*2*(g + 1)/3
Let k(x) be the second derivative of -x**4/60 - 4*x**3/15 - 16*x - 2. Factor k(a).
-a*(a + 8)/5
Let j(o) be the third derivative of o**5/15 - o**4/24 + 8*o**2. Let j(a) = 0. Calculate a.
0, 1/4
Let v = -9 - -12. Suppose 3 = v*n - 6. Suppose -6 - 21*r**4 + 0*r - 15*r**n + 15*r + 30*r**2 - 3*r**2 = 0. What is r?
-1, 2/7, 1
Let o(h) be the third derivative of -2*h**2 + 0*h - 7/100*h**5 + 1/40*h**4 + 0*h**3 + 3/40*h**6 + 1/140*h**8 + 0 - 13/350*h**7. Factor o(k).
3*k*(k - 1)**3*(4*k - 1)/5
Let r(h) = h + 5. Let t(v) = -v - 4. Let m(a) = 4*r(a) + 5*t(a). Let l be m(-2). Suppose 4/5*s**l - 3/5*s - 1/5 = 0. What is s?
-1/4, 1
Let d(a) be the first derivative of 2*a**3/3 - 5*a**2 - 12*a + 38. Let d(r) = 0. Calculate r.
-1, 6
Let y(m) be the second derivative of m**6/270 + m**5/60 + m**4/36 - 5*m**3/6 + 4*m. Let h(x) be the second derivative of y(x). Suppose h(i) = 0. What is i?
-1, -1/2
Let j(i) = 5*i**2 + i - 3. Suppose -3*x = -x - 6. Let b(g) = -26*g**2 - 6*g + 16. Let h be 1 + (-1 - 16/(-1)). Let n(a) = h*j(a) + x*b(a). Factor n(p).
2*p*(p - 1)
Suppose -13 + 1 = 4*i. Let l = 6 + i. Find k, given that k**l - 3*k**3 + 0*k**5 + k + k**5 = 0.
-1, 0, 1
Let m(z) = -11*z**4 + 20*z**3 - 6*z**2. Let b(c) = 10*c**4 - 20*c**3 + 6*c**2. Let x(w) = 3*b(w) + 4*m(w). Solve x(a) = 0.
0, 3/7, 1
Let a = 5/113 - -93/452. Factor -1/2*w**2 - 1/4*w**3 + 0 - a*w.
-w*(w + 1)**2/4
Let c(g) be the third derivative of g**6/360 + g**5/60 - g**4/72 - g**3/6 - 7*g**2. Factor c(b).
(b - 1)*(b + 1)*(b + 3)/3
Let k(i) = 2*i - 20. Let y be k(12). Let x(c) be the second derivative of 1/66*c**y + 0*c**2 + 1/22*c**5 - 1/33*c**3 + 3*c + 0 + 1/55*c**6. Factor x(d).
2*d*(d + 1)**2*(3*d - 1)/11
Let y(l) be the first derivative of -8*l**5/5 - 3*l**4/2 + 6*l**3 - 2*l**2 + 7. Find c such that y(c) = 0.
-2, 0, 1/4, 1
Let h(w) = 6*w - 51. Let k be h(9). Let o(m) = -m**3 - 3*m**2 - 3*m. Let b be o(-2). Determine j so that -2*j - 1/3*j**b - k = 0.
-3
Let o be 1/3*-1 - 300/(-90). Factor -2/3 - 4/3*r**2 - o*r.
-(r + 2)*(4*r + 1)/3
Let w be (12/(-24))/((-1)/6). Let -4*l**3 + 2*l**3 - 3*l**4 + 6*l**3 - 7*l**3 + w*l**2 + 3*l = 0. Calculate l.
-1, 0, 1
Let r = 741/2 - 366. Factor -27/2*i**3 - r*i - 27/2*i**2 - 1/2.
-(3*i + 1)**3/2
Let i(y) = 51*y**2 + 26*y + 4. Suppose 0 = -5*k - 5, -2*f + 0*k + 2 = 2*k. Let l(r) = -103*r**2 - 51*r - 8. Let p(u) = f*l(u) + 5*i(u). Factor p(s).
(7*s + 2)**2
Let x(s) be the first derivative of 2/9*s**3 + 2 + 1/3*s**2 + 3*s - 1/6*s**4. Let l(t) be the first derivative of x(t). What is f in l(f) = 0?
-1/3, 1
Let o(u) be the third derivative of -u**7/665 - 7*u**6/1140 - u**5/114 - u**4/228 + 18*u**2. Factor o(y).
-2*y*(y + 1)**2*(3*y + 1)/19
Suppose 13 = -2*w - 1. Let r be 2 + (1 + w)/(-3). Determine t so that 48*t**3 - 18*t**2 - 7*t**4 - 12*t**r + 0*t + 2*t - 13*t**4 = 0.
