of g(i). Solve m(o) = 0 for o.
-2, -1
Let n(u) be the first derivative of -u**5/5 + 5*u**4/6 - 28*u**3/27 + 4*u**2/9 + 5. What is s in n(s) = 0?
0, 2/3, 2
Solve -20/7*h + 50/7*h**2 + 2/7 = 0.
1/5
Suppose 109 = 6*z - 11. Let s = 23 - z. Factor 2/11*p**2 + 0 + 6/11*p**4 + 2/11*p**5 + 0*p + 6/11*p**s.
2*p**2*(p + 1)**3/11
Let r(z) be the first derivative of 1/2*z**3 + 3/4*z**2 - 3 + 1/8*z**4 + 1/2*z. Factor r(k).
(k + 1)**3/2
Factor -4/3*j**4 - 8*j**2 + 16/3*j - 4/3 + 16/3*j**3.
-4*(j - 1)**4/3
Find p, given that 8/7*p + 2/7*p**2 + 6/7 = 0.
-3, -1
Suppose 5*f + 7*a - 3*a = 0, 4*f + 4*a + 4 = 0. Solve -2*j**2 + 4*j + 0*j**2 - 4*j**3 + 0*j**f + 2*j**4 = 0.
-1, 0, 1, 2
Let c(o) be the second derivative of 2*o**7/21 - 2*o**6/15 - o**5/5 + o**4/3 - 4*o. Find l such that c(l) = 0.
-1, 0, 1
Suppose 2*h - 3*h + 3 = 0. Let l(x) be the second derivative of -2/9*x**h + 0*x**2 + 0*x**4 - 2*x + 0 + 1/20*x**5 + 1/90*x**6. Factor l(p).
p*(p - 1)*(p + 2)**2/3
Let x = -1321 + 9202/7. Let d = x - -239/35. Factor -2/5*b**2 - 2/5*b**3 + 2/5*b + d.
-2*(b - 1)*(b + 1)**2/5
Factor 0 + 1/5*b**5 + b**3 + 4/5*b**4 + 0*b + 2/5*b**2.
b**2*(b + 1)**2*(b + 2)/5
Let k be 657/378 + 3/7. Let t = k - 2. Factor 1/3*c - t - 1/6*c**2.
-(c - 1)**2/6
Let b = 275 - 273. Factor -50/7*o**3 + 32/7*o + 8/7 + 10/7*o**b.
-2*(o - 1)*(5*o + 2)**2/7
Suppose -24*w = -28*w + 12. Let -3/2*k - 9/4*k**2 + 0 - 3/4*k**w = 0. What is k?
-2, -1, 0
Let l(y) be the first derivative of -y**5/10 + y**4/3 - y**3/3 - 6*y - 3. Let n(g) be the first derivative of l(g). Factor n(f).
-2*f*(f - 1)**2
Let g = 1745/3 + -581. Factor -4/3 + 2/3*v**2 - g*v.
2*(v - 2)*(v + 1)/3
Let q(z) be the first derivative of -3/7*z**2 - 2/21*z**3 + 2 + 0*z. Factor q(l).
-2*l*(l + 3)/7
Let n be (-2)/(((-12)/(-39))/(-4)). Suppose 4 = w + c, 2*w + 3*w + 2*c = n. Find d such that -4*d**3 + 2*d**3 - 2 + 4*d**3 - 6*d**2 + w*d = 0.
1
Let a(h) be the second derivative of -h**7/168 - h**6/40 - h**5/40 + h**4/24 + h**3/8 + h**2/8 - 7*h. Solve a(f) = 0 for f.
-1, 1
Let t(q) be the third derivative of 3/50*q**6 + 3*q**2 - 3/175*q**7 + 0*q - 2/15*q**4 - 1/30*q**5 + 0 + 4/15*q**3. Suppose t(y) = 0. Calculate y.
-2/3, 2/3, 1
Let m be 1 + ((-100)/(-24) - 2) - 3. Let h(g) be the second derivative of -1/8*g**4 - m*g**3 - 1/40*g**5 + 0 + 0*g**2 - g. Determine w so that h(w) = 0.
-2, -1, 0
Let z(m) be the third derivative of m**7/420 + m**6/240 - m**5/120 - m**4/48 + 2*m**2. Factor z(g).
g*(g - 1)*(g + 1)**2/2
Suppose 23 = 5*f - 2*x, 11 = 4*f - 4*x - 17. Let m(j) be the first derivative of -3/2*j**2 - 1/2*j**f - 2*j - 1/16*j**4 - 2. Solve m(d) = 0 for d.
-2
Let a(s) be the third derivative of -s**4/12 - s**3/3 + 3*s**2. Let p be a(-2). Determine l so that 0 + 1/2*l**p + 1/2*l = 0.
