- 2/5 - 6/5*p**2 + m*p**3.
2*(p - 1)**3/5
Let f(a) = -90*a**2 + 9*a + 11. Let l = 4 + -6. Let o(x) = 18*x**2 - 2*x - 2. Let b(k) = l*f(k) - 11*o(k). Determine s, given that b(s) = 0.
0, 2/9
Let f be (1 - -1) + -1 + -1. Suppose 2*h + 2*h - 6 = 3*v, f = -v + 5*h - 13. Factor 0*o**2 - 2*o**2 + v*o + 0*o**2.
-2*o*(o - 1)
Let f be (1/(-1))/((-2)/4). Suppose 2 = f*h - 2*m, 2 = 2*h - 0*m - m. Solve -r**3 + 2*r**2 + h - 2*r**2 + 2*r**2 - 3*r + r**2 = 0 for r.
1
Suppose -4*n + 14 + 14 = 0. Let p = 9 - n. Let 2/3*a + 0 - 2/3*a**p = 0. What is a?
0, 1
Let r(f) be the first derivative of f**5 + 15*f**4/2 + 15*f**3 + 20. Let r(w) = 0. What is w?
-3, 0
Let w(j) = j**3 + 6*j**2 - 6*j + 9. Let r be w(-7). Let m = 1 + r. Factor -m*q - q + 0*q + 2*q**3 - 2*q**2.
2*q*(q - 2)*(q + 1)
Let v(l) be the first derivative of -1/7*l**2 + 10 + 1/7*l + 1/21*l**3. Suppose v(m) = 0. What is m?
1
Let h(o) be the third derivative of 0 - 1/90*o**5 + 1/630*o**7 + 1/2*o**3 - 1/6*o**4 + 1/90*o**6 - 2*o**2 + 0*o. Let h(v) = 0. Calculate v.
-3, 1
Factor -3/4*u**2 - 15/8*u**5 - 27/8*u**3 + 0*u - 9/2*u**4 + 0.
-3*u**2*(u + 1)**2*(5*u + 2)/8
Let v(m) be the third derivative of -1/24*m**4 + 1/12*m**3 + 1/120*m**6 + 0*m**5 + 0*m + 0 - 1/420*m**7 - m**2. Determine s so that v(s) = 0.
-1, 1
Find m such that -2/3*m**3 - 16/3*m + 8/3 + 10/3*m**2 = 0.
1, 2
Let w(y) = -3*y**2 + 12*y - 4. Let j be w(3). Let o(f) be the first derivative of 0*f**3 + 0*f**4 + 0*f**2 - 2 - 2/5*f**j + 0*f. Determine x so that o(x) = 0.
0
Let t = -2341/45 + 279/5. Let m(b) be the first derivative of 7/3*b**6 - 2 - t*b**4 - 52/27*b**3 + 4/9*b + 5/9*b**2 + 16/15*b**5. What is r in m(r) = 0?
-1, -1/3, 2/7, 1
Factor 10*x**2 + 10*x**3 + 14*x + 2*x**4 + 4 + 3*x**2 + 5*x**2.
2*(x + 1)**3*(x + 2)
Factor 1/3*o**2 + 1/6*o - 1/6*o**3 - 1/3.
-(o - 2)*(o - 1)*(o + 1)/6
Let a be 0/(-2 + 3)*1. Let g = 2 + a. Factor 1 - 3 - g*r**2 + 4.
-2*(r - 1)*(r + 1)
Let b(j) be the second derivative of 3*j**5/100 - 3*j**4/20 + j**3/5 + 12*j. Factor b(o).
3*o*(o - 2)*(o - 1)/5
Let t(u) be the second derivative of -27*u**5/20 - u**4/2 - 2*u. Let t(v) = 0. What is v?
-2/9, 0
Solve 46 + 5*t**2 - 5*t**3 - 46 = 0.
0, 1
Suppose -217*t = -212*t. Suppose t - 2/9*l - 2/9*l**2 = 0. Calculate l.
-1, 0
Factor 2/13*n**4 + 8/13 + 30/13*n**2 - 2*n - 14/13*n**3.
2*(n - 4)*(n - 1)**3/13
Let d(k) = 7*k**3 - 4*k**4 - k**4 - k**2 - 4*k**4 - 2*k**3. Let z(s) = 4*s**4 - 2*s**3. Let o(h) = 2*d(h) + 5*z(h). Factor o(u).
2*u**2*(u - 1)*(u + 1)
Let o be (30/25)/(2/10). Factor -9*s**2 - 7*s**2 - 14*s + 0 - o*s**3 - 4.
-2*(s + 1)**2*(3*s + 2)
Let s(b) be the first derivative of 2/9*b + 2/27*b**3 - 2 + 2/9*b**2. Determine f so that s(f) = 0.
