h that 1/4*r**2 + 0 + 1/4*r = 0.
-1, 0
Let i be (-3)/(4 - 1) + 1. Factor a + 5*a**2 + 2 + i*a - 6*a**2.
-(a - 2)*(a + 1)
Let w(m) be the second derivative of m**8/168 - 2*m**7/105 + m**6/60 - 3*m**2/2 + 3*m. Let a(q) be the first derivative of w(q). Find k such that a(k) = 0.
0, 1
Suppose -4*v + 2*v = -6. Factor -2*w**v + 2*w**5 + w**5 + 2*w**4 + w**5.
2*w**3*(w + 1)*(2*w - 1)
Let x = 16/17 - 110/153. Suppose -3*n = -2*n. Find z such that -x*z**3 + n*z + 0 - 2/9*z**2 = 0.
-1, 0
Let n(s) be the second derivative of -s**7/21 - 3*s**6/10 - 4*s**5/5 - 7*s**4/6 - s**3 - s**2/2 - s. Factor n(q).
-(q + 1)**4*(2*q + 1)
Let a(f) be the third derivative of f**6/120 - f**5/20 + f**4/12 + 5*f**2. Suppose a(j) = 0. Calculate j.
0, 1, 2
Let s(o) be the first derivative of -o**4/18 - 2*o**3/9 - o**2/3 + 4*o + 2. Let x(i) be the first derivative of s(i). Determine l, given that x(l) = 0.
-1
Let a(l) = -l + 7. Let z be a(4). Let 12/5*w**z + 0*w - 3/5*w**2 + 0 - 9/5*w**4 = 0. Calculate w.
0, 1/3, 1
Factor 0*v**3 + 0*v + 0*v**4 + 1/3*v**5 + 0*v**2 + 0.
v**5/3
Let i(b) be the third derivative of 0*b - 4/27*b**3 - 1/27*b**4 - 1/270*b**5 + 0 + 2*b**2. Find w such that i(w) = 0.
-2
Let n be ((-12)/(-462))/((-3)/(-42)). Find i such that n*i - 2/11 - 2/11*i**2 = 0.
1
Let j = 4 - 0. Factor -5*z**2 - 3*z - 2*z**3 + 6*z**3 - 3*z**4 + 5*z + 2*z**j.
-z*(z - 2)*(z - 1)**2
Let 172*s**3 + 36*s**2 - 56*s**3 + 12*s + 3*s**5 + 18*s**4 - 77*s**3 = 0. Calculate s.
-2, -1, 0
Let j(a) = -3*a**2 - 12*a. Let c(v) = -v. Let q(t) = 6*c(t) - j(t). Determine l so that q(l) = 0.
-2, 0
Let d(t) be the third derivative of -t**9/211680 - t**8/70560 + t**7/8820 + t**5/60 - t**2. Let h(y) be the third derivative of d(y). Let h(n) = 0. Calculate n.
-2, 0, 1
Let x(o) be the third derivative of -o**5/100 + o**3/10 - 14*o**2. Let x(q) = 0. Calculate q.
-1, 1
Let k = 11 - 11. Let p(l) = l. Let a be p(k). Factor 0*v + a - 1/2*v**2 + 1/2*v**4 + 0*v**3.
v**2*(v - 1)*(v + 1)/2
Let z(x) be the first derivative of x**5/50 - x**4/30 - x**3/15 + x**2/5 + x + 2. Let d(p) be the first derivative of z(p). Factor d(n).
2*(n - 1)**2*(n + 1)/5
Let j(x) be the first derivative of 5*x**3/3 - 20*x - 12. Solve j(r) = 0.
-2, 2
Let k(r) be the third derivative of r**5/15 - r**4/24 + r**3/6 + 3*r**2. Let s be k(1). What is j in 8*j**3 + 2*j**5 + 4 + 4*j**2 - 8*j**s - 5 + 5 - 10*j = 0?
-1, 1, 2
Let w(i) be the second derivative of 2*i**5/75 + i**4/30 - i**3/45 - 10*i. Determine o, given that w(o) = 0.
-1, 0, 1/4
Let i(v) be the first derivative of -v**5/5 - v**4/4 + v**3/3 + v**2/2 - 1. Let i(h) = 0. What is h?
-1, 0, 1
Let t(y) = 2*y - 4*y + 0 - 6. Let u be t(-4). Find x, given that -5 - 2*x**3 + 3 - 6*x**2 - 4*x - u*x = 0.
-1
Let o(c) be the second derivative of 0 - 2/7*c**2 - c - 1/105*c**6 - 1/21*c**3 + 1/70*c**5 + 1/14*c**4. Suppose o(v) = 0. What is v?