-1, 0
Suppose 2*c = -c. Let h(n) be the first derivative of c*n + 1/9*n**3 + 1 + 0*n**2 + 0*n**4 - 1/15*n**5. Factor h(p).
-p**2*(p - 1)*(p + 1)/3
Let a(y) be the third derivative of -2*y**2 + 0*y**4 + 0 + 0*y**3 + 0*y - 1/84*y**8 - 1/6*y**6 - 8/105*y**7 - 2/15*y**5. Suppose a(l) = 0. What is l?
-2, -1, 0
Let o(r) be the first derivative of r**6/160 - r**5/240 - r**4/32 + r**3/24 + 5*r**2/2 - 5. Let w(q) be the second derivative of o(q). Factor w(y).
(y - 1)*(y + 1)*(3*y - 1)/4
Let u(o) be the third derivative of -9*o**2 - 1/420*o**6 + 0 + 0*o + 0*o**5 + 1/28*o**4 + 2/21*o**3. Let u(w) = 0. Calculate w.
-1, 2
Let z(g) be the first derivative of -2*g**6/9 + 14*g**5/15 - 3*g**4/2 + 10*g**3/9 - g**2/3 - 6. Factor z(n).
-2*n*(n - 1)**3*(2*n - 1)/3
Let b be 0 + (15/(-12))/(-5). Let j(y) be the first derivative of 1/16*y**4 - b*y - 1/4*y**3 + 3/8*y**2 + 2. What is x in j(x) = 0?
1
Factor 16/3*i - 4/3*i**2 - 4.
-4*(i - 3)*(i - 1)/3
Determine x so that 0*x**3 + 0 + 3/5*x**5 - 3/5*x - 6/5*x**2 + 6/5*x**4 = 0.
-1, 0, 1
Let i(a) = -2*a + 1. Let o = 11 + -12. Let d be i(o). Factor 2/7 + 6/7*q**2 + 2/7*q**d + 6/7*q.
2*(q + 1)**3/7
Let u(y) be the second derivative of -y**5/60 + y**4/24 - 3*y**2/2 - 5*y. Let c(s) be the first derivative of u(s). Find k such that c(k) = 0.
0, 1
Let n(t) be the third derivative of -7*t**6/180 + 8*t**5/45 - t**4/9 - 24*t**2. Solve n(b) = 0 for b.
0, 2/7, 2
Let i(m) = 8*m**4 - 13*m**3 - 14*m**2 + 7*m - 2. Let n(y) = 9*y**4 - 12*y**3 - 15*y**2 + 6*y - 3. Let c(x) = -3*i(x) + 2*n(x). Suppose c(p) = 0. What is p?
-1, 0, 1/2, 3
Let k be (2/(-4) - -3)/5. Let w(l) be the first derivative of 1/12*l**4 + 1/3*l**3 + k*l**2 - 2 + 1/3*l. Factor w(j).
(j + 1)**3/3
Let k = -15 + 21. Let p be 21/k + 9/(-3). Suppose -1/2*g**2 - p*g + 1 = 0. What is g?
-2, 1
Let v = 331/51 - 82/17. Factor -q + 2/3 + q**3 + v*q**4 - 7/3*q**2.
(q - 1)*(q + 1)**2*(5*q - 2)/3
Factor 6*m**2 + 2*m**5 - 3*m**3 + 7*m**5 - 6*m**5 - 6*m**4.
3*m**2*(m - 2)*(m - 1)*(m + 1)
Determine q so that -23/5*q**3 + 7/5*q**5 - 4/5*q - q**4 + 29/5*q**2 - 4/5 = 0.
-2, -2/7, 1
Factor -4*r**2 + 0 + 0*r - 3*r - 5*r - 4.
-4*(r + 1)**2
Factor -1/8*w**4 + 1/4*w + 0 + 1/8*w**2 - 1/4*w**3.
-w*(w - 1)*(w + 1)*(w + 2)/8
Let z(t) be the first derivative of 2*t**5/5 - 7*t**4/10 - 46*t**3/15 - t**2 + 12*t/5 + 3. Find g, given that z(g) = 0.
-1, 2/5, 3
Let v(d) = -d - 2. Suppose -2*a - 5 + 1 = 0. Let s be v(a). Factor 0*i**3 - 2/7*i**5 + 0*i - 2/7*i**4 + 0*i**2 + s.
-2*i**4*(i + 1)/7
Let y(d) = -d - 6. Let p be y(-9). Factor z - p + 3 + z**2 - 1 - z**3 + 0*z.
-(z - 1)**2*(z + 1)
Let o be ((-16)/(-100))/((-1)/(-20)). Let u(d) be the first derivative of 0*d + d**4 + 5/2*d**6 - 1 + 0*d**3 + 0*d**2 - o*d**5. Find m such that u(m) = 0.