0, 1/4, 1
Determine j so that 6*j**2 - 3 - 3*j**4 + 4*j + 24*j**3 - 12*j**5 - 25*j + 9*j = 0.
-1, -1/4, 1
Let p(z) be the first derivative of 1 + 0*z + 0*z**4 + 2/9*z**3 - 2/15*z**5 + 0*z**2. Solve p(c) = 0 for c.
-1, 0, 1
Let u(h) = -14*h - 25. Let o be u(-2). Factor 1/4*i**2 + 1/4*i**5 + 3/4*i**o + 0 + 0*i + 3/4*i**4.
i**2*(i + 1)**3/4
Find u such that 0*u + 2/7*u**2 + 2/7*u**3 - 2/7*u**4 - 2/7*u**5 + 0 = 0.
-1, 0, 1
Suppose -m - 22 - 3 = 5*q, -m + 15 = -3*q. Suppose 5*w - r - 19 = 0, -w + r + 23 = -4*r. Suppose j**2 - 1/2*j**w + m + 1/2*j - j**4 = 0. What is j?
-1, -1/2, 0, 1
Factor 3*c**2 - 378*c**4 + 4*c**3 - 4*c + c**2 + 374*c**4.
-4*c*(c - 1)**2*(c + 1)
Let h(a) be the first derivative of a**6/180 - a**4/36 + a**2 - 1. Let w(p) be the second derivative of h(p). Factor w(u).
2*u*(u - 1)*(u + 1)/3
Let u(x) be the third derivative of 1/4*x**4 + 2/3*x**3 + 0*x + 0 + 1/30*x**5 - 6*x**2. Let u(g) = 0. Calculate g.
-2, -1
Let d(r) be the first derivative of -r**3/4 + 5*r**2/8 - r/2 + 25. Factor d(f).
-(f - 1)*(3*f - 2)/4
Let c(q) be the first derivative of -1/4*q**4 + 0*q + 0*q**3 + 0*q**2 + 2. Factor c(a).
-a**3
Suppose 5*k + 3 = -12. Let s be (-2)/3*(0 + k). Suppose s*w**3 + 4/3*w**2 - 4/3 - 2*w = 0. What is w?
-1, -2/3, 1
Let n(a) = -4*a**5 - 10*a**4 - 32*a**3 + 46*a**2 - 10. Let w(h) = h**5 + 3*h**4 + 11*h**3 - 15*h**2 + 3. Let i(f) = -3*n(f) - 10*w(f). Factor i(m).
2*m**2*(m - 2)*(m - 1)*(m + 3)
Let g(w) be the third derivative of w**5/210 - w**3/21 - 10*w**2. Determine i, given that g(i) = 0.
-1, 1
Suppose -132 = 2*l - 136. Factor 2/3*x**3 + 0 - 2/3*x - 2/3*x**l + 2/3*x**4.
2*x*(x - 1)*(x + 1)**2/3
Let b(x) be the second derivative of -x**4/18 - 11*x. Factor b(g).
-2*g**2/3
Let n be (128/24*2/24)/1. Suppose 2/9*h**2 - n*h + 2/9 = 0. What is h?
1
Suppose -25 = 5*t + 5. Let x be t/33 - (-408)/308. Find i such that 0 - 2/7*i - 2/7*i**5 + x*i**4 - 12/7*i**3 + 8/7*i**2 = 0.
0, 1
Let u(n) be the second derivative of -n**6/40 - n**5/20 + n**4/8 + n**3/2 - n**2/2 - 5*n. Let p(h) be the first derivative of u(h). Factor p(j).
-3*(j - 1)*(j + 1)**2
Let p(f) be the second derivative of -f**3/6 - f**2 + 12*f. Let n be p(-2). Factor 0*x**2 - 4/5*x**4 - 2/5*x**5 + n - 2/5*x**3 + 0*x.
-2*x**3*(x + 1)**2/5
Let d(q) = 6*q**2 - 4. Suppose -a = -4, 32 + 0 = 3*g + 5*a. Let w(p) = -5*p**2 + 3. Let s(z) = g*w(z) + 3*d(z). Factor s(o).
-2*o**2
Let h(l) be the first derivative of -8/25*l**5 + 0*l + 0*l**3 + 1/15*l**6 + 0*l**2 + 2/5*l**4 - 3. Factor h(g).
2*g**3*(g - 2)**2/5
Let p(g) = 7*g**3 + 4*g**2 - 3*g + 5. Let m(n) = 6*n**3 + 4*n**2 - 2*n + 4. Let z(h) = -5*m(h) + 4*p(h). Let z(s) = 0. Calculate s.