-1
Determine b, given that 12*b**5 - 54*b**4 - 8*b**2 - 21 + 48*b**3 - 52*b**5 + 21 = 0.
-2, 0, 1/4, 2/5
Let r(n) be the third derivative of n**5/42 + n**4/12 + 2*n**3/21 + 6*n**2. Determine p so that r(p) = 0.
-1, -2/5
Let p(d) = d**2 - 5*d - 3. Let o be p(6). Let 3*v**2 - o*v**3 + v**2 - v**2 = 0. Calculate v.
0, 1
Let r(q) be the first derivative of -q**6/30 + q**5/25 + q**4/10 - 2*q**3/15 - q**2/10 + q/5 + 6. Suppose r(k) = 0. What is k?
-1, 1
Suppose -5*h - 14 = -4*q + q, -4*q = -5*h - 17. Let z be (-6)/(-3) + q + -1. Factor -2/3*r**z + 0*r + 2/3*r**2 + 2/3*r**3 - 2/3*r**5 + 0.
-2*r**2*(r - 1)*(r + 1)**2/3
Let f(t) = -3*t**4 + 3*t**3 - 5*t**2 - 3*t - 4. Let k(u) = -2*u**4 + 2*u**3 - 4*u**2 - 2*u - 3. Let o(i) = 3*f(i) - 4*k(i). Suppose o(l) = 0. What is l?
-1, 0, 1
Let d(q) be the second derivative of q**8/16800 - q**7/3150 + q**6/1800 + q**4/3 + 4*q. Let l(i) be the third derivative of d(i). Factor l(v).
2*v*(v - 1)**2/5
Let g(j) be the second derivative of -j**8/13440 - j**7/2016 - j**6/1440 - 7*j**4/12 - 2*j. Let s(t) be the third derivative of g(t). Let s(p) = 0. What is p?
-2, -1/2, 0
Let x(f) be the second derivative of -f**9/30240 + f**8/6720 - f**7/5040 - f**4/4 + 2*f. Let k(a) be the third derivative of x(a). Factor k(w).
-w**2*(w - 1)**2/2
Let a(t) be the second derivative of -t**8/1344 + t**6/480 + 5*t**2/2 + 6*t. Let h(s) be the first derivative of a(s). Solve h(l) = 0 for l.
-1, 0, 1
Find w such that -17*w**3 + 16*w - 18*w**2 - 29*w**3 + 8*w**4 + 4*w**5 + 32 - 22*w**2 + 26*w**3 = 0.
-2, -1, 1, 2
Let m be (3 - 2)*(-89 + -6). Let s = -183/2 - m. Find p, given that p**4 + 0 - s*p**5 - p**2 + 0*p + 7/2*p**3 = 0.
-1, 0, 2/7, 1
Let -4/11*a**4 + 0*a**2 - 6/11*a**3 + 2/11*a + 0 = 0. What is a?
-1, 0, 1/2
Find t, given that 15*t**5 + 145*t**4 + 205*t**3 + 4*t - 37*t - 7*t + 59*t**2 - 24*t**2 = 0.
-8, -1, 0, 1/3
Factor -2/5*q**5 + 2/5*q + 0*q**3 + 4/5*q**4 - 4/5*q**2 + 0.
-2*q*(q - 1)**3*(q + 1)/5
Let r(b) = -b**2 + 18*b + 2. Let v be r(18). Factor -1/3*k**4 + 4/3*k - k**3 + 0 + 0*k**v.
-k*(k - 1)*(k + 2)**2/3
Let c(l) = 4*l**3 + l + 2. Let z be c(2). Factor 13*j**3 + 8*j + z*j**2 + 10*j**3 - 7*j**3.
4*j*(j + 2)*(4*j + 1)
Let y(x) = -6*x**2 - 8*x - 21. Let t(f) = f**2 + 1. Let o(j) = -5*t(j) - y(j). Suppose o(h) = 0. What is h?
-4
Suppose 1 + 11 = 4*z - 4*g, 2*z + 5*g + 15 = 0. Let c = 2 + z. Suppose v**c + v**2 - 12 - 12*v - 3*v**2 - 2*v**2 = 0. What is v?
-2
Let c(m) = m + 1. Let f be 0 - (1 + 0)*-10. Let v(n) = -2*n**2 + 12*n + 10. Let s(d) = f*c(d) - v(d). Factor s(h).
2*h*(h - 1)
Suppose k = -3*r + 4 - 0, -2*r - 19 = 5*k. Suppose r*y + 5 = -10, -2*j = 2*y + 4. Find b, given that -b + 2*b + 0*b - 3*b**2 + j*b**3 - b**4 = 0.
0, 1
Let h(m) be the third derivative of m**8/840 + m**7/420 - m**3/3 + 2*m**2. Let q(b) be the first derivative of h(b). Factor q(x).