0, 2/5, 2/3
Let n(g) be the third derivative of g**8/26880 - g**7/10080 - g**6/2880 + g**5/480 + g**4/24 - 2*g**2. Let a(k) be the second derivative of n(k). Factor a(t).
(t - 1)**2*(t + 1)/4
Suppose 4*z = -2 + 10. Let j(u) be the third derivative of 0*u + 1/300*u**6 + 0*u**3 + 0 + u**z + 1/150*u**5 + 0*u**4. Suppose j(y) = 0. What is y?
-1, 0
Let s(x) be the first derivative of -2*x**6/15 + x**5/5 + 6*x - 5. Let g(m) be the first derivative of s(m). Factor g(i).
-4*i**3*(i - 1)
Suppose 4*y = 8 + 4. Factor 5*w**3 - 2*w - 3*w**y - 2*w**2 + 0*w**4 + 2*w**4.
2*w*(w - 1)*(w + 1)**2
Let c(k) be the second derivative of k**5/30 + 7*k**4/18 + 5*k**3/3 + 3*k**2 - 24*k. What is x in c(x) = 0?
-3, -1
Let o(r) = 18*r - 339. Let h be o(19). Factor 3*q**5 + 3/4*q**2 + 0 + 6*q**4 + 15/4*q**h + 0*q.
3*q**2*(q + 1)*(2*q + 1)**2/4
Let u(g) be the second derivative of -g**7/420 - g**6/360 + g**5/60 + g**4/24 + g**3/6 + 3*g. Let f(o) be the second derivative of u(o). Factor f(z).
-(z - 1)*(z + 1)*(2*z + 1)
Let -2/7*z**3 + 0 - 6/7*z**2 + 6/7*z**4 + 2/7*z = 0. What is z?
-1, 0, 1/3, 1
Let r(b) be the first derivative of -b**4/10 - 14*b**3/15 + 59. What is u in r(u) = 0?
-7, 0
Let o(z) = -z**3 - 4*z**2 + 6*z + 7. Let u be o(-5). Let f = -262/3 + 88. Suppose -2/3 - f*l**u + 4/3*l = 0. Calculate l.
1
Let f(w) = -w + 13. Let h be f(9). Let 0 + 1/4*z**h - 1/2*z**2 + 0*z - 1/4*z**3 = 0. What is z?
-1, 0, 2
Suppose 9 = 3*a + 3. Factor 2 - 2 - a - 9*c - 6*c**2 - c**2.
-(c + 1)*(7*c + 2)
Let g(v) = -375*v**5 - 395*v**4 - 110*v**3. Let h(n) = 17*n**5 + 18*n**4 + 5*n**3. Let t(c) = -2*g(c) - 45*h(c). Factor t(w).
-5*w**3*(w + 1)*(3*w + 1)
Suppose -8*s**3 - 8*s**3 + 6*s + 48*s**2 - 3 - 69*s**4 - 98*s**3 + 24*s**4 + 108*s**5 = 0. Calculate s.
-1, -1/4, 1/3, 1
Suppose 3*o = -h + 19, -2 = -0*h + h - 4*o. Let m be 5*2/h*2. Factor p - m - p - 2*p**3 - 6*p**2 - 6*p.
-2*(p + 1)**3
Let y(k) be the first derivative of 5*k**6/6 - 5*k**4/2 + 5*k**2/2 + 4. Determine f, given that y(f) = 0.
-1, 0, 1
Let w(i) be the second derivative of 0 + 1/3*i**3 + 0*i**2 + 1/15*i**6 - 1/10*i**5 - 8*i - 1/6*i**4. Solve w(k) = 0 for k.
-1, 0, 1
Let x = 8 + -5. Solve -3*i - 2 + x*i**2 + 0 - 4 = 0 for i.
-1, 2
Factor 0 + 3*w**2 + 3/2*w**3 + 0*w.
3*w**2*(w + 2)/2
Let y(m) be the second derivative of -2/3*m**3 - 1/5*m**5 + 0*m**2 + 0 - 2/3*m**4 + 9*m. Factor y(f).
-4*f*(f + 1)**2
Suppose 41 = 5*u + 26. Suppose 2*l = -l - 3*w + 6, 4*l - 2*w = 32. Factor u*m - 5*m - 4*m + 3*m**3 - l*m**2 + 9*m.
3*m*(m - 1)**2
Suppose 13/5*x**2 + 4/5 - 12/5*x - 6/5*x**3 + 1/5*x**4 = 0. What is x?
1, 2
Find r such that -2/5*r**3 + 2/5*r**4 + 0*r + 0*r**2 + 0 = 0.
0, 1
Suppose -2/11*m**3 - 2/11*m - 4/11*m**2 + 0 = 0. Calculate m.
-1, 0
Let b = -801/7 - -115. Factor -2/7*y**3 - b*y - 6