f 0*k + 1/12*k**3 + 1/16*k**4 + 0*k**2 - 1. Suppose h(p) = 0. Calculate p.
-1, 0
Let s(z) be the first derivative of 5*z**3/3 - 5*z - 16. Let s(k) = 0. Calculate k.
-1, 1
Let h = 43/9 + -40/9. Let b(v) be the first derivative of 0*v**2 + 3/4*v**4 + 0*v + 3/5*v**5 + 1 + 1/6*v**6 + h*v**3. Factor b(x).
x**2*(x + 1)**3
Let h(b) be the second derivative of -b**8/240 + b**7/420 + 7*b**6/360 - b**5/60 - b**3/2 - 2*b. Let w(o) be the second derivative of h(o). Factor w(x).
-x*(x - 1)*(x + 1)*(7*x - 2)
Let p(m) be the third derivative of -1/240*m**6 - m**2 + 1/120*m**5 + 0 + 0*m**3 + 1/24*m**4 + 0*m. Factor p(t).
-t*(t - 2)*(t + 1)/2
Let r(l) = l**2 - 9*l + 12. Let m be r(8). Let p = m - 1. Let -u**2 - u**2 + 0*u**2 + 2*u**p = 0. What is u?
0, 1
Let b(j) = -4*j**2 + 51*j + 49. Let g(o) = 20*o**2 - 256*o - 244. Let u(a) = -16*b(a) - 3*g(a). Factor u(w).
4*(w - 13)*(w + 1)
Suppose -2 = -d + 1. Let y be (6/(-18))/((-2)/d). Factor 0 + 0*v + y*v**2.
v**2/2
Factor -6/7*a**2 + 8/7*a + 8/7.
-2*(a - 2)*(3*a + 2)/7
Let k = 17 - 15. Suppose -24*q**3 - k*q**4 + 7*q**5 - 12*q**2 - q**4 + 2*q**5 = 0. What is q?
-1, -2/3, 0, 2
Let d(p) = -2*p + 14. Let z be d(6). Let h(r) be the third derivative of 0 - 1/48*r**4 - 1/24*r**3 - 2*r**z - 1/240*r**5 + 0*r. Factor h(j).
-(j + 1)**2/4
Let y(s) be the first derivative of -s**6/24 - 3*s**5/20 - s**4/8 + s**3/6 + 3*s**2/8 + s/4 + 12. Factor y(b).
-(b - 1)*(b + 1)**4/4
Let s(j) = -j**2 - 4*j + 6. Let x be s(-5). Let o be 6 + -5 + 4*x. Suppose -3*h**2 - 1 - h**2 + o*h**2 = 0. Calculate h.
-1, 1
Let i(j) be the third derivative of 1/12*j**4 + 0*j + 1/30*j**5 + 1/180*j**6 + 1/6*j**3 + 0 - 2*j**2. Let x(k) be the first derivative of i(k). Factor x(d).
2*(d + 1)**2
Let f(x) = x**2 - 6. Let j be f(-3). Suppose -6 = p - j*p. Let 0 - 2/5*c**p + 2/5*c**2 + 0*c = 0. What is c?
0, 1
Let k(u) be the third derivative of 0 + 1/1512*u**8 - 7/108*u**4 + 2/27*u**3 - 4*u**2 + 0*u - 2/945*u**7 - 1/270*u**6 + 4/135*u**5. Solve k(s) = 0 for s.
-2, 1
Let b = 144 + -1727/12. Let t(f) be the first derivative of 0*f + 0*f**2 + b*f**3 - 3 - 1/16*f**4. Factor t(d).
-d**2*(d - 1)/4
Factor 27/7*f**2 + 6/7 - 3*f - 15/7*f**3 + 3/7*f**4.
3*(f - 2)*(f - 1)**3/7
Determine x, given that -2/11*x**4 + 0*x + 2/11*x**3 + 0 + 0*x**2 = 0.
0, 1
Let l(y) be the first derivative of 5*y**6/8 + 7*y**5/4 + 11*y**4/8 + y**3/2 + 7*y**2/2 - 2. Let m(u) be the second derivative of l(u). Factor m(p).
3*(p + 1)*(5*p + 1)**2
Let k = -143/13920 - -3/145. Let v(c) be the third derivative of -2*c**2 + 0 - k*c**4 + 1/12*c**3 + 0*c - 1/240*c**5. Factor v(f).
-(f - 1)*(f + 2)/4
Let b(u) = u**2 + 6*u + 2. Let y be b(-6). Determine x, given that -4 + 0*x**2 + y*x + 4 - x**2 = 0.
0, 2
Let p(q) = 7*q**3 - 2*q**3 - 3*q - q**2 + 3 - 6. Let l(j) = -j**4 - j**2 - j - 1. Let n(i) = -3*l(i) + p(i). What is d in n(d) = 0?
