- 1)/4
Suppose 0 - 3/8*w**2 - 45/8*w = 0. Calculate w.
-15, 0
Let 2 - 7 + 12*x + 6 - 1 + x**2 = 0. What is x?
-12, 0
Let v(w) be the first derivative of w**8/560 - 3*w**7/280 - w**6/30 - 23*w**3/3 + 4. Let h(c) be the third derivative of v(c). Factor h(d).
3*d**2*(d - 4)*(d + 1)
Let y = 1844 + -1840. Let u(c) be the first derivative of 0*c**3 + 1/36*c**y - 5 - 1/45*c**5 + 0*c**2 + 0*c. Factor u(p).
-p**3*(p - 1)/9
Let s be 3*(-2)/6 - 445/(-443). Let g = s - -2648/2215. Factor -2/5*i**2 + g*i - 4/5.
-2*(i - 2)*(i - 1)/5
Let w be 0/2*(-3)/(-3). Suppose w = g + 3 - 7. Factor 3*u + 0*u - u**2 - u - g*u + u**3.
u*(u - 2)*(u + 1)
Factor 0 + 5*a**3 + 1 - 3*a**3 - 3*a**2 + 5*a - 5*a.
(a - 1)**2*(2*a + 1)
Let w(a) = -a**2 + 1. Let x(f) = 2*f**3 + 3*f**2 + 6*f + 5. Suppose -61*b = -59*b + 2. Let r = 11 + -8. Let h(j) = b*x(j) + r*w(j). Factor h(n).
-2*(n + 1)**3
Let w(t) = -16*t**2 + 66*t - 9. Let u(m) = -4*m**2 + 16*m - 2. Let f(k) = 9*u(k) - 2*w(k). Find d, given that f(d) = 0.
0, 3
Let g(u) = 9*u**3 + 55*u**2 + 158*u + 142. Let m(f) = 11*f**3 + 55*f**2 + 157*f + 143. Let k(p) = -3*g(p) + 2*m(p). Let k(x) = 0. Calculate x.
-7, -2
Let d(s) be the second derivative of 0*s**3 + 1/300*s**5 - s - 5/2*s**2 - 1/60*s**4 + 0. Let b(j) be the first derivative of d(j). Find w, given that b(w) = 0.
0, 2
Let o be ((-4)/(-16) - 0)*(-40)/(-15). Factor -7/9*a**2 - 19/9*a + o.
-(a + 3)*(7*a - 2)/9
Let v(m) be the third derivative of m**5/240 - 5*m**4/48 - 13*m**3/8 - 113*m**2 + 3. Factor v(h).
(h - 13)*(h + 3)/4
Let m be -35*14/105*15/(-20). What is j in -3 - 1/2*j**2 + m*j = 0?
1, 6
Let n(f) be the third derivative of f**6/60 - f**5/6 - 8*f**4/3 - 12*f**3 + 266*f**2. Find o, given that n(o) = 0.
-2, 9
Let d(q) be the third derivative of q**9/3024 - q**7/840 - 4*q**3/3 - 10*q**2. Let s(k) be the first derivative of d(k). Factor s(u).
u**3*(u - 1)*(u + 1)
Let w(z) = -4*z**2 - 8*z - 12. Let k = -30 - -17. Let t(r) = 8*r**2 + 15*r + 25. Let y(f) = k*w(f) - 6*t(f). Find j such that y(j) = 0.
-3, -1/2
Factor 6*o**2 - 3*o**5 + 3*o**3 + 66*o**4 - 57*o**4 + 10*o**3 + 14*o**3 + 3*o**3 - 15 - 27*o.
-3*(o - 5)*(o - 1)*(o + 1)**3
Let j be (1 + 1371)*-5*(4 + -6). Factor 4*m**5 - 140*m**4 + 1960*m**3 + 29102 + 31740*m + 16280*m - 96330 - j*m**2.
4*(m - 7)**5
Let w = 2/661 - -5266/7271. Factor -w*t + 2/11*t**2 - 10/11.
2*(t - 5)*(t + 1)/11
Factor 6*b - 1407*b**4 + 1408*b**4 - 11*b**2 + b**3 + 3*b**3.
b*(b - 1)**2*(b + 6)
Let t(w) be the first derivative of w**5/20 + 17*w**4/16 - 19*w**3/12 - 17*w**2/8 + 9*w/2 - 113. Determine k, given that t(k) = 0.
-18, -1, 1
Let v(b) be the second derivative of b**8/9240 + b**7/1540 + b**6/660 + b**5/660 + 7*b**3/3 + 7*b. Let o(h) be the second derivative of v(h). Factor o(n).
2*n*(n + 1)**3/11
Let j(k) = -3*k**3 + 45*k**2 - 30*k - 6. Let c(n) = -4*n**3 + 43*n**2 - 29*n - 7. Let o(g) = -6*c(g) + 5*j(g). Factor o(r).
