- 2*t. Let b = c - 16. Find w such that 17/3*w**b + 8/3 - 14/3*w**4 - 20/3*w + w**5 + 2*w**2 = 0.
-1, 2/3, 1, 2
Suppose -2*b = 4*f - 32 + 4, 2*b - 30 = -2*f. Suppose b*d - 11*d + 4 + 31*d + 81*d**2 = 0. Calculate d.
-2/9
Suppose 90*j = 87*j + 9. Let h(i) be the second derivative of -1/50*i**5 + 1/15*i**4 - 1/15*i**j + 0*i**2 + 3*i + 0. Determine p so that h(p) = 0.
0, 1
Let w be (1 - 4) + (0 - -3). Factor w*m - 2/3*m**2 + 0.
-2*m**2/3
Suppose -4*v + v = 0. Suppose v*l - 3*l + 9 = 0. Let 3*n**l + 4*n**2 - 3*n**2 - 2*n**3 - 1 - n = 0. Calculate n.
-1, 1
Suppose 83 + 113 = 49*a. Factor -4/9*x**3 + 2/9*x**a + 4/9*x - 2/9 + 0*x**2.
2*(x - 1)**3*(x + 1)/9
Let k(d) = 3*d**2 - 11*d + 10. Let w be k(10). Factor -200*h**3 + w*h**3 - h**4.
-h**4
Let r(o) = 5*o**2 + 2*o + 1. Let c be (-1)/(1 - 0 - 0). Let y be r(c). Factor 2 - s + 3*s**2 - 2*s**2 + y*s.
(s + 1)*(s + 2)
Let h(y) be the third derivative of -y**6/540 - y**3/3 - 2*y**2. Let f(s) be the first derivative of h(s). Determine l so that f(l) = 0.
0
Suppose 3/4*w**4 + 5/4*w**3 + 1/2*w**2 + 0*w + 0 = 0. What is w?
-1, -2/3, 0
Let w = 56 + -166/3. Let f(n) be the first derivative of -w*n**3 - 1 - 4/7*n - 9/7*n**2. Factor f(o).
-2*(o + 1)*(7*o + 2)/7
Let l(k) = -99*k**3 + 6*k**2. Let f(j) = -32*j + 14*j**3 + 16*j - j**2 + 16*j. Let m(u) = -27*f(u) - 4*l(u). Solve m(t) = 0 for t.
-1/6, 0
Factor 5*z + 16*z**3 - 12*z**2 - 7*z - 8 - 16*z - 18*z.
4*(z - 2)*(z + 1)*(4*z + 1)
Let b(o) be the third derivative of -o**6/8 + 13*o**5/40 - o**4/8 - o**3/4 - 11*o**2. Solve b(l) = 0.
-1/5, 1/2, 1
Suppose -2*x = x + 12, 0 = 2*t + 3*x + 8. Let b be (-85)/(-357) - 1*2/(-6). Let -2/7*c**t + 2/7*c + b = 0. What is c?
-1, 2
Let h = -1 + 3. Suppose -a - h = -4. Suppose -2*l - 5*l - a*l**4 + 4*l**3 + 3*l + 2*l**2 = 0. What is l?
-1, 0, 1, 2
Let y be (-33)/(-90) + (-2)/6. Let c(u) be the second derivative of -1/5*u**2 + 1/50*u**5 + 0 - 1/15*u**3 + y*u**4 + 3*u. Factor c(j).
2*(j - 1)*(j + 1)**2/5
Let n(f) be the first derivative of f**6/30 + f**5/10 + f**4/12 - f**2/2 + 5. Let i(h) be the second derivative of n(h). Factor i(x).
2*x*(x + 1)*(2*x + 1)
Let y(i) be the third derivative of 0 + 0*i**3 + 3*i**2 + 1/40*i**6 + 0*i - 1/70*i**7 + 0*i**5 + 0*i**4. Let y(z) = 0. What is z?
0, 1
Let x(b) = b**2 - 10*b + 16. Let t be x(12). What is s in -52*s**4 + 16*s**2 - 26*s**5 - t*s**3 + 6*s**5 + 24*s**3 = 0?
-2, -1, 0, 2/5
Determine h so that -h - 3*h**5 + 3*h**5 - 2*h**4 + 2*h**2 + h**5 = 0.
-1, 0, 1
Factor 3*o**2 + 8*o + o + 6*o.
3*o*(o + 5)
Let r(a) be the second derivative of 1/2*a**2 + 1/60*a**5 + 0*a**4 + 0 + a - 1/6*a**3. Let d(p) be the first derivative of r(p). Suppose d(v) = 0. Calculate v.
-1, 1
Let r(t) be the third derivative of -t**7/385 - t**6/165 + t**5/330 + t**4/66 + 12*t**2. Suppose r(a) = 0. Calculate a.