-1, 1, 2
Let u(s) = -2*s**2 + 10 - 16 + 2*s**2 + 7*s**2 + s. Let d(c) = c**2 - 1. Suppose 0*k - 1 = -k. Let v(x) = k*u(x) - 6*d(x). Find q such that v(q) = 0.
-1, 0
Suppose 2*f + 5*c = -2*f + 17, 4*f = -4*c + 16. Determine p, given that 0*p**2 - 3 + 3*p + f*p**2 - p + 3*p**3 - 5*p = 0.
-1, 1
Let a(l) be the third derivative of l**8/420 + 3*l**7/140 + 11*l**6/180 - l**4/3 - 5*l**3/6 - 5*l**2. Let o(x) be the first derivative of a(x). Factor o(n).
2*(n + 1)*(n + 2)**2*(2*n - 1)
Determine m so that 2/3*m**3 + 4/3*m**2 - 14/3*m + 8/3 = 0.
-4, 1
Suppose c = -4*q - 3*c + 16, -3*q + 12 = -2*c. Let y be q/(-9)*15/(-10). Factor -2/3*x**2 - y*x + 0.
-2*x*(x + 1)/3
Let c be 10/6 - 59/(-59). Factor 0*j + c - 2/3*j**2.
-2*(j - 2)*(j + 2)/3
Suppose 4*p + 2 = 22. Let g(b) be the first derivative of 0*b - 2 - 1/8*b**2 + 1/12*b**3 - 1/20*b**p + 1/16*b**4. Determine r, given that g(r) = 0.
-1, 0, 1
Let h(p) = 7*p**5 + 7*p**4 - 9*p**3 - 7*p**2 + 6*p + 4. Let r(b) = -6*b**5 - 6*b**4 + 9*b**3 + 6*b**2 - 6*b - 3. Let y(z) = -3*h(z) - 4*r(z). Factor y(d).
3*d*(d - 1)**2*(d + 1)*(d + 2)
Let a = -35/4 + 119/12. Factor 3/2*n - a*n**2 - 1/3.
-(n - 1)*(7*n - 2)/6
Let c(p) be the second derivative of 0 + 1/3*p**4 - 6*p + 8*p**2 - 8/3*p**3. Suppose c(a) = 0. Calculate a.
2
Let a(r) = -15*r**2 - 105*r. Let m(g) = -10*g**2 - 70*g. Let z(w) = -5*a(w) + 7*m(w). Factor z(u).
5*u*(u + 7)
Let z(s) be the first derivative of -s**5/40 + s**4/24 + s**3/6 - 4*s + 3. Let x(d) be the first derivative of z(d). Find h such that x(h) = 0.
-1, 0, 2
Let p(f) be the second derivative of -f**8/1680 + f**7/420 - f**6/360 + f**3 - f. Let c(u) be the second derivative of p(u). Factor c(a).
-a**2*(a - 1)**2
Let h = 274/3 - 90. Factor 10*y**3 - 2/3*y**2 + 0 - h*y - 38/3*y**4 + 14/3*y**5.
2*y*(y - 1)**3*(7*y + 2)/3
Suppose 0*v - 1/6*v**2 + 0 = 0. What is v?
0
Let c be 6/51 + 868/714. Factor u**3 - 5/3*u + c*u**2 - 2/3.
(u - 1)*(u + 2)*(3*u + 1)/3
Let f(h) be the second derivative of -h**7/3360 + h**6/480 - h**5/160 + h**4/96 + h**3/2 - 2*h. Let d(s) be the second derivative of f(s). Factor d(c).
-(c - 1)**3/4
Let g be (-3)/2 + -7 + 153/18. Find m, given that -2/3*m**2 + g*m + 0 = 0.
0
Let u be 6/(-21) + 86/(-140) + 1. Let h(r) be the second derivative of -u*r**2 + 0 - 1/15*r**3 - 1/60*r**4 - 4*r. Factor h(b).
-(b + 1)**2/5
Let a(j) = 2*j**2 + 22*j - 6. Let w(k) = 5*k**2 + 65*k - 19. Suppose 3*b + 10 = -5*g - b, 4*b - 38 = 3*g. Let v(t) = g*w(t) + 17*a(t). Factor v(m).
4*(m - 3)*(m - 1)
Suppose -b + 19 = 4*h, 3*b + 1 = 4*h - 6. Suppose -q - 1 = -2*f - 6, -7 = -h*q - 5*f. Factor 3/4 - 3/4*s**2 - 3/4*s**q + 3/4*s.
-3*(s - 1)*(s + 1)**2/4
Let f(p) = p**5 + p**3 + p**2 + p + 1. Let w(n) = 33*n**5 - 9*n**4 - 9*n**3 + 3*n**2 + 6*n + 6. Let z(y) = -6*f(y) + w(y). Factor z(m).
