- 4*i**c + 0*i + 10*i**4 - i**2.
3*i*(i - 1)*(i + 1)**3
Suppose -10 = -5*j + 2*d, 3*d - 1 = 4*j - 2. Find k, given that -4 - 3*k**2 + 10*k + k**2 + 2*k**2 - j*k**2 = 0.
1/2, 2
Let w be (455/(-56))/13 - 3/(-4). Let p(o) be the first derivative of -4 - w*o**2 - 1/12*o**3 + 0*o. Factor p(j).
-j*(j + 1)/4
Factor 0 - 2/9*z**3 - 2/9*z + 4/9*z**2.
-2*z*(z - 1)**2/9
Let z be (22/(-55))/(12/(-40)). Suppose z + 68/3*o**2 + 10*o + 14*o**3 = 0. Calculate o.
-1, -1/3, -2/7
Let b(p) be the third derivative of 0*p + 4/15*p**3 + 1/150*p**5 + 0 + 1/15*p**4 - 6*p**2. Suppose b(c) = 0. What is c?
-2
Let y(c) be the first derivative of -7 + 45/2*c**4 - 10*c**5 - 16*c**3 + 0*c + 4*c**2. Solve y(a) = 0 for a.
0, 2/5, 1
Let w(g) = -g**2 + 35*g + 116. Let m be w(38). Suppose -1/2*p**m + p - 1/2 = 0. Calculate p.
1
Let c(m) be the second derivative of -1/210*m**5 + 2/3*m**3 + m + 0 + 0*m**2 - 1/1260*m**6 - 1/84*m**4. Let p(z) be the second derivative of c(z). Factor p(t).
-2*(t + 1)**2/7
Suppose -2*c - 3*c - 3*o = -87, -61 = -3*c - 4*o. Let b = c - 15. Factor b - 6/7*q**2 - 4/7*q**3 - 2/7*q.
-2*q*(q + 1)*(2*q + 1)/7
Suppose 11*d = 10*d + 4. Let -1/2*g**3 + 0*g**d + 1/4*g**5 + 0*g**2 + 0 + 1/4*g = 0. What is g?
-1, 0, 1
Let j be (-7)/(-14)*6 + (-4)/6. Let g(q) be the first derivative of -1/6*q**6 + 3 - 9/4*q**4 - q**2 + 0*q - q**5 - j*q**3. Factor g(d).
-d*(d + 1)**3*(d + 2)
Let v be ((-30)/(-8))/(2/8). Suppose -3*y + 8*y = v. Factor -2*k**y + 5*k**3 + 5*k**3 - 4*k - 2*k**2 + 6*k**4.
2*k*(k + 1)**2*(3*k - 2)
Let a = 592/2121 - -2/303. Let z(q) be the first derivative of -1/7*q**6 + 10/21*q**3 + 0*q + 1/14*q**4 + 3 - 2/7*q**5 + a*q**2. Suppose z(o) = 0. What is o?
-1, -2/3, 0, 1
Let i(t) be the first derivative of t**4/34 - 2*t**3/51 - 2*t**2/17 - 5. Find q such that i(q) = 0.
-1, 0, 2
Suppose -4*z = -2*b - 12, 3*z - 3*b - 3 = 6. Factor -2*h**3 + 4*h**4 - 1 - 2*h + 4*h**3 - z*h**4.
(h - 1)*(h + 1)**3
Let d(f) = 3*f**5 - f**3 + 3*f - 5. Let y(t) = 3*t**5 + 3*t - 6. Let q(h) = 6*d(h) - 5*y(h). Suppose q(x) = 0. Calculate x.
-1, 0, 1
Let h(q) = -7*q - 1. Let k be h(-1). Let t = 10 - k. Factor w**4 + 4*w**4 + 3*w**3 - 2*w**t.
3*w**3*(w + 1)
Let o be ((-5 - -5)*(2 - 1))/(-1). Let q(n) be the third derivative of -1/84*n**4 + 0*n + 1/210*n**5 + 2*n**2 + 0*n**3 + o. Factor q(s).
2*s*(s - 1)/7
Suppose -6*z + 2*z + 16 = 0. Suppose -24 = -d - 4*i, 3*d + z*i = -4 + 36. Suppose 2/3*y**2 + 1/3 - y + 2/3*y**3 + 1/3*y**5 - y**d = 0. Calculate y.
-1, 1
Let r(i) = -10*i**3 - 9*i**2 - 7*i - 9. Let q(y) = -y**3 - y**2 - 2*y - 1. Let f(x) = 35*q(x) - 5*r(x). Factor f(d).
5*(d - 1)*(d + 2)*(3*d - 1)
Let h(q) be the second derivative of 0 + 0*q**2 - 1/6*q**3 - 4*q + 1/12*q**4 + 1/20*q**5 - 1/30*q**6. Let h(v) = 0. What is v?