2*x**3*(x + 1)
Suppose 3*a - 5 - 1 = 0. Factor -4*i**4 + 0*i - 4*i + a*i**4 + 4*i**3 + 2 + 0*i.
-2*(i - 1)**3*(i + 1)
Let h(m) be the first derivative of 2*m**6 + 21*m**5/5 + 3*m**4/2 - m**3 - 1. Suppose h(u) = 0. What is u?
-1, 0, 1/4
Let k(j) be the first derivative of 2*j + 3/50*j**5 + 1/15*j**4 - 3 + 0*j**2 + 0*j**3 + 1/75*j**6. Let w(h) be the first derivative of k(h). Factor w(i).
2*i**2*(i + 1)*(i + 2)/5
Find r such that 1/3 - 1/3*r**3 + 1/3*r - 1/3*r**2 = 0.
-1, 1
Factor 2*m**2 + 68*m - 9*m + 2*m**2 + 196 - 3*m.
4*(m + 7)**2
Factor 0 - 2/5*h + 2/5*h**2.
2*h*(h - 1)/5
Factor 6*h**2 - 2*h**4 + 2*h**3 + 10*h**2 - 12*h**2.
-2*h**2*(h - 2)*(h + 1)
Let y(s) be the first derivative of 6/5*s**3 + 7/5*s**2 + 4/5*s + 1/2*s**4 - 1 + 2/25*s**5. Factor y(j).
2*(j + 1)**3*(j + 2)/5
Let a(g) be the third derivative of g**8/1008 - g**7/420 - g**6/720 + g**5/120 - g**4/144 - 6*g**2. Determine p, given that a(p) = 0.
-1, 0, 1/2, 1
Let l(s) be the first derivative of s**6/180 + s**5/30 - 4*s**3/3 - 4. Let a(c) be the third derivative of l(c). Factor a(t).
2*t*(t + 2)
Let c(a) be the third derivative of 3*a**6/280 + a**5/60 - a**4/84 + 7*a**2. Factor c(r).
r*(r + 1)*(9*r - 2)/7
Let z = -2/119 + 123/238. Let a + z*a**2 + 1/2 = 0. What is a?
-1
Factor -2/7*o**4 + 0*o + 0 + 4/7*o**3 - 2/7*o**2.
-2*o**2*(o - 1)**2/7
Let o(y) be the third derivative of -y**4/12 + 2*y**3/3 + 5*y**2. Let i be o(0). Let -i*x**3 - 4*x**2 - 2*x - 2/5*x**5 - 2/5 - 2*x**4 = 0. Calculate x.
-1
Factor -8/11*o**2 + 10/11*o - 4/11 + 2/11*o**3.
2*(o - 2)*(o - 1)**2/11
Let x = 201 - 401/2. What is m in -x*m**2 - 3/2*m - 1 = 0?
-2, -1
Let a(v) = 10*v**2. Let l(u) = u**3 + u. Let t(f) = a(f) - 5*l(f). Factor t(q).
-5*q*(q - 1)**2
Let p(f) be the third derivative of -1/1050*f**7 + 1/300*f**6 + 0 + f**2 - 1/300*f**5 + 0*f + 0*f**4 + 0*f**3. Determine a so that p(a) = 0.
0, 1
Let d(p) = -p**2 - p. Let r(a) = -22*a - 6. Let z(i) = 6*d(i) - r(i). Suppose z(s) = 0. What is s?
-1/3, 3
Factor -2/7*g**3 - 160/7*g - 34/7*g**2 - 128/7.
-2*(g + 1)*(g + 8)**2/7
Let i(r) = r**3 - 12*r**2 + r - 7. Let n be i(12). Let a be (7 - 2) + (2 - n). Let -2/9 + 28/9*u**3 - 10/9*u - 2*u**5 + 2/3*u**4 - 4/9*u**a = 0. What is u?
-1, -1/3, 1
Suppose -2*d - 2*d + 12 = 0. Suppose -2 = -4*w + d*w. Suppose -1/6*v - 1/2*v**w - 1/6*v**4 - 1/2*v**3 + 0 = 0. Calculate v.
-1, 0
Let o = 1/52 - -301/572. Determine q, given that 4/11*q**3 - 8/11*q - 2/11*q**4 - 8/11 + o*q**2 = 0.
-1, 2
Let i be (-6)/(-4)*10/15. Find y such that 3*y**2 + i + 6*y - 3*y + 0*y**3 + y**3 = 0.
-1
Let v = 506/7 - 72. Suppose 2/7*h**3 - 2/7*h**5 + 0*h + 0 - 2/7*h**2 + v*h**4 = 0. What is h?
-1, 0, 1
Factor -3/7*q + 0 + 3/7*q**2.
3*q*(q - 1)/7
Factor -4*n**3 - n**2 - n**4 + n**3 -