 91/8 + -193/24. Suppose -4/3*m + b - 2*m**3 - g*m**2 = 0. Calculate m.
-1, -2/3, 0
Suppose 2*b + 293 = -283. Let w be (-4)/(-18) + (-440)/b. What is f in 1/4*f**4 + w*f + 9/4*f**2 + 5/4*f**3 + 1/2 = 0?
-2, -1
Factor -20/9*l - 50/9 - 2/9*l**2.
-2*(l + 5)**2/9
Let i(u) be the second derivative of u**6/60 + 3*u**5/80 - u**4/48 - u**3/8 - u**2/8 + 27*u. Factor i(b).
(b - 1)*(b + 1)**2*(2*b + 1)/4
Let k(b) be the second derivative of 1/7*b**2 + 0 - 1/70*b**5 - 3*b - 1/42*b**4 + 1/21*b**3. What is i in k(i) = 0?
-1, 1
Let l be 9 - (1 - 0)/(-1). Let f = l + -10. Find p such that 0*p**2 + 0 + 0*p + 2/7*p**3 - 2/7*p**5 + f*p**4 = 0.
-1, 0, 1
Let v be (-84)/(-15) - (-12)/(-20). Suppose 2*o + 1 = v. Factor -3*c**3 + o*c + 2*c**3 - c.
-c*(c - 1)*(c + 1)
Let t(h) be the first derivative of h**4/32 + h**3/4 + 3*h**2/4 + h - 5. Determine s so that t(s) = 0.
-2
Let g be -1 + 2 + (-5)/10. Let a(l) be the first derivative of 0*l - g*l**2 - 1/3*l**3 + 1. Factor a(r).
-r*(r + 1)
Let c(g) be the third derivative of 1/420*g**6 + 4*g**2 + 0*g**3 - 1/210*g**5 + 0*g**4 + 0*g + 0. Solve c(h) = 0 for h.
0, 1
Let y(z) be the first derivative of 4*z**3/21 - 2*z**2/7 - 8*z/7 + 23. Suppose y(v) = 0. What is v?
-1, 2
Let s be 3/(-5) - 1641/(-1860). Let v = s + -1/31. Suppose 0*f**4 + 0*f**2 - 1/4*f**5 + 0 + 1/2*f**3 - v*f = 0. Calculate f.
-1, 0, 1
Let c(h) = -10*h**3 - 2*h**2 + 56*h - 20. Let s(i) = 20*i**3 + 5*i**2 - 114*i + 41. Let l(x) = -7*c(x) - 4*s(x). Factor l(w).
-2*(w - 2)*(w + 3)*(5*w - 2)
Let h(w) be the first derivative of -2*w**6/9 + 8*w**5/15 + 2*w**4/3 - 16*w**3/9 - 2*w**2/3 + 8*w/3 + 22. Determine a so that h(a) = 0.
-1, 1, 2
Let j be (-70)/(-36) + -3*3/6. Suppose 16/9*m**3 - j*m + 0 + 10/9*m**4 + 2/9*m**2 = 0. Calculate m.
-1, 0, 2/5
Let d(t) = 3*t + 14. Let q be d(-11). Let s = 21 + q. Factor 0 - 2/11*j**s - 4/11*j + 2/11*j**3.
2*j*(j - 2)*(j + 1)/11
Let b(q) be the second derivative of 7*q**4/12 - 13*q**3/6 + 13*q**2/2 + 2*q. Let j(s) = 4*s**2 - 7*s + 7. Let u(c) = 6*b(c) - 10*j(c). Factor u(i).
2*(i - 2)**2
Let -145*k + 65*k + 20 - 121*k**2 - 55*k**3 - 114*k**2 + 80*k**2 = 0. Calculate k.
-2, -1, 2/11
Suppose 6*x = -16*x + 7*x. Factor x*h**2 + 3/5*h - 1/5*h**3 + 2/5.
-(h - 2)*(h + 1)**2/5
Let z be -11 - 6*(-1)/(-2). Let y be ((-4)/(-14))/((-2)/z). Factor 2*b**2 + 2*b**y + 0*b - 2*b - 5*b**2 - 1.
-(b + 1)**2
Let c(y) be the second derivative of y**6/900 - y**5/300 - y**3 + 6*y. Let a(k) be the second derivative of c(k). Suppose a(i) = 0. What is i?
0, 1
Let a(w) be the second derivative of w**5/40 - w**4/8 + w**3/6 - 2*w + 9. Suppose a(j) = 0. Calculate j.
0, 1, 2
Suppose -y + 2 + 16 = -2*j, -104 = -5*y - 4*j. Let p = y + -18. Determine c, given that 0*c - 2/11*c**3 + 0 + 4/11*c**p = 0.
0, 2
Let v be 6/1 - (-100)/(-25). Solve -a + 2/3 + 1/3*a**v = 0.
1, 2
Let c = -212 - -212. Find p, given that 0 - 3/5*p**3 + c*p - 3/5*p**2 = 0.
-1, 0
Suppose -8*s = -15 - 17. Determine x, given that 6/11*x**2 - 8/11 + 2/11*x**s - 8/11*x**3 + 8/11*x = 0.
-1, 1, 2
Factor 2 - 8/9*n**3 - 4/9*n**2 + 8/3*n + 2/9*n**4.
2*(n - 3)**2*(n + 1)**2/9
Suppose 5*g + 3*f - 13 = 0, -f + 0 = 3*g - 11. Find p such that 0*p**2 + 7*p + g*p + 0*p**2 + 4*p**2 = 0.
-3, 0
Suppose h = 8 - 6. Let d = 6 + -1. Find i, given that -2*i**3 + h*i**2 - i**d - 3*i**4 + 1 + 4*i + 0*i - i = 0.
-1, 1
Suppose m + 2*m + 30 = 4*g, -2*m + 26 = 5*g. Let d be (g/(-3))/(-2 - 5). Factor 0 + d*z - 6/7*z**2 + 6/7*z**3 - 2/7*z**4.
-2*z*(z - 1)**3/7
Let y = -6401/171 + 650/19. Let q = y + 50/9. Factor -3*z**2 + 0 + 2/3*z + q*z**3.
z*(z - 1)*(7*z - 2)/3
Let q(j) be the third derivative of -j**9/12096 + j**8/6720 + j**7/3360 - j**6/1440 + j**3/6 + 3*j**2. Let y(n) be the first derivative of q(n). Factor y(s).
-s**2*(s - 1)**2*(s + 1)/4
Suppose 36 = 2*v - 2. Suppose -8*t**2 - 4 - v*t - t - 4 = 0. Calculate t.
-2, -1/2
Suppose -3*w = 2*w - 45. Suppose -3*u - 5*i = w, -u - i = -0*u + 1. Factor 2*f - 1 + u*f - f**2 - 2*f + 0.
-(f - 1)**2
Factor 2/3*r**2 - 2/3*r - 2/3 + 2/3*r**3.
2*(r - 1