-1, 0, 1
Let h(c) be the third derivative of c**5/12 + 5*c**4/4 + 15*c**3/2 + 17*c**2. What is i in h(i) = 0?
-3
Let l(h) be the third derivative of h**7/420 - h**6/40 + 3*h**5/40 - 25*h**2. Factor l(m).
m**2*(m - 3)**2/2
Let j(d) = d**2 + 1. Let n be j(0). Let u(i) = -5*i**2 + 2*i - 5. Let k(g) = -g**2 + g - 1. Let w(a) = n*u(a) - 4*k(a). Let w(y) = 0. What is y?
-1
Let q(s) be the second derivative of 0 + 1/21*s**3 + 0*s**4 + s + 0*s**6 + 1/147*s**7 + 0*s**2 - 1/35*s**5. Factor q(a).
2*a*(a - 1)**2*(a + 1)**2/7
Let q(i) = -i**3 + i**2 + i. Let f(h) = 4*h**3 - 9*h**2 - 10*h - 2 - 1 + 1. Let j(s) = -f(s) - 5*q(s). Determine w, given that j(w) = 0.
-2, -1
Let p(r) be the second derivative of -r**4/138 - r**3/23 - 2*r + 17. Find f such that p(f) = 0.
-3, 0
Let z(p) be the first derivative of 1/3*p**3 + 0*p - p**2 - 2. Solve z(f) = 0 for f.
0, 2
Suppose 4*m + 2*y = 22, -m - 2*y + y = -8. Suppose -6*h - 2 = -5*a - 2*h, -a + 8 = 3*h. Factor -u**3 - u**a + m*u**2 + 3*u**3.
2*u**2*(u + 1)
Suppose 10 - 1 = 3*l. Let c(x) be the first derivative of 9/4*x**2 + 7/6*x**l - 3 + x. Factor c(r).
(r + 1)*(7*r + 2)/2
Let g(o) be the second derivative of 1/6*o**3 + 1/16*o**5 + 1/2*o**2 + 0 - 13/48*o**4 + 8*o. Determine n so that g(n) = 0.
-2/5, 1, 2
Let w(r) = -r - 4. Let x be w(6). Let n be x/(-15) - (-2)/(-3). Factor -1/5*u**3 + 0 - 1/5*u**2 + n*u.
-u**2*(u + 1)/5
Let q(t) be the first derivative of -t**5/5 + 3*t**4 - 18*t**3 + 54*t**2 - 81*t - 11. Solve q(m) = 0 for m.
3
Let a = -259/10 + 26. Let o(c) be the second derivative of 1/42*c**7 + 1/30*c**6 + 0*c**2 - a*c**5 + 0 + 0*c**4 - 3*c + 0*c**3. Factor o(f).
f**3*(f - 1)*(f + 2)
Suppose 7*r + r = 0. Let w(g) be the second derivative of 1/36*g**4 - 2*g + r*g**2 + 0 + 0*g**3. Suppose w(d) = 0. Calculate d.
0
Let s(u) be the first derivative of -u**3/24 + u**2/16 + u/4 - 11. What is c in s(c) = 0?
-1, 2
Let m(a) be the third derivative of a**6/150 + a**5/50 + a**4/60 - 17*a**2. Factor m(w).
2*w*(w + 1)*(2*w + 1)/5
Determine c so that -8*c**5 + 0*c**5 - 5*c**2 + 4*c**5 - 12*c**4 - 12*c**3 + c**2 = 0.
-1, 0
Let l(b) = b. Let p(g) = 2*g. Let o(c) = l(c) - p(c). Suppose -k + 8 = 7. Let d(m) = 2*m**3 - 5*m. Let f(h) = k*d(h) - 3*o(h). Let f(u) = 0. What is u?
-1, 0, 1
Let x be ((-6)/(-10))/(2/10). Suppose 6 = x*j - 3. Let j*a**4 + 2*a**3 + a**4 - a - 4*a**2 - 3*a**5 + a + a = 0. Calculate a.
-1, 0, 1/3, 1
Let s = 17 - -2. Find j such that 3*j**4 + 19*j**2 - s*j**2 - 2*j**3 - j**3 = 0.
0, 1
Suppose -2*b + 7*b + 2*i = 110, -5*b = 3*i - 115. Suppose s = -5*c - s + 8, 5*c + 5*s = b. Find d such that 0*d - 1/2*d**5 + 0*d**3 + 0 - 1/2*d**4 + c*d**2 = 0.
-1, 0
Let a be (-1 - 2) + (21 - -1). Let r = -10 + a. Factor -12 - 4 + r*o - 3*o**2 + 10.