3*(r - 2)**2*(3*r + 1)
Solve -1/4*m**3 + 1/4*m - 1/8 + 0*m**2 + 1/8*m**4 = 0 for m.
-1, 1
Let c(f) be the second derivative of 21*f**5/100 + 303*f**4/20 + 38*f**3 + 126*f**2/5 + 210*f. Let c(z) = 0. Calculate z.
-42, -1, -2/7
Suppose 5*x + 21 = 11*j - 8*j, 5*j = 4*x + 22. Factor 0*k + 1/8*k**j - 1/8.
(k - 1)*(k + 1)/8
Let x(g) be the first derivative of -g**5/15 + g**4/3 + 16*g**3/3 - 7*g**2 + 26. Let n(d) be the second derivative of x(d). Factor n(i).
-4*(i - 4)*(i + 2)
Suppose 5*h = -2*q - 8, 5*h - 221*q + 222*q + 4 = 0. Find x, given that -x + h + 5/2*x**2 - 3/2*x**3 + 1/2*x**5 - 1/2*x**4 = 0.
-2, 0, 1
Let k(a) = -a**2 - a. Let c(m) = -36*m**2 + 10*m - 24 + 9 - 14*m**2 + 5*m**3. Let i(t) = c(t) - 25*k(t). Find u, given that i(u) = 0.
1, 3
Solve 40 - 12/5*b**2 + 2/5*b**3 - 6*b = 0 for b.
-4, 5
Let n = -12 + 16. Let q be 21/(-4)*(-16)/n. Find i such that -4*i**2 + q*i**3 + i**4 + 5*i**5 - 4*i**5 - 25*i**3 = 0.
-2, -1, 0, 2
Let b(i) be the first derivative of -i**7/84 + i**6/60 + i**5/40 - i**4/24 - 31*i - 38. Let c(y) be the first derivative of b(y). Let c(x) = 0. Calculate x.
-1, 0, 1
Let q be 450/(-2275)*-13 - 1*2. Factor -q*o**3 - 2/7*o**2 + 0*o - 2/7*o**4 + 0.
-2*o**2*(o + 1)**2/7
Let d(b) be the third derivative of 7*b**6/24 + 97*b**5/6 - 35*b**4/3 + 93*b**2. Factor d(n).
5*n*(n + 28)*(7*n - 2)
Let c(g) = 2*g**5 - 4*g**4 - 4*g**3 + 20*g**2 - 22*g + 6. Let k(b) = 4*b**5 - 7*b**4 - 9*b**3 + 39*b**2 - 43*b + 11. Let h(a) = -10*c(a) + 4*k(a). Factor h(o).
-4*(o - 2)*(o - 1)**3*(o + 2)
Let f = 50 + -50. Suppose 9*q - 29 - 7 = f. Factor -4/5*j**q - 8/5*j + 0 + 0*j**3 + 12/5*j**2.
-4*j*(j - 1)**2*(j + 2)/5
Let b(q) be the second derivative of -29*q - 5/18*q**3 + 1/6*q**5 + 5/6*q**2 - 5/18*q**4 + 0 + 1/18*q**6 - 5/126*q**7. Find s, given that b(s) = 0.
-1, 1
Let p be -1 + (0 - 5) - (-18 - -8). Find t such that 1/11*t**p + 0 - 2/11*t + 0*t**3 - 3/11*t**2 = 0.
-1, 0, 2
Let n be ((-27)/5 + 3)*(-5)/3. Let z(g) be the third derivative of -1/168*g**n + 0 + 6*g**2 - 1/420*g**5 + 0*g + 0*g**3. Factor z(c).
-c*(c + 1)/7
Let b(v) = 6*v + 3*v + 2 - 2 + 1 + v**2. Let x(u) = u**2 + 4*u + 1. Let q(o) = 6*b(o) - 11*x(o). Factor q(k).
-5*(k - 1)**2
Let r(t) be the first derivative of -2*t**3/9 - 58*t**2/3 + 119. What is i in r(i) = 0?
-58, 0
Let k = -30 - -14. Let v be k/(-88)*22/6. Factor -v*a**3 - 4/3*a**2 + 0 + 0*a.
-2*a**2*(a + 2)/3
Factor -2/15*f**2 - 32/5 + 32/15*f.
-2*(f - 12)*(f - 4)/15
Factor 1/7*u**3 - 4/7*u + 2/7*u**2 - 8/7.
(u - 2)*(u + 2)**2/7
Let p(b) be the third derivative of -b**6/240 - b**5/20 + 66*b**2. Factor p(h).
-h**2*(h + 6)/2
Let a(l) be the first derivative of l**4/5 + 28*l**3/5 - 252*l**2/5 + 416*l/5 + 48. Determine b, given that a(b) = 0.