-1, -2/3, 0
Let c(t) = -2*t**2 + 2*t + 7. Let f(k) = -7*k**2 + 9*k + 27. Let h = 12 - 34. Let y(p) = h*c(p) + 6*f(p). What is w in y(w) = 0?
-4, -1
Let d be 4 + -3 - (1 - 1). Let n be -1 + d - (-4)/2. Factor 3*f**4 + 2*f**2 - 5*f**4 - 3*f**3 + n*f + f**3.
-2*f*(f - 1)*(f + 1)**2
Determine b so that 4/17*b**2 - 14/17*b + 8/17 + 2/17*b**3 = 0.
-4, 1
Let q(w) be the third derivative of 25*w**8/224 + w**7/28 - w**6/5 + w**5/10 - 9*w**2. Factor q(f).
3*f**2*(f + 1)*(5*f - 2)**2/2
Let d(j) be the first derivative of j**4/2 + 2*j**3 - 23. Let l(u) = 8*u**3 + 25*u**2 - u. Suppose -b = b - 18. Let x(f) = b*d(f) - 2*l(f). Factor x(i).
2*i*(i + 1)**2
Let a(n) be the third derivative of n**6/10 - n**5/4 - n**4/2 + 5*n**3/2 - 2*n**2 + 15. Factor a(u).
3*(u - 1)*(u + 1)*(4*u - 5)
Let n(v) = v + 5. Let b(m) = -3*m - 14. Let g(k) = 4*b(k) + 11*n(k). Let y be g(-5). What is q in 7*q**2 - q**2 + q**4 - 15*q**y + 6*q**3 - 4*q + 6*q**5 = 0?
-2/3, 0, 1
Let t(r) be the third derivative of -r**9/4320 - 3*r**8/4480 - r**7/2520 + r**4/12 - 5*r**2. Let n(z) be the second derivative of t(z). Factor n(f).
-f**2*(f + 1)*(7*f + 2)/2
Let l(n) = -14*n**3 - 6*n**2 + 8*n + 5. Let i(m) = -15*m**3 - 6*m**2 + 9*m + 6. Let w(f) = 5*i(f) - 6*l(f). Factor w(d).
3*d*(d + 1)*(3*d - 1)
Factor 0 + 4/7*x - 2/7*x**2.
-2*x*(x - 2)/7
Let q(x) be the third derivative of -1/210*x**7 + 0*x**4 + 6*x**2 + 1/60*x**5 + 1/120*x**6 + 0*x + 0*x**3 + 0 - 1/336*x**8. Factor q(g).
-g**2*(g - 1)*(g + 1)**2
Let r(w) be the second derivative of -w**4/24 + 5*w**3/2 - 225*w**2/4 - 7*w - 2. Factor r(l).
-(l - 15)**2/2
Let t(o) be the second derivative of -o**9/1008 - o**8/280 - o**7/280 + 2*o**3/3 - 5*o. Let g(y) be the second derivative of t(y). Let g(k) = 0. Calculate k.
-1, 0
Let z be ((-10)/(-4) - 3)*-14. Find b such that -z*b + 7*b - 2*b**2 = 0.
0
Let u(x) = -6*x**2 + 2. Let m(b) = 31*b**2 - 9. Suppose -3*s + 44 = s. Let c(n) = s*u(n) + 2*m(n). Factor c(a).
-4*(a - 1)*(a + 1)
Let l = 62 - 247/4. Let l + 1/4*k**2 + 1/2*k = 0. Calculate k.
-1
Let i = 110 + -108. Determine s, given that 1/2*s**i + 1/6*s - 1/3 = 0.
-1, 2/3
Let n(x) be the third derivative of x**7/140 + x**6/80 - 3*x**5/40 - x**4/16 + x**3/2 + 13*x**2. Solve n(z) = 0 for z.
-2, -1, 1
Let y(o) be the second derivative of 0*o**2 + 2*o - 1/24*o**4 - 1/6*o**3 + 0. Factor y(d).
-d*(d + 2)/2
Let s = 155/246 - -3/82. Factor 0 + 2/3*f**3 + 2/3*f**2 - s*f - 2/3*f**4.
-2*f*(f - 1)**2*(f + 1)/3
Suppose 0 = -3*s + 6*s - 6. Factor 6*k + 3*k**3 + k**s - 7*k**2 - k**3 - 2 + 0.
2*(k - 1)**3
Let n = 121/4 - 30. Find k such that 0*k + 1/4 - n*k**2 = 0.
-1, 1
Let d(h) be the first derivative of -16/3*h**3 + 2*h**5 + 0*h - 4*h**2 + 4 + 7/2*h**4. Factor d(i).