-1, 0, 2/3
Let q(w) be the first derivative of -w**6/120 - w**5/40 + w**4/4 + 4*w**3/3 - 3. Let j(s) be the third derivative of q(s). Factor j(u).
-3*(u - 1)*(u + 2)
Let z(u) be the third derivative of -1/15*u**6 + 3*u**2 + 2/105*u**7 + 0*u**5 + 0*u + 1/3*u**4 - 2/3*u**3 + 0. Find m, given that z(m) = 0.
-1, 1
Let y(s) be the third derivative of s**6/840 + s**5/420 - 3*s**2. Factor y(v).
v**2*(v + 1)/7
Factor 0*m - 18*m**3 + 0*m + 4*m**2 + 0*m + 14*m**4.
2*m**2*(m - 1)*(7*m - 2)
Suppose -5*i = -2*i - 6. Suppose 4*h - 4*w + 12 = 0, -i*h - 2*h - w + 3 = 0. Find t, given that h + 0*t - 1/3*t**2 = 0.
0
Let v(g) = 18*g**3 + 18*g**2 + 8*g - 4. Let j(c) = 37*c**3 + 36*c**2 + 17*c - 9. Let b(f) = 4*j(f) - 9*v(f). Let b(z) = 0. Calculate z.
-1, -2/7, 0
Suppose -5*p - 10 = 5*b, 0*b - 2*p = b + 6. Let c(m) be the second derivative of m - 1/12*m**4 - 1/6*m**3 + 0*m**b + 0. Factor c(k).
-k*(k + 1)
Let q(v) = 2*v + 32. Let t be q(-14). Factor 2/3*i + 0 - 1/3*i**t + 0*i**3 + i**2.
-i*(i - 2)*(i + 1)**2/3
Let b(y) be the first derivative of -y**4/12 + y**2/2 + y - 1. Let c(k) be the first derivative of b(k). Factor c(i).
-(i - 1)*(i + 1)
Let d(u) = 3*u + 6. Let k be d(-5). Let l be -2 - (60/k + 2). Factor l*p**3 + 8*p**2 + 16/3 + 1/3*p**4 + 32/3*p.
(p + 2)**4/3
Factor -12/5*i**2 + 2/5*i - 8/5*i**4 + 18/5*i**3 + 0.
-2*i*(i - 1)**2*(4*i - 1)/5
Let z(x) be the second derivative of -x**4/48 + x**3/12 + 8*x. Suppose z(o) = 0. What is o?
0, 2
Let v(j) = -j + 4. Let x(o) = -5*o**2 - 11*o + 10. Let f(t) = -2*t**2 - 5*t + 5. Let m(l) = 7*f(l) - 3*x(l). Let h(g) = 3*m(g) - 4*v(g). Factor h(p).
(p - 1)*(3*p + 1)
Let m(d) be the first derivative of -3*d**4/4 - d**3 + 3*d**2/2 + 3*d - 10. Factor m(q).
-3*(q - 1)*(q + 1)**2
Factor 1/6*u**2 - 1/2*u**3 + 1/3*u + 0.
-u*(u - 1)*(3*u + 2)/6
Let n = -118 + 828/7. Factor 0 + 0*f + 0*f**3 + n*f**5 + 4/7*f**4 + 0*f**2.
2*f**4*(f + 2)/7
Let q(y) = -y**3 - y**2 - y. Let d(o) = -o**4 - 6*o**3 - 5*o**2 - 6*o. Let j(c) = -d(c) + 6*q(c). Determine k so that j(k) = 0.
-1, 0, 1
Let q = 23 + 3. Let g be q/12 - (-6)/(-36). Determine o so that 2/7*o**4 + 2/7*o + 0 - 2/7*o**3 - 2/7*o**g = 0.
-1, 0, 1
Let b(z) be the third derivative of -z**6/180 + 7*z**5/270 - 4*z**3/27 + 28*z**2. What is g in b(g) = 0?
-2/3, 1, 2
Let q(t) be the second derivative of t**4/72 + 2*t**3/9 + 7*t**2/12 + 23*t. Factor q(x).
(x + 1)*(x + 7)/6
Let g(a) be the third derivative of 0*a**3 + 0*a + a**2 - 7/60*a**5 + 1/8*a**6 - 3/70*a**7 + 1/24*a**4 + 0. Solve g(d) = 0 for d.
0, 1/3, 1
Factor 5/6*w**3 + 0 + 5/3*w + 5/2*w**2.
5*w*(w + 1)*(w + 2)/6
Let g(s) be the third derivative of s**5/72 - s**4/12 + s**3/9 - 39*s**2. Solve g(d) = 0.
2/5, 2
Let k be -1*3/(-2)*2/9. Factor 2/3*g + 0 + k*g**3 + g**2.
g*(g + 1)*(g + 2)/3
Factor 0*u + 0 - 2/5*u**3 + 4/5*u**2.