3*m**2*(m - 1)*(3*m + 1)**2
Suppose -13*q**4 + 5 + 3*q**5 - 3*q**2 + 17*q**3 + 598*q - 1 - 606*q = 0. Calculate q.
-2/3, 1, 2
Let m = 1915/14 - 273/2. Find p such that 2/7*p**5 - 8/7*p**2 + m*p + 0 - 8/7*p**4 + 12/7*p**3 = 0.
0, 1
Let v(m) be the third derivative of 0 + 0*m - 2*m**2 + 0*m**4 + 0*m**3 - 1/120*m**6 + 0*m**5. Factor v(j).
-j**3
Let f(c) be the second derivative of 11*c**4/3 + 26*c**3/3 + 4*c**2 - 7*c. Factor f(t).
4*(t + 1)*(11*t + 2)
Suppose 0*x + 12 = -x - 5*t, 3 = -t. Suppose 0 = x*y + 5*o + 19, 5*y - o - 17 = -2. Determine w, given that -3 + 1 - w**4 + 5*w**y - w**2 - w**4 = 0.
-1, 1
Suppose h - 15 = 3*r, -2*h + 15 = -0*h - 3*r. Let h*c - 3/2*c**2 + 0 = 0. Calculate c.
0
Factor -4/3 - 34/9*i + 14/9*i**3 + 32/9*i**2.
2*(i - 1)*(i + 3)*(7*i + 2)/9
Suppose -3 - 6 = -3*u. Let w(j) be the first derivative of -2/3*j**3 - u - 1/3*j**6 + 2/5*j**5 + 0*j + 1/2*j**4 + 0*j**2. Factor w(p).
-2*p**2*(p - 1)**2*(p + 1)
Let r(f) be the second derivative of -f**6/120 - f**5/40 - f**4/48 + 6*f. Let r(h) = 0. Calculate h.
-1, 0
Let c(i) = -i**2 + 9*i - 9. Let o be c(8). Let s be (-6)/(-3) - (o - -3). Find b, given that 1/4*b**4 + s*b + 0 + 1/4*b**2 - 1/2*b**3 = 0.
0, 1
Let m(f) be the first derivative of -f**7/84 - f**6/60 + f**5/40 + f**4/24 - 3*f + 2. Let v(g) be the first derivative of m(g). Factor v(y).
-y**2*(y - 1)*(y + 1)**2/2
Let s(u) be the third derivative of u**7/504 + 7*u**6/1080 + u**5/180 + u**3/3 + u**2. Let f(w) be the first derivative of s(w). Factor f(y).
y*(y + 1)*(5*y + 2)/3
Let f(c) be the second derivative of c**7/168 - c**5/40 + c**3/24 + 11*c. Find k such that f(k) = 0.
-1, 0, 1
Let q(n) = n**2 + 1. Let o(z) = -5*z**3 + 9*z**2 + 20*z - 6. Let j(t) = o(t) + 6*q(t). Find s, given that j(s) = 0.
-1, 0, 4
Let g = 7 - 5. Factor 2 + 8*p**g + 2 - 3*p - 2*p**3 - 7*p.
-2*(p - 2)*(p - 1)**2
Let f(k) = 2*k**2 + 4*k. Let w be f(-2). Suppose 1/2*v**2 + v + w = 0. What is v?
-2, 0
Let z(i) be the first derivative of i**5/10 - 5*i**4/24 + i**3/18 + i**2/12 + 16. Factor z(f).
f*(f - 1)**2*(3*f + 1)/6
Solve -9/5*c**3 - 4/5*c**5 + 11/5*c**4 + 1/5*c**2 + 0 + 1/5*c = 0 for c.
-1/4, 0, 1
Factor 0 + 2*d + 1/2*d**3 - 5/2*d**2.
d*(d - 4)*(d - 1)/2
Determine b, given that 2*b + 4*b + 0*b**2 - 3*b**2 = 0.
0, 2
Let u be (-2)/1 - (-11 - -4). Let h = u + -3. What is m in m**2 + m - h*m + 0 - 2 = 0?
-1, 2
Let a = 23 + -16. Let -3 - 8*i**2 - 3*i + 1 + a*i + 6*i = 0. Calculate i.
1/4, 1
Let i(u) be the third derivative of 1/36*u**4 - 1/18*u**3 - 1/180*u**5 + 0 + 0*u - 2*u**2. Let i(b) = 0. Calculate b.
1
Let n = 3 + -3. Let a be -4 + ((-18)/(-2) - (5 + -2)). Let