2*i*(i - 1)*(i + 2)*(5*i + 2)
Let y = 22 - 3. Let z = y + -13. Factor 4 + 3*c**2 - z*c - c**2 + 0*c**2.
2*(c - 2)*(c - 1)
Factor 0 - 1/7*h**2 - 1/7*h.
-h*(h + 1)/7
Let w(v) = -v**3 - v - 1. Let r(f) = -f + 3. Let k be r(4). Let t(l) = -3*l**3 - 4*l**2 + 5*l + 5. Let u(d) = k*w(d) - t(d). Let u(m) = 0. What is m?
-1, 1
Let o = -218 + 218. Factor 4/3 - 1/3*v**2 + o*v.
-(v - 2)*(v + 2)/3
Factor -2/3*c**2 - 2/3 + 4/3*c.
-2*(c - 1)**2/3
Let v(f) be the third derivative of -f**5/30 + f**4/2 - 3*f**3 - 7*f**2. Determine o, given that v(o) = 0.
3
Let s(y) = y + 4. Let k be s(-4). Let i(l) be the second derivative of 0*l**3 - 1/36*l**4 - 2*l + k*l**2 + 0. Factor i(f).
-f**2/3
Let t(c) be the first derivative of -3*c**5/40 + 39*c**4/32 - 6*c**3 + 27*c**2/4 - 25. Let t(j) = 0. Calculate j.
0, 1, 6
Let b be (40 + -6)*1/5. Let g(t) be the first derivative of b*t**5 + 4 + 22/3*t**3 + 21/2*t**4 + 0*t + 2*t**2 + 5/3*t**6. Let g(m) = 0. What is m?
-1, -2/5, 0
Find g such that -2*g**2 - 2*g**3 - 3*g**4 - g**5 + g**2 + g**2 = 0.
-2, -1, 0
Let s(r) be the second derivative of r**6/180 + r**5/180 - 3*r**2/2 + 3*r. Let w(v) be the first derivative of s(v). What is q in w(q) = 0?
-1/2, 0
Suppose -2*n + 3 = -n. Factor -d**2 + 0*d**2 + 9 - 9 + d**n.
d**2*(d - 1)
Let z(u) = -18*u**4 - 8*u**3 + 6*u**2 - 6. Let h(f) = -17*f**4 - 7*f**3 + 5*f**2 - 5. Let l(v) = -6*h(v) + 5*z(v). Let l(x) = 0. Calculate x.
-1/6, 0
Let v(l) be the first derivative of l**7/945 + l**2 - 3. Let w(f) be the second derivative of v(f). Suppose w(a) = 0. What is a?
0
Suppose -6 = u + 3*x - 0, -3*u = 4*x + 8. Suppose -4*m + 4 = u, 2*w + 5*m - 5 + 0 = 0. Suppose 0*b + w - 1/3*b**3 - 1/3*b**2 = 0. Calculate b.
-1, 0
Let h = -5 - -5. Find a, given that 2*a + 20*a**2 + h*a**3 + 6*a**3 - 4 + 4*a**3 - 4*a**2 = 0.
-1, 2/5
Suppose 8*p - 7*p = 0. Let u(x) be the third derivative of -2*x**2 + p + 1/300*x**6 - 1/60*x**4 + 1/75*x**5 - 2/15*x**3 + 0*x. Determine t so that u(t) = 0.
-2, -1, 1
Let m be 74/44 - 21/14. Find o, given that -2/11*o + 2/11*o**2 + 2/11*o**3 - m*o**4 + 0 = 0.
-1, 0, 1
Let o(f) = -6*f**3 + 2*f**2 + 4*f + 5. Let a = 11 - 5. Let n(v) = 7*v**3 - v**2 + 4*v**2 - 6 - 5*v - 5*v**2. Let b(y) = a*o(y) + 5*n(y). Factor b(i).
-i*(i - 1)**2
Factor 92*j**2 - 10 + 11*j - 3 + 5 + j + 72*j**3.
4*(j + 1)*(2*j + 1)*(9*j - 2)
Let k(q) be the first derivative of -2/3*q**3 - 81/20*q**5 + 3*q**4 + 0*q**2 + 4 + 4*q. Let g(l) be the first derivative of k(l). Suppose g(f) = 0. What is f?
0, 2/9
Let m(l) be the first derivative of l**5/5 - l**4/2 - 4*l**3/3 + 4*l**2 - 5. What is v in m(v) = 0?
-2, 0, 2
Factor 3*j**4 - 8*j**2 - 6*j**2 + j**5 + 10*j**2.
j**2*(j - 1)*(j + 2)**2
Suppose 33 = 4*w + 13. Suppose 0