-1, 0
Let v(o) be the second derivative of -o**4/24 - o**3/8 - o**2/8 - 46*o. Factor v(c).
-(c + 1)*(2*c + 1)/4
Suppose 6*n = n + 15. Let z(u) be the third derivative of -1/15*u**4 + u**2 + 1/150*u**5 + 4/15*u**n + 0 + 0*u. Determine g, given that z(g) = 0.
2
Let c be ((-2)/11)/((-12)/33). Factor -2*d + 3*d**2 + c*d**4 - 2*d**3 + 1/2.
(d - 1)**4/2
Let o(r) be the second derivative of -r**4/12 - r**3/2 - 16*r. Determine v, given that o(v) = 0.
-3, 0
Suppose -4*g - 2 + 12 = -k, -5*k - g + 13 = 0. Let p(h) = -2*h - 2. Let c be p(-2). Factor 4*b**3 + 0*b**3 + 2*b**2 - k*b**3 + c*b**2.
2*b**2*(b + 2)
Let n(x) be the third derivative of -1/180*x**6 + 0 + 2*x**2 - 1/36*x**4 + 1/45*x**5 + 0*x + 0*x**3. Factor n(z).
-2*z*(z - 1)**2/3
Let f(a) be the second derivative of a**5/270 - a**4/54 + a**3/27 - a**2/2 - 3*a. Let i(z) be the first derivative of f(z). Factor i(t).
2*(t - 1)**2/9
Factor 1/10*c**2 + 11/5*c + 121/10.
(c + 11)**2/10
Let i(f) = -34*f**4 + f**3 - 5*f**2 - 5*f + 5. Let s(y) = 171*y**4 - 6*y**3 + 24*y**2 + 24*y - 24. Let t(r) = -24*i(r) - 5*s(r). Factor t(w).
-3*w**3*(13*w - 2)
Let f = -2474/15 + 165. Let c(u) be the first derivative of 0*u**2 - 1 + f*u**3 - 1/20*u**4 + 0*u. What is w in c(w) = 0?
0, 1
Let k(w) = 2*w**3. Let z be k(1). Let t = -195/4 - -49. Factor 1/4*m + 0 + t*m**z.
m*(m + 1)/4
Let b(i) = 16*i**2 + i. Let x be b(1). Suppose -5*n + 15 = f, -4*n - 4*f + x = -11. Factor 7*o**4 + 2*o - 4*o**3 + 3*o**n - 7*o**3 - o**3.
o*(o - 1)**2*(7*o + 2)
Find v such that 12*v**2 - 21/4*v**3 - 33/4*v + 3/2 = 0.
2/7, 1
Let d = 731 + -727. Let 2/5*i**5 + 6/5*i**3 + 2/5*i**2 + 6/5*i**d + 0 + 0*i = 0. What is i?
-1, 0
Let b be (0 + (-4)/(-256))*-2. Let y = 9/32 + b. Suppose -g + 1 + y*g**2 = 0. What is g?
2
Let h(r) be the third derivative of 7*r**2 - r**3 + 1/6*r**4 + 0 + 1/6*r**5 + 0*r. Solve h(d) = 0 for d.
-1, 3/5
Let l(w) be the third derivative of w**8/72 + 23*w**7/315 + 13*w**6/180 - 19*w**5/90 - 5*w**4/9 - 4*w**3/9 - 46*w**2. Let l(k) = 0. Calculate k.
-2, -1, -2/7, 1
Suppose 0*r - 4*o = -5*r - 50, -o + 20 = -2*r. Let t = 21/2 + r. What is m in 1/2*m**4 + 0*m**2 - t + m - m**3 = 0?
-1, 1
Let n(h) be the second derivative of h**7/11340 - h**6/1620 - h**5/180 + h**4/3 + 7*h. Let g(j) be the third derivative of n(j). Suppose g(v) = 0. What is v?
-1, 3
Let l = 19 - 4. Suppose -5*c = -4*g + 1 - 11, 3*c = -3*g + 6. Factor -l*u**4 - 9*u**3 - 2*u**c + 8*u**2 + 0*u**2.
-3*u**2*(u + 1)*(5*u - 2)
Let u(p) = -3*p**3 - 12*p**2 - 7*p - 6. Let q(i) = 2*i**3 + 8*i**2 + 5*i + 4. Let h(o) = 8*q(o) + 5*u(o). Factor h(t).
(t + 1)**2*(t + 2)
Let m(v) = -8*v**4 + 16*v**3 + 24*v**2 - 37*v - 27. Let h(a) = -12*a**4 + 24*a**3 + 36*a**2 - 56*a - 40. Let y(k) = -5*h(k) + 8*m(k). Factor y(q).
-4*(q - 2)**2*(q + 1)**2
Factor 15