-26, 1, 4
Factor -29/7*q**3 - 55/7*q**2 + 0 - 1/7*q**4 - 27/7*q.
-q*(q + 1)**2*(q + 27)/7
Suppose 7/2*k**2 - 1/2*k**4 - 3 - 23/4*k + 23/4*k**3 = 0. Calculate k.
-1, -1/2, 1, 12
Suppose 2 + 15 = t. Suppose 15*f = t*f. Factor -3*j**3 + f*j**3 + 28*j**2 - 28*j**2.
-3*j**3
Let t be ((-200)/160)/(10*7/(-16)). Find m such that t*m**3 + 0*m**2 - 6/7*m - 4/7 = 0.
-1, 2
Let q = 3 + -1. Factor -40 + 8*v**4 - 10*v**q + 8*v + 15*v**3 - 3*v**4 - 68*v.
5*(v - 2)*(v + 1)*(v + 2)**2
Let j = -63 + 64. Let g be (-1 + j - 3) + (-1020)/(-300). Determine a so that 0 - g*a**2 + 2/5*a**3 - 2/5*a + 2/5*a**4 = 0.
-1, 0, 1
Let m = -162 + 165. Let g(w) be the first derivative of -2/21*w**m + 5 + 1/7*w**2 + 4/7*w. Solve g(t) = 0.
-1, 2
Let g(n) = -9*n**5 + 39*n**4 - 60*n**3 - 6*n**2 + 69*n - 21. Let b(z) = z**5 - z**4 + z**3 - 2*z - 1. Let v(h) = 6*b(h) + g(h). Factor v(j).
-3*(j - 9)*(j - 1)**3*(j + 1)
What is z in 4*z - 173*z**5 - z - 1125*z**3 - 150*z**4 + 168*z**5 - 3*z = 0?
-15, 0
Let p(r) be the third derivative of r**5/150 + r**4/10 - 16*r**3/15 - r**2 - 27*r. What is u in p(u) = 0?
-8, 2
Find k such that 2/5*k**3 + 18/5 - 18/5*k**2 - 2/5*k = 0.
-1, 1, 9
Let a be -3 + (-2 - -15) + -8. Factor 6/7*h**3 + 3/7*h**4 + 0*h - 9/7*h**a + 0.
3*h**2*(h - 1)*(h + 3)/7
Let o(m) = m**3 + m**2 + 1. Let v(g) = 12*g**3 - 20*g**2 - 48*g + 8. Let p(i) = 24*o(i) - v(i). Solve p(z) = 0 for z.
-2, -1, -2/3
Factor 4/7 + 2/7*a**2 + 6/7*a.
2*(a + 1)*(a + 2)/7
Let z(h) = -h**2 + 5*h + 6. Let w(m) = 7*m**2 + m. Let s be w(-1). Let j be z(s). Factor l + 3*l + j*l - 6*l**3 - l + 3*l**5.
3*l*(l - 1)**2*(l + 1)**2
Let t = 130/51 + -344/255. Find y such that 4/5 + t*y**3 - 8/5*y**2 - 2/5*y = 0.
-2/3, 1
Factor 4 - u - 1/2*u**3 - 5/2*u**2.
-(u - 1)*(u + 2)*(u + 4)/2
Find v such that 51/7*v**2 - 3/7*v**3 - 1815/7 - 33/7*v = 0.
-5, 11
Factor 2/9*s**3 - 14/9*s + 4/3 + 0*s**2.
2*(s - 2)*(s - 1)*(s + 3)/9
Let l = 2294 - 2291. Determine a, given that 0 + 4/5*a**5 + 32/5*a**l + 0*a + 16/5*a**2 + 4*a**4 = 0.
-2, -1, 0
Let c(i) = 477*i**3 + 1007*i**2 + 590*i + 67. Let p(v) = 238*v**3 + 503*v**2 + 295*v + 33. Let l(x) = 3*c(x) - 7*p(x). Factor l(q).
-5*(q + 1)**2*(47*q + 6)
Suppose -9*g = -15*g + 72. Let j be g*((-21)/8)/(-7). Factor -1 - j*b - 7/2*b**2.
-(b + 1)*(7*b + 2)/2
Suppose -d + 3*d = -4*h - 40, 0 = 2*h + 2*d + 18. Let l = 13 + h. Factor -u**2 + u**3 + 2*u**l - 4*u**2.
u**2*(u - 3)
Let c be 2 + -2 - (27/(-3) + 4). Let l(s) = -s**3 + 6. Let q be l(0). Factor -2*w - 5*w - c*w + 4*w + q*w**3 + 2*w**4.
2*w*(w - 1)*(w + 2)**2
Let g(i) be the third derivative of -i**7/42 - 11*i**6/24 - 11*i**5/6 + 25*i**4/2 + 60*i**3 + i**2 - 53. Factor g(c).
-5*