)*(d + 1)**2
Let m(r) = r**2 - 7*r. Let z be m(7). Let p(d) be the third derivative of 0*d**4 + 0*d - d**2 + 0*d**3 + 1/210*d**5 + 1/420*d**6 + z. Let p(v) = 0. What is v?
-1, 0
Let i(f) be the third derivative of -f**6/280 + f**5/70 - f**4/56 + 17*f**2. Determine n, given that i(n) = 0.
0, 1
Suppose 2*l - 2 = -2*c, c + l + 5 = 2*c. Suppose -2*o - o + 6 = 0. Determine n so that 3*n**c - 18*n**5 + 18*n**4 + n**3 + 4*n**3 - 8*n**o = 0.
-2/3, 0, 2/3, 1
Let h(l) = -14*l**2 + 8*l - 11. Suppose 5 = v - 2*c - 7, 5*v + 5*c = 15. Let r(z) = -5*z**2 + 3*z - 4. Let n(p) = v*h(p) - 17*r(p). What is f in n(f) = 0?
1, 2
Suppose 9*g**5 - 13*g**5 + 7*g**5 - 6*g**3 + 3*g = 0. What is g?
-1, 0, 1
Let j(f) be the third derivative of f**9/3780 - f**8/3360 - f**7/1260 - f**4/8 + 2*f**2. Let w(u) be the second derivative of j(u). Factor w(m).
2*m**2*(m - 1)*(2*m + 1)
Let d be (-6)/(-8)*(5 - 1). Suppose -12*y + 16*y - 12 = 0. Factor b**d + 2*b - y*b**3 - 4*b - 4*b**2.
-2*b*(b + 1)**2
Let l(y) be the first derivative of 2*y**3/3 + y**2 - 7. Solve l(a) = 0.
-1, 0
Factor -6 + 16*a**2 + 0 - 19*a**2 - 4*a - 5*a.
-3*(a + 1)*(a + 2)
Let u(y) be the third derivative of y**6/1260 - y**4/84 + y**3/2 + 3*y**2. Let r(c) be the first derivative of u(c). Factor r(b).
2*(b - 1)*(b + 1)/7
Suppose 15 = 3*n + 2*n. Factor -11*y**n - 3*y**2 + 13*y**3 + 3*y**4 + 3*y - 5*y**3.
3*y*(y - 1)**2*(y + 1)
Let o be 5/(-15) + (-10)/6. Let x(m) = -m**2 - 3*m. Let u be x(o). Factor -15*z**u + 3*z - 3*z + 16*z**2.
z**2
Let a(l) be the third derivative of -3*l**7/70 - l**6/40 + l**5/10 - 3*l**2. Solve a(i) = 0 for i.
-1, 0, 2/3
Let y(u) be the second derivative of u**5/30 - u**3/9 - 2*u. Factor y(q).
2*q*(q - 1)*(q + 1)/3
Suppose -8 = 7*j - 36. Suppose 8/13*d**3 - 18/13*d**j + 0 + 0*d - 18/13*d**5 + 8/13*d**2 = 0. What is d?
-1, -2/3, 0, 2/3
Let b = 5 + -1. Let -b*w**2 + 0*w**2 + 3*w**2 - 2*w = 0. What is w?
-2, 0
Let o(t) be the third derivative of 3*t**6/400 - 7*t**5/600 - t**4/120 + 18*t**2. Factor o(k).
k*(k - 1)*(9*k + 2)/10
Suppose 0 = 3*b - b + 126. Let d = b + 191/3. Factor d - s + 1/3*s**2.
(s - 2)*(s - 1)/3
Factor -6/5 - 3/5*u + 3/5*u**2.
3*(u - 2)*(u + 1)/5
Suppose -4*d - 1130 = -9*d. Let w = 692/3 - d. Suppose -w*a**2 + 8/3*a**3 + 2/3 + 4/3*a = 0. What is a?
-1/4, 1
Let d(g) be the second derivative of g**4/28 + 9*g**3/7 + 51*g**2/14 - 10*g - 3. Let d(i) = 0. What is i?
-17, -1
Let o(g) = g**2 + g. Let w(q) = q**3 + 3*q**2 + 3*q. Let a(h) = -o(h) - w(h). Factor a(x).
-x*(x + 2)**2
Let j(x) be the first derivative of x**4/4 - x**3/3 - x**2 - 2. Suppose j(h) = 0. What is h?
-1, 0, 2
Let c be 2/(-3) + 88/99. Solve c*g**3 + 2/9*g - 4/9*g**2 + 0 = 0.
0, 1
Factor -413*h**4 - 6 + 16*h**2 - 511*h**2 - 975*h**3 + 38*h**4 - 93*h.