-3*(o - 2)*(o - 1)
Let t(w) = 5*w - 5. Let a be t(2). Let c(y) be the second derivative of -1/18*y**4 + 0 + 1/18*y**3 - 2*y - 1/20*y**a + 0*y**2. Suppose c(o) = 0. Calculate o.
-1, 0, 1/3
Factor -8/7 - 10/7*q - 2/7*q**2.
-2*(q + 1)*(q + 4)/7
Let f(l) = -5*l**3 + 2*l**2 + 9*l - 4. Let m(n) = -26*n**3 + 11*n**2 + 45*n - 19. Let h(j) = -11*f(j) + 2*m(j). Solve h(d) = 0.
-2, 1
Let m = -6550/7 - -937. Find u such that -m*u**3 - 3*u**2 - 3/7 - 15/7*u = 0.
-1, -1/3
Let b(c) = 5*c**3 - 3*c**2 - 4. Let h(u) = 9*u**3 - 5*u**2 - 7. Let w = 5 - 9. Let l(g) = w*h(g) + 7*b(g). Factor l(q).
-q**2*(q + 1)
Let p(y) be the second derivative of y**6/6 - y**5/2 + 5*y**4/12 - 14*y. Factor p(c).
5*c**2*(c - 1)**2
Let n = 169/110 - 2/55. Factor -2 - 1/4*x**3 - n*x**2 - 3*x.
-(x + 2)**3/4
Let n(p) = -26*p**2 + 30*p - 15. Let f(s) = 9*s**2 - 10*s + 5. Let w(d) = 11*f(d) + 4*n(d). Determine i so that w(i) = 0.
1
Let h(i) be the first derivative of i**5/40 + i**4/4 + 3*i**3/4 - 27*i/8 + 5. Factor h(d).
(d - 1)*(d + 3)**3/8
Let d(v) be the first derivative of 0*v - 2/15*v**3 - 4 - 1/5*v**2. Suppose d(x) = 0. What is x?
-1, 0
Let g be ((-3)/9*-1)/(3/18). Let j(c) be the first derivative of -4*c - 2*c**2 + g - 1/3*c**3. Suppose j(u) = 0. What is u?
-2
Let 6*r - 710*r**3 + 3*r**4 - 4*r**2 + 710*r**3 - 5*r**2 = 0. What is r?
-2, 0, 1
Let v be 10/4 + (-6)/(-12). Suppose -m - 10 = -4*i, -2*i + 12 + 2 = -5*m. Factor 1 + v - i - 2*h**2.
-2*(h - 1)*(h + 1)
Let t(r) be the third derivative of 2*r**7/315 + 7*r**6/270 + r**5/27 + r**4/54 + 2*r**2 - 24*r. Factor t(l).
4*l*(l + 1)**2*(3*l + 1)/9
Factor -32/3 - 16/3*n - 2/3*n**2.
-2*(n + 4)**2/3
Let p be 4/(-3) - 3422/(-1239). Find s, given that 4/7 - p*s**3 - 4/7*s**2 + 10/7*s = 0.
-1, -2/5, 1
Let v(t) = 5*t**2 - t. Suppose 0 = -x + 3*x - 2. Let a be v(x). Factor 1/4*m**3 + 0*m + 0 - 1/4*m**a + 0*m**2.
-m**3*(m - 1)/4
Solve 4/11 - 18/11*b + 10/11*b**2 - 14/11*b**4 + 18/11*b**3 = 0.
-1, 2/7, 1
Factor 3/5 + 1/5*j**2 - 4/5*j.
(j - 3)*(j - 1)/5
Let x(n) be the third derivative of 2*n**7/105 - 4*n**6/15 + 8*n**5/5 - 16*n**4/3 + 32*n**3/3 - 2*n**2. Factor x(s).
4*(s - 2)**4
Let s(f) be the first derivative of 7*f**6/10 - 6*f**5/25 - 63*f**4/20 - 8*f**3/5 + 6*f**2/5 - 22. Find r, given that s(r) = 0.
-1, 0, 2/7, 2
Suppose -4*h - n + 2 = -3, 0 = 4*h - 4*n - 20. Suppose -3*z + 36 = -18. Factor 8/9 + z*i**h + 8*i.
2*(9*i + 2)**2/9
Let v(p) be the first derivative of -p**3 + 27*p**2/14 - 6*p/7 - 6. What is g in v(g) = 0?
2/7, 1
Let n(i) be the third derivative of -i**5/90 + i**4/6 - i**3 + 2*i**2. Determine r so that n(r) = 0.
3
Suppose -2*z + 2*p + 14 = 0, -3*z + 4*p + 0*p + 26 = 0. Let a(o) be the first derivative of -2/3*o**3 + o**z + 4*o + 3. Factor a(i).
-2*(i - 2)*(i + 1)
Let s(c) be the first derivative