-2*u**2*(u - 2)/5
Suppose -4*i = -10*n + 8*n - 6, -2*i - 1 = -5*n. Determine d so that 0 - 2/3*d**3 - i*d**2 - 4/3*d = 0.
-2, -1, 0
Suppose 2/5*l**3 + 2/5*l + 0 + 4/5*l**2 = 0. What is l?
-1, 0
Let l(t) = t**2. Let w be l(1). Suppose -5*i + 11 = x, -5*x - w = -2*i - 2. Determine v so that -i*v**2 + v**3 - v**3 + 4*v**3 = 0.
0, 1/2
Let r(s) be the first derivative of 0*s - 3 - 2/3*s**3 + 0*s**4 + 2/5*s**5 + 0*s**2. Factor r(w).
2*w**2*(w - 1)*(w + 1)
Let k(x) be the third derivative of 7*x**6/660 - 23*x**5/330 + 5*x**4/33 - 4*x**3/33 + 26*x**2. Suppose k(a) = 0. Calculate a.
2/7, 1, 2
Suppose q - 2*q = 0. Let h(n) be the third derivative of 1/210*n**5 + 0 + 3*n**2 + 0*n + 0*n**4 + q*n**3 + 1/420*n**6. Factor h(u).
2*u**2*(u + 1)/7
Let o(a) = a**3 - 3*a**2 - 5*a + 8. Let n be o(4). Solve -1 + 3/2*p**3 - 5/2*p**n - 3/2*p + 7/2*p**2 = 0.
-1, -2/5, 1
Let r(g) be the second derivative of -3/20*g**5 + 1/2*g**3 + 1/12*g**4 - g + 0 - 1/2*g**2. What is p in r(p) = 0?
-1, 1/3, 1
Let g(a) = -9*a**3 - 3*a + 3. Let u be 24/(-9) - 2/(-3). Let i(v) = v**4 - 8*v**3 + v**2 - 2*v + 2. Let j(n) = u*g(n) + 3*i(n). Factor j(z).
3*z**2*(z - 1)**2
Suppose -3*t + x + 210 = 0, -3*x = 3*t - 213 + 3. Let w = -39 + t. Factor -43*z**2 + 60*z**3 - 8*z**4 - 10*z**4 - 8 - w*z**2 + 40*z.
-2*(z - 1)**2*(3*z - 2)**2
Let v(x) be the second derivative of x**5/20 - 5*x**4/18 + x**3/2 - x**2/3 - 21*x. Solve v(b) = 0 for b.
1/3, 1, 2
Let w(i) = 8*i**2 + 11*i - 3. Let p(o) = -o - 1 + 2*o**2 - o**2 + 2*o. Let v = 1 + -3. Let h(b) = v*w(b) + 14*p(b). Factor h(d).
-2*(d + 2)**2
Suppose g + 4*m + 1 = 7, -5*g + 14 = 4*m. Suppose -3*b - 9 = f, -3*b - 13 = -f + 2. Let 6*r**2 - 2*r - 7*r**f - r**g + 3*r**2 + r**2 = 0. What is r?
0, 2/7, 1
Let z(g) be the second derivative of g**5/190 - g**4/114 - g**3/57 + g**2/19 - 5*g. Factor z(y).
2*(y - 1)**2*(y + 1)/19
Let v = -19 + 58/3. Factor -1/3*h**2 + 0*h - 1/3*h**3 + v*h**4 + 0 + 1/3*h**5.
h**2*(h - 1)*(h + 1)**2/3
Let a(p) be the first derivative of 2*p**5/25 - p**4/20 - 2*p**3/15 + p**2/10 - 6. Suppose a(f) = 0. What is f?
-1, 0, 1/2, 1
Determine d, given that 2/7*d**3 + 6/7 - 2/7*d - 6/7*d**2 = 0.
-1, 1, 3
Let j(p) = -p**2 + 5*p + 3. Let m be j(4). Factor -4*h + 3 - m + 10*h - 2*h**2.
-2*(h - 2)*(h - 1)
Let a be (-639)/216 + 3 + 0. Let z(v) be the third derivative of 1/60*v**5 - 2*v**2 - 1/3*v**3 + 0 + 0*v + a*v**4. Factor z(n).
(n - 1)*(n + 2)
Factor -1/3*u + 0 - 1/3*u**2.
-u*(u + 1)/3
Let i be 70/42 - 2/(-6). Find r, given that 0*r + 2/5 - 2/5*r**i = 0.
-1, 1
Let r be 0/(9/(36/16)). What is i in 2/5*i**3 - 4/5*i**2 + 0 + r*i = 0?
0, 2
Let u be (3/(-1))/(1 - 2). Suppose 10 = 5*j - 0*j. Le