-3*(h + 2)*(5*h + 1)**3
Let w(u) = u**2 + 5*u + 6. Let x be w(-4). Suppose -11*l**2 - 17*l**2 + 28*l**x - 2*l**3 + 3*l**4 = 0. Calculate l.
0, 2/3
Suppose -1/2*u - 1/8*u**2 - 1/2 = 0. What is u?
-2
Suppose q - 5*w = 27, 0*q + 5*q - 15 = w. Let v(x) be the first derivative of -3/2*x**q + 0*x - 2 + x**3. Suppose v(i) = 0. What is i?
0, 1
Factor 0*x + 0 + 2/9*x**2.
2*x**2/9
Factor 5*j**2 + 2 - 4*j**2 + j - 2*j**2 + 0*j**2.
-(j - 2)*(j + 1)
Let v(o) = o**3 - 5*o**2 - 2*o + 10. Let i be v(5). Let f(b) be the first derivative of 4/9*b**3 - 3 + 0*b + i*b**2 + 4/3*b**4 + b**5. Solve f(x) = 0.
-2/3, -2/5, 0
Let g(q) = -6*q**4 + 3*q**3 + 4*q**2. Let y(k) = k**4 - k**3 - k**2. Let j(z) = 3*g(z) + 15*y(z). Factor j(t).
-3*t**2*(t + 1)**2
Let h(i) be the first derivative of -2*i**5/65 + i**4/13 + 2*i**3/13 - 8*i**2/13 + 8*i/13 - 8. Solve h(a) = 0.
-2, 1, 2
Let l(r) be the first derivative of r**5/10 - r**4/8 - r**3/6 + r**2/4 - 10. Suppose l(y) = 0. What is y?
-1, 0, 1
Let w = 680 - 4758/7. Factor -2/7*h + w*h**5 - 4/7*h**2 + 0 + 0*h**3 + 4/7*h**4.
2*h*(h - 1)*(h + 1)**3/7
Let p = -10 - -9. Let z be p/((7/(-4))/7). Factor -1/4*f**z + 0*f + 0*f**2 + 0 + 1/4*f**3.
-f**3*(f - 1)/4
Solve -1/6*m**3 - 1/3 - 2/3*m**2 - 5/6*m = 0 for m.
-2, -1
What is m in -2/7 - 6/7*m + 2/7*m**5 + 6/7*m**4 - 4/7*m**2 + 4/7*m**3 = 0?
-1, 1
Let y be (12/(-10))/((-15)/50). Let u(n) be the second derivative of 0 + 0*n**2 + 2*n + 1/12*n**y + 1/3*n**3. Factor u(o).
o*(o + 2)
Let n(v) be the third derivative of 1/60*v**5 + 1/6*v**3 + 0 + 0*v + 1/12*v**4 + 3*v**2. Factor n(q).
(q + 1)**2
Let z(m) = 8*m**4 - 7*m**3 - 18*m**2 + 20*m + 23. Let c(l) = -105*l**4 + 90*l**3 + 235*l**2 - 260*l - 300. Let b(t) = -3*c(t) - 40*z(t). Factor b(h).
-5*(h - 2)**2*(h + 1)**2
Let x(v) be the first derivative of v**5/30 - v**4/3 + v**2/2 + 4. Let c(m) be the second derivative of x(m). Factor c(z).
2*z*(z - 4)
Let w(o) = o**2 - 7*o + 9. Let j be w(6). Let z be (0 - (-2)/2) + 2. Determine a so that -a**4 + 0*a**4 + a**5 - j*a**z + a**5 + a**2 + a = 0.
-1, -1/2, 0, 1
What is n in 0 + 4/7*n**2 + 0*n - 6/7*n**3 + 2/7*n**4 = 0?
0, 1, 2
Let x(v) be the second derivative of -1/20*v**6 + 1/8*v**4 + 0 + 0*v**2 - 1/40*v**5 - 3*v + 1/12*v**3. Factor x(n).
-n*(n - 1)*(n + 1)*(3*n + 1)/2
Suppose 3 = q + 1. Let x be q/(-30) + 12/18. Factor 2/5*v**2 + 2/5*v**3 + 1/5 - x*v - 3/5*v**4 + 1/5*v**5.
(v - 1)**4*(v + 1)/5
Let r(g) be the first derivative of -3*g**4/5 + 7*g**3/5 + 21*g**2/5 + 9*g/5 + 22. Let r(d) = 0. Calculate d.
-1, -1/4, 3
Let t(x) be the second derivative of x**7/84 - x**6/60 - x**5/20 + x**4/12 + x**3/12 - x**2/4 + 6*x. Solve t(v) = 0 for v.
-1, 1
Let j(t) = 5*t**2 + 13*t + 15. Let l(m) = 5*m**2 + 14*m + 15. Let x(z) = -6*j(z) + 7*l(z). Let x(o) = 0. What is o?
-3, -1
Let r be 15/6*8/10. Suppose -2 = p - r*p. Let a(b) = 3*b**3 + b**2. Let v(m) = 12*m**3 + 3*m**2. Let j(k) = p*v(k) - 9*a(k). Determine z, given that j(z) = 0.
-1, 0
Let h(g) = -g - 2. Let l be h(-5). Factor -75*m - l*m**2 + 75*m.
-3*m**2
Let r = 392 + -392. Determine t, given that -t**2 + r*t + 4/3 - 1/3*t**3 = 0.
-2, 1
Let s(d) be the third derivative of 0 + 0*d**3 - 1/1050*d**7 + d**2 + 0*d**4 - 1/300*d**5 + 0*d + 1/300*d**6. Let s(l) = 0. Calculate l.
0, 1
Let w be 3/6*0 - -18. Suppose -3*g + 16 = -2*d, -3*g - 5*d - w = -5*g. Factor 2*x**2 - g*x - 22 + 22.
2*x*(x - 2)
Let d(x) be the second derivative of -x**7/210 + x**6/75 - x**5/100 - 6*x. Factor d(m).
-m**3*(m - 1)**2/5
Let p(g) = -6*g**2 - 2*g + 2. Let t(q) = -q**4 - 7*q**2 - 3*q + 2. Let i(z) = 3*p(z) - 2*t(z). What is w in i(w) = 0?
-1, 1
Let o(n) be the second derivative of 2/9*n**2 + 0 + 1/54*n**4 + 3*n + 1/9*n**3. Let o(k) = 0. Calculate k.
-2, -1
Let c = 88/7 - 1049/84. Let m(p) be the second derivative of 0 + 1/6*p**3 - p + 0*p**2 - c*p**4. Factor m(i).
-i*(i - 1)
Let a(i) be the third derivative of 4/21*i**3 + 0 + 3*i**2 + 0*i**4 - 1/210*i**5 + 0*i. Solve a(x) = 0.
-2, 2
Suppose -5*v + l + 12 = 2*l, 2*l + 6 = 5*v. Let -1 + 14*c - 1 - 2 - 4*c**v - 6*c**2 = 0. What is c?
2/5, 1
Factor 363*u - 181*u + u**4 - 4*u**3 - 184*u + 5*u**2.
u*(u - 2)*(u - 1)**2
Let z(u) = u + 8. Let w be z(0). Let j be w/10*(-65)/(-78). Find t, given that 2/3*t - 2/3*t**2 - j*t**3 + 2/3 = 0.
-1, 1
Factor r**2 + 1/4*r**3 + r + 0.
r*(r + 2)**2/4
Let a(u) be the third derivative of -u**6/720 + u**5/72 - 7*u**4/144 + u**3/12 - 18*u**2. Solve a(d) = 0 for d.
1, 3
Let p = 1118 - 1116. Suppose -2/5*u**p + 2/15*u**3 + 0*u + 8/15 = 0. What is u?
-1, 2
Let 13 + 2*x**4 + 0*x**4 - 2*x - 17 + 6*x**3 + 2*x**2 - 4*x = 0. What is x?
-2, -1, 1
Let t(z) = z**2 - 10*z - 6. Let i be t(11). Let n(x) be the third derivative of 0*x**3 + 0*x + 0 + 0*x**4 - 1/150*x**i + 1/300*x**6 - 2*x**2. Factor n(d).
2*d**2*(d - 1)/5
Let f(g) = 3*g**3 - 3*g**2 - 8*g + 2. Let p(z) = 3*z**3 - 3*z**2 - 9*z + 3. Let d(q) = 3*f(q) - 2*p(q). Determine w, given that d(w) = 0.
-1, 0, 2
Let x(o) be the second derivative of o**4/12 + o**3/15 - 12*o. Let x(w) = 0. Calculate w.
-2/5, 0
Suppose 3*s - 2*s = 8*s. Factor s*p + 1/3*p**2 - 2/3*p**3 + 0.
-p**2*(2*p - 1)/3
Let g be (-32)/(-252) - 24/(-56). Find a such that -a - 1/9*a**4 + g*a**3 + 0 - 1/3*a**2 = 0.
-1, 0, 3
What is l in 31 - 31 - 3*l**4 + 3*l**3 = 0?
0, 1
Let -6*d**2 + 4*d**2 + d - 2 + 0*d**2 + 3*d**2 = 0. What is d?
-2, 1
Let s(l) = 10*l**2 + 12*l**3 - 2*l**2 - 4*l + 1 - 3. Let u(w) = 17*w**2 + 0 + 0*w + 25*w**3 - 5*w - 5 - 3*w. Let c(a) = -5*s(a) + 2*u(a). Factor c(p).
-2*p*(p + 1)*(5*p - 2)
Let d = -92 - -60